The system shown has the unique solution (2, y, z). Solve the system and select the values that complete the solution. y = 0 y = 2 y = 3 z = 0 z = 2 z = 3

The formula for calculating the future value of an investment compounded annually is:

FV = P(1 + r)^t

where:

FV = future value of the investment

P = principal or initial investment

r = annual interest rate as a decimal

t = number of years the investment is held

In this problem, the principal is given as $4700, the annual interest rate is given as 5.25%, and the time is measured in years since 2007.

So we can write the function as:

y = 4700(1 + 0.0525)^t

In this function, y represents the future value of the investment (in dollars) and t represents the number of years since 2007.

The above function can be written in the form A or A B , where A and B are constants or variable expressions that have no variables in common.

A = 4700

B = 1 + 0.0525

y = A*B^t

So the exponential function for the problem is:

y = 4700*(1+0.0525)^t

Answer: Figure 2 (The rectangle)

Hope this helps :)

Step-by-step explanation:

Quadrilaterals are shapes that have 4 (connected) sides

Answer:

the second figure

Step-by-step explanation:

Quadrilaterals have a maximum and minimum of four

This is an algebraic word problem that is evaluated to give the total pieces of cake Mary distributed to be 35.

In algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.

We shall represent the total pieces of cake Mary distributed with the letter x, so that:

x - 4x/5 = 7 {the pieces left that got to the 7}

(5x - 4x)/5 = 7

x/5 = 7

x = 5 × 7 {cross multiplication}

x = 35.

Therefore, the algebraic word problem is solved to give us the total pieces of cake Mary distributed to be 35.

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The number of ways randomly an  integer which is a composite number generated by a computer between 10 and 20 is equal to option c. 6.

As given in the question,

Total number of integer between 10 and 20 where 20 is inclusive = 10

Composite numbers between 10 and 20 where 20 is inclusive are :

12, 14, 15, 16, 18 ,20

Total number of ways an integer which is a composite number generated between 10 and 20( inclusive )

= 6

Therefore, the number of ways randomly an integer which represents a composite number generated by a computer between 10 and 20 ( inclusive ) is equal to option C. 6.

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Two events are said to be mutually exclusive in the framework of probability theory if they cannot occur simultaneously or at the same time.

In the context of probability theory, two events are said to be mutually exclusive if they cannot happen simultaneously or at the same time. Alternatively, disjunct occurrences are those that are mutually exclusive. The likelihood that two events will occur simultaneously is 0 if they are deemed to be disconnected events.

Events that cannot exist or occur at the same moment are referred to as mutually exclusive events. There are never two occurrences that can happen at the same moment. The probability of A and B occurring simultaneously is P(A and B)= 0 if A and B are two mathematical events that are mutually exclusive.

a. Being female and preferring basketball are mutually exclusive.

b. Being male and preferring football are mutually exclusive.

c. Being female and preferring hockey are mutually exclusive.

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There are a total of 27 steps on the staircase.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Let x be the total number of steps in the staircase.

Larry climbs exactly 2/3 of the stairs.

Number of steps Larry climbed = 2x/3

She goes back exactly 1/2 of the way to the bottom.

Number of steps returned = (2x/3) (1/2) = 2x/6 = x/3

She is at x/3 steps from the bottom.

From that spot, she climbs exactly 2/3 of the way to the top.

Remaining steps to the top = x - x/3 = 2x/3

Number of steps Larry climbed = 2/3 of the way to the top = (2/3)(2x/3) = 4x/9

So we get,

x/3 + 4x/9 + 6 = x

x - x/3 - 4x/9 = 6

x - 7x/9 = 6

2x/9 = 6

2x = 54

x = 27

Hence there are 27 steps in the staircase.

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The complete question is as follows :

Lara starts at the bottom of a long staircase. She climbs exactly 2/3 of the stairs. Then, she goes back down exactly 1/2 of the way to the bottom. From that spot, she climbs exactly 2/3 of the way to the top. Finally from there, she climbs 6 stairs to reach the top. How many stairs are in the staircase?

Here we are interested in finding the slope of the line. From the given graph we can see that that the line passes through points (-6,0) and (0,3) . We know that slope can be calculated by ,

[tex]\longrightarrow slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1} =\tan\theta =\dfrac{rise}{run}[/tex]

[tex]\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]

[tex]\longrightarrow m =\dfrac{0-3}{-6-0}\\[/tex]

[tex]\longrightarrow m =\dfrac{-3}{-6}\\ [/tex]

[tex]\longrightarrow m =\dfrac{1}{2}=0.5[/tex]

And we are done!

Answer:

x=10

Step-by-step explanation:

The triangles CAB and PMB are similar. And since each side of CAB is 2 times longer than the side of PMB, we can write the equation:

3x=2(x+5)

3x=2x+10

x=10

Answer:

21x+35y=?

Step-by-step explanation:

multiply 3 by 7

multiply 5 by 7

you can't add different variables together

Answer:

Parallel Line: [tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]

Perpendicular Line: [tex]y=\frac{5}{4}x-8[/tex]

Step-by-step explanation:

Perpendicular lines have a slope that is the negative reciprocal of each other. So for example if one line has a slope of: [tex]\frac{a}{b}[/tex], where "a" and "b" are just some constants, then a perpendicular line would have a slope of: [tex]-\frac{b}{a}[/tex], so the slope fraction is just flipped and it's the opposite sign.

Parallel lines never intersect meaning they will have the same slope, since as one goes to the right one and up or down some amount, the only way for the other line to never intersect is to also go up or down by the same amount, which is essentially the slope. The only other condition is that parallel lines must have different y-intercepts, otherwise they have the same slope and y-intercepts meaning they're just the same line and instead of never intersecting they actually intersect at infinitely many points.

The slope-intercept form is especially useful as we can simply look at it and determine the slope and y-intercept, hence the name slope-intercept form. We want to convert into this form to determine the slope of the equation given to us so we can find the perpendicular and parallel lines.

We're given the equation in standard form:

[tex]4x+5y=9[/tex]

We want to convert this into slope-intercept form, which we can do by isolating the y variable. We want to get rid of the 4x term on the left side by subtracting 4x, and we want to do this to both sides to maintain equality:

[tex]4x-4x+5y=9-4x[/tex]

Simplify:
[tex]5y=-4x+9[/tex]

Now we want to get rid of the coefficient of 5 from the left side, and this coefficient is just multiplication so to cancel out multiplication, we divide, specifically by 5 in this case, and on both sides to maintain equality:

[tex]\frac{5y}{5}=\frac{-4x+9}{5}[/tex]

Simplify:
[tex]y=-\frac{4}{5}x+\frac{9}{5}[/tex]

Now we know the slope is: [tex]-\frac{4}{5}[/tex]

For this we simplify find the negative reciprocal so we flip the fraction and "flip" the sign, or in other words if it's negative it becomes positive, if it's positive it becomes negative so: [tex]-\frac{4}{5}\to \frac{5}{4}[/tex]

We can represent the general equation of a perpendicular line in slope-intercept form: [tex]y=\frac{5}{4}x+b[/tex], where "b" is some constant number. We're given that it passes through the point (4, -3) which we can plug in as (x, y) to solve for that value "b"

[tex]-3=\frac{5}{4}(4)+b[/tex]

Simplify on the right side

[tex]-3=5+b[/tex]

Subtract 5 from both sides

[tex]-8=b[/tex]

So now we have the perpendicular line equation: [tex]y=\frac{5}{4}x-8[/tex]

For this we don't have to do anything to the slope, since for parallel lines the slope is the same, so we know the slope is: [tex]-\frac{4}{5}[/tex] and we can plug this into the slope-intercept form to get a general equation for a parallel line: [tex]y=-\frac{4}{5}x+b\text{ where }b\ne\frac{9}{5}[/tex]

Since we're given that it passes through the point (4, -3) we can plug this in as (x, y) to find a definitive equation.

[tex]-3=-\frac{4}{5}(4)+b[/tex]

Simplify on the right side:

[tex]-3=-\frac{16}{5}+b[/tex]

Rewrite the left side to have a denominator of 5:

[tex]-\frac{15}{5}=-\frac{16}{5}+b[/tex]

Add 16/5 to both sides:

[tex]\frac{1}{5}=b[/tex]

So now let's plug this into a general equation we had above to get:
[tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]

The equation describes the relationship between the rate of change of with respect to time and the rate of change of with respect to time is dx/dt -2 dy/dt              

Well   x + 2y = k                   (constant)

differentiