Amadou is going to invest $16,000 and leave it in an account for 20 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest tenth of a percent, would be required in order for Amadou to end up with $44,000?

Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

The median wait time for Speed Slide is 2 minutes longer than the median wait time for Wave Machine and the IQR for both rides is 6 minutes.

A box plot, also known as a box and whisker plot, is a graphical representation of a data set that shows the distribution of the data along a number line.

In the box plots show a random sample of wait times for two rides at a water park is shown in figure.

If we compare the wait times in the box plots,

then for, Speed Slide: Median = 11

IQR= Q1 - Q3           (Calculation formula of IQR)

      = 12 - 6

IQR = 6 minutes

for wave slide: median: 9

IQR= Q1 - Q3           (Calculation formula of IQR)

      = 11 - 9

IQR = 2 minutes

The median wait time for Speed Slide is 2 minutes longer than the median wait time for Wave Machine and the IQR for both rides is 6 minutes.

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The probability that a randomly chosen card that is less than 7 is the 5 of diamonds is 5%.

There are four suits in a standard deck of 52 cards: diamonds, clubs, hearts, and spades. Each suit has 13 cards, with ranks ranging from 2 (low) to 10, jack, queen, king, and ace (high).

If a randomly chosen card from the deck is less than 7, there are only two possibilities: it is either a 2, 3, 4, 5, or 6 of any suit, or it is the 5 of diamonds.

There are 20 cards that are less than 7 in the deck (4 cards of each of the 5 ranks). Out of these 20 cards, only one is the 5 of diamonds.

Therefore, the probability that a randomly chosen card that is less than 7 is the 5 of diamonds is:

1/20 = 0.05 = 5%

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OR is the perpendicular bisector and R is the vertex of a pair of congruent angles in the diagram.

What is perpendicular bisector and a pair of congruent angles ?

A perpendicular bisector is a geometric tool that is commonly used in mathematics and geometry. It is used to divide a line segment into two equal parts and is constructed by first finding the midpoint of the line segment. The perpendicular bisector is then constructed by drawing a line perpendicular to the line segment at its midpoint.

In geometry, two angles are said to be congruent if they have the same measure. This means that they have the same size and shape, even if they are oriented differently. In other words, if you were to place one angle on top of the other, they would perfectly overlap.

Explanation of the true statements:

In the given diagram ,

PR=RN and OR is perpendicular .

Hence, OR is the perpendicular bisector because a perpendicular bisector is a line that passes through the midpoint of a line segment and intersects it at a right angle, dividing the segment into two equal parts.

The vertex of a pair of congruent angles is the point where the two angle bisectors intersect.
Hence, R is the vertex of a pair of congruent angles in the diagram.

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Given: We have the expression [tex]\sqrt[3]{875x^5y^9}[/tex]

Step-1: [tex]\sqrt[3]{875x^5y^9}[/tex]

Step-2: [tex](875\times x^5 \times y)^{1/3}[/tex]                              [break the cube root as power [tex]1/3[/tex]]

Step-3: [tex](125.7)^{1/3}\times x^{5/3} \times y^{9/3}[/tex]                    [break [tex]875=125\times7[/tex]]

                                                                     [tex]125=5^3[/tex]

Step-4: [tex](5^3)^{1/3}\times7^{1/3}\times x^{(1+2/3)}\times y^{9/3}[/tex]       [ [tex]\frac{5}{3} =1+\frac{2}{3}[/tex] ]

Step-5: [tex]5^1\times7^{1/3}\times x^1\times x^{2/3}\times y^{3}[/tex]                [break the power of [tex]x[/tex]]

Step-6: [tex]5\times x\times y^{3} \ (7^{1/3}\times x^{2/3})[/tex]

Step-7: [tex]5xy^3 \ (7x^2)^{1/3}[/tex]

Step-8: [tex]5xy^3\sqrt[3]{7x^2}[/tex]

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Answer: Supergirl = 19 and Wonder Woman = 8

Step-by-step explanation:

Let g represent the quantity of Supergirl keychains and w represent the quantity of Wonder Woman keychains.

                            Qty       Cost

Supergirl                 g         $3g

Wonder Woman     w       $2w

Total                       27       $73

Qty:     g +  w  = 27  →   -2(g +  w  = 27)    →    -2g - 2w = -54

Cost: 3g + 2w = 73  →     1(3g + 2w = 73)  →     3g + 2w =  73

                                                                           g          =  19

Input g = 19 into one of the original equations to solve for w:

g  + w = 27

(19) + w = 27

        w = 8

The inverse of the coefficient matrix is A^-1 = [-2 2]. The solution to the system of equations is x = -1 and y = 1/5.

To solve the system of equations:

2x + 2y = 1

2x - 3y = 0

We can write this system in matrix form as:

[2 2] [x] [1]

[2 -3] [y] = [0]

The coefficient matrix is:

[2 2]

[2 -3]

To find the inverse of the coefficient matrix, we can use the following formula:

A^-1 = (1/|A|) adj(A)

where |A| is the determinant of A and adj(A) is the adjugate of A.

The determinant of the coefficient matrix is:

|A| = (2)(-3) - (2)(2) = -10

The adjugate of the coefficient matrix is:

adj(A) = [-3 2]

[-2 2]

Therefore, the inverse of the coefficient matrix is:

A^-1 = (1/-10) [-3 2]

[-2 2]

Multiplying both sides of the matrix equation by A^-1, we get:

[x] 1 [-3 2] [1]

[y] = -10 [-2 2] [0]

Simplifying the right-hand side, we get:

[x] [-1]

[y] = [1/5]

Therefore, the solution to the system of equations is:

x = -1

y = 1/5

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_____The given question is incomplete, the complete question is given below:

solve the systems of equations by finding the inverse of the coefficient matrix. a. 2x+2y=1 2x-3y-0

2 gallons of blue paint are used for the walls, which cover 700 square feet.

What is surface area?

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

Let's call the surface area of the trim "T" and the surface area of the walls "W". We know that the ratio of T to W is 1:10, which means that:

T = (1/11) * W

We also know that 2 gallons of blue paint are used for the walls. Let's call the amount of white paint needed for the trim "P" (in pints).

We can use the fact that the total surface area of the room is equal to the surface area of the walls plus the surface area of the trim:

W + T = total surface area

Since T = (1/11) * W, we can substitute and simplify:

W + (1/11) * W = total surface area

(12/11) * W = total surface area

Now we can use the fact that 2 gallons of blue paint are used for the walls to find the surface area of the walls:

2 gallons = 16 pints

2 gallons = W / 350 (since 1 gallon covers 350 square feet)

W = 700 square feet

Now we can use the formula above to find the total surface area of the room:

total surface area = (12/11) * W

total surface area = (12/11) * 700

total surface area = 763.64 square feet

We know that the blue paint covers the walls, so we don't need to worry about that. We only need to find the amount of white paint needed for the trim. Let's call the amount of white paint needed per square foot of trim "p" (in pints). Then the total amount of white paint needed is:

P = p * T

We know that the ratio of the surface area between the trim and the walls is 1:10, so we can use that to find the surface area of the trim:

T = (1/11) * W

T = (1/11) * 700

T = 63.64 square feet

Now we just need to find the amount of white paint needed per square foot of trim. Since the trim is white, we don't need to worry about coverage, so we just need to find the surface area of the trim in square pints:

P = p * T

P = p * 63.64

Finally, we know that 1 gallon of paint is equal to 8 pints, so we can convert the total amount of white paint needed from pints to gallons:

P = p * 63.64

P / 8 = gallons of white paint needed

Putting it all together, we get:

2 gallons of blue paint are used for the walls, which cover 700 square feet.

The total surface area of the room is (12/11) * 700 = 763.64 square feet.

The surface area of the trim is (1/11) * 700 = 63.64 square feet.

The total amount of white paint needed is P = p * 63.64.

The amount of white paint needed in gallons is P / 8.

We don't know the value of p, so we can't solve for P directly. However, we do know that the ratio of the surface area between the trim and the walls is 1:10. This means that the surface area of the trim is 1/11 of the total surface area of the room.

Therefore, we can solve for p as follows:

T = (1/11) * W

63.64 = (1/11) * 700

p = P / T

p = P / 63.64

Hence, 2 gallons of blue paint are used for the walls, which cover 700 square feet.

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The proof that the lines CD and XY are parallel is shown below in paragraghs

Given that

∠CAY ≅ ∠XBD

This means that the angles CAY and XBD are congruent angles

The above means that

By the corresponding angles, we have

∠BXY = ∠AYX

∠ACD = ∠BDC

By the congruent angles above, the following lines are parallel

Line AC and BX

Line AY and BD

Line CD and XY

Hence, the lines CD and XY are parallel

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The matches of Histogram, Bin, Descriptive Statistics, Mean, Median and Standard Deviation are C, E, D, A, F, G and B respectively.

The Match the definition are given.

Histogram - C). is a graph of the frequency distribution of a set of data

Bin - E). a group in a histogram

Descriptive Statistics - D). values calculated from a data set and used to describe some basic characteristics of the data set

Mean - A). The scatter around a central point

Median - F). the middle value of a sorted set of data

Mode - G). is the most commonly occurring value in a data set

Standard Deviation - B). is a measure of a data’s variability

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There are 92 elements in A but not in B.

In mathematics, a set is a well-defined collection of objects or elements. Sets are denoted by uppercase symbols, and the number of elements in a finite set is denoted as the cardinality of the set enclosed in curly braces {…}.

Empty or zero quantity:

Items not included. example:

A = {} is a null set.

Finite sets:

The number is limited. example:

A = {1,2,3,4}

Infinite set:

There are myriad elements. example:

A = {x:

x is the set of all integers}

Same sentence:

Two sets with the same members. example:

A = {1,2,5} and B = {2,5,1}:

Set A = Set B

Subset:

A set 'A' is said to be a subset of B if every element of A is also an element of B. example:

If A={1,2} and B={1,2,3,4} then A ⊆ B

Universal set:

A set that consists of all the elements of other sets that exist in the Venn diagram. example:

A={1,2}, B={2,3}, where the universal set is U = {1,2,3} 

n(A ∪ B) = n(A – B) + n(A ∩ B) + n(B – A)

Hence, There are 92 elements in A but not in B.

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Answer:

The answer to your problem is, B, 0.5

Step-by-step explanation:

We are given the following table below;

              X             Y               Z             Total

A             32           10             28              70

B              6             5              25              36

C             18            15              7                40

Total       56           30            60              146

As we know that the conditional probability formula of P(A/B) is given by:

P(A/B) =  [tex]\frac{P(AnB)}{P(b)}[/tex]

P(C/Y) = [tex]\frac{P(CnY)}{P(Y)}[/tex]

P ( Y ) = [tex]\frac{30}{146}[/tex] and P(CnY) = [tex]\frac{15}{146}[/tex] [ because of the third column shown ]

Thus, the answer is, B. 0.5

Feel free to ask any questions down below \/ !

The ordered pair that respect the given conditions are: (6,-12) and (-12,6).

A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

You should convert the text of the question into equations. See below.

From equation 1, you have x=-72/y. Thus, applying the substitution method, you can solve this question by following the steps below:

1) Replace  x=-72/y into equation 2. Then, you have:

[tex]\frac{-72}{y} +y=-6\\ \\[/tex]

-72+y²=-6y

y²+6y-72=0

2) Solving the quadratic equation y²+6y-72=0 for finding y:

Δ=b²-4ac

Δ=6²-4*1*(-72)

Δ=36+288

Δ=324

[tex]y=\frac{-b\pm \sqrt{\Delta} }{2a} =\frac{-6\pm \sqrt{324} }{2*1}=\frac{-6\pm18 }{2}[/tex]. Therefore,

y1=(-6-18)/2=-12

or

y2=(-6+18)/2=12/2=6

3) Finding x

If  x=-72/y and y=-12 or y=6. You have

For y=-12, x=-72/-12, thus x=6

For y=6, x=-72/6, thus x=-12

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The equation that represents the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

Explanation:

To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).

Therefore, the equation for the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

This can also be written as:

Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)

Therefore, the value of the collection after 5 years is $246.90.

Answer: 254.26

Step-by-step explanation:

The required value is 1.5(IQR) equals 6.

A dataset is a collection of facts that relates to a particular subject. The test results of each pupil in a particular class are an illustration of a dataset. Datasets can be expressed as a table, a collection of integers in a random sequence, or by enclosing them in curly brackets.

The IQR (interquartile range) is the difference between the third quartile (Q3) and the first quartile (Q1). So, we first need to calculate IQR:

IQR = Q3 - Q1 = 16 - 12 = 4

Now we can calculate 1.5 times the IQR:

1.5(IQR) = 1.5(4) = 6

Therefore, 1.5(IQR) equals 6.

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Complete question:

The five-number summary of a data set is given below.

Minimum: 3 Q1: 12 Median: 15 Q3: 16 Maximum: 20

Which of the following equals 1.5(IQR)?

By looking at the vertex of the graph, we can see that the fourth graph is the correct option.

Here we want to see which one of the given graphs represents the given absolute value function.

Remember that for the absolute value function:

f(x) = |x - a| + b

Has a vertex at the point (a, b) and opens up.

Then in this particular case, with the function f(x)=∣x+1∣−3, the vertex will be at the point (-1, -3), so we just need to identify which one of the given graphs has that vertex, we can see that the correct option is the fourth option.

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Answer:

The shaded region in all of the answers are equal.

Step-by-step explanation:

Since squares have equal sides, the area of each square is 12 squared or 144.

The area of the circle in A is pi*radius squared. The diameter is 12, because that is the side length of the square. This means the radius is 6 because the radius of a circle is always half the diameter. So, the area equals 36pi.

The area of the shaded region of A is 144-36pi.

In B, the diameter of each circle is half of what it was in the circles in answer A. So, the diameter is 6 and the radius is 3. The area of each circle is 9pi, and 9 pi * 4 circles is 36pi.

The area of the shaded region of B is 144-36pi.

In C, the diameter of each circle is a third of what it was in the circles in answer A. So, the diameter is 4, and the radius is 2. The area of each circle is 4pi, and 4pi * 9 circles is 36pi.

The area of the shaded region of C is 144-36pi.

Answer:

x = 30

Step-by-step explanation:

We know

The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.

2x + 3x + 10 = 160

5x + 10 = 160

5x = 150

x = 30

The  angles can be named with one letter  are 2.

Angles are a type of geometric shape which are formed when two straight lines intersect at a point. They are measured in degrees, usually between 0 and 360. Angles can be classified as acute, right, obtuse, straight and reflex, and the sum of any three angles in a triangle will always equal 180 degrees. Angles can be used in various ways, from providing stability in construction work to helping to identify other shapes. They can also be used to measure the size and shape of objects and to calculate distances and areas on maps. Angles are an important part of mathematics, geometry and trigonometry, and are used in a variety of applications in science and engineering.

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Answer:8

Step-by-step explanation:8x1=8

Answer:

It is a tangent

Step-by-step explanation:

A tangent is a straight line that brushes the circumference of a circle.

The limit of f(x, y) as (x, y) approaches (0, 0) depends on the path taken, the limit does not exist, and we can conclude that the function f(x, y) do not have a limit as (x, y) → (0, 0).

To show that the function f(x, y) does not have a limit as (x, y) → (0, 0), we need to show that the limit does not exist, either because the limit is infinite or because the limit does not exist.

We are given that the limit of f(x, y) as (x, y) → (0, 0) when y → infinity is infinity. This means that as y approaches infinity, the function f(x, y) becomes arbitrarily large, regardless of the value of x. However, this does not imply that the limit of f(x, y) exists as (x, y) → (0, 0).

To see why, consider the sequence of points (x_n, y_n) = (1/n, n) as n approaches infinity. As y_n → infinity, we have

lim (x_n, y_n) → (0, 0) f(x_n, y_n) = infinity.

However, if we consider the sequence of points (x_n, y_n') = (1/n, n^2) instead, as n approaches infinity, we have

lim (x_n, y_n') → (0, 0) f(x_n, y_n') = 0.

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there is a 20% chance that the point chosen at random will lie on bg.

To find the probability that a point chosen at random will be on the line segment bg, we need to consider the length of bg in relation to the length of the entire line segment ak.

Let us assume that ak is a straight line segment, and bg is a smaller segment that lies entirely within it. To find the probability, we need to divide the length of bg by the length of ak.

Let the length of bg be x and the length of ak be y. Then the probability that a point chosen at random will be on bg is:

Probability = Length of bg / Length of ak

Probability = x / y

However, we need to be careful here. If we choose a point anywhere on ak, it may not necessarily lie on bg. There are an infinite number of points on ak, but only one segment bg. Therefore, the probability we are looking for is actually the ratio of the lengths of bg to ak.

So, if we know the lengths of bg and ak, we can find the probability by dividing them. For example, if bg is 2 units long and ak is 10 units long, the probability of choosing a point on bg is:

Probability = 2 / 10

Probability = 0.2 or 20%

In this case, there is a 20% chance that the point chosen at random will lie on bg.

In conclusion, the probability of a point chosen at random on ak being on bg is directly proportional to the length of bg in relation to the length of ak. Therefore, we need to find the ratio of the lengths of the two line segments to determine the probability.

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what is the probability  a point is chosen at random on ak and then the point will be on bg. dont forget to reduce the products?

Answer:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values, we get:

m = (5 - (-10)) / (6 - 3) = 15/3 = 5

Now that we have the slope, we can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

Substituting the values of m, x1, and y1, we get:

y - (-10) = 5(x - 3)

Simplifying and rearranging the equation, we get:

y + 10 = 5x - 15

y = 5x - 25

Therefore, the equation of the line passing through (3,-10) and (6,5) in slope-intercept form is y = 5x - 25.

Step-by-step explanation:

#trust me bro

Answer:

Jika 16,5% dari suatu jumlah adalah 891, kita dapat menggunakan persamaan:

0,165x = 891

di mana x adalah jumlah aslinya. Kita ingin menyelesaikan persamaan ini untuk x.

Kita dapat memulai dengan membagi kedua sisi dengan 0,165:

x = 891 / 0,165

x = 5400

Jadi, jumlah aslinya adalah 5400.
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The function f(x,y) has only minimum value at (1,0) is -1 and maximum value does not exist.

The given function is f(x,y)=x²+y²-2x

First find the partial derivative with respect to x and y

f'(x)=2x-2

f'(y)=2y

f'(x)=0=f'(y)

2x-2=0

x=1

and y=0

Now we will cheak maxima and minima at (1,0)

f''(x,y)=2 and f"(x,y)=2 and f"(x,y)=0( derivative of first order of x with respect to y)

We know that

rt-s²≥0 and r positive then f is minimum and  r negative maximum

r=2 , t=2 and s=0

rt-s²≥0 and r is positive so f(x,y) is minimum at (1,0)

f(1,0)=1-2=-1

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In one of his experiments conducted with animals, Thorndike found that cats learned to escape from a puzzle box is increased gradually

To quantify the learning process, Thorndike used a mathematical formula known as the Law of Effect equation. The equation is:

B = f(log S1/S2)

where B represents the strength of the behavior, S1 represents the satisfaction of the positive consequence, and S2 represents the degree of frustration or negative consequence.

In the context of Thorndike's puzzle box experiment, the Law of Effect equation can be used to describe how the cat's behavior changed over time as it learned to escape the puzzle box more quickly and efficiently. Initially, the cat's behavior was weak because it did not know which actions would lead to a positive outcome.

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The probability of choosing a letter from n to q would be = 2/5

Probability is defined as the expression that is used to represent the possibility of an outcome of an event which can be solved with the formula = chosen events/ total outcomes.

The number of cards in the box = 10

The various cards are labelled as follows= j, k, l, m, n, o, p, q, r, and s.

The number of cards from n to q = 4

Therefore the probability that a number from n to q will be chosen = 4/10 = 2/5.

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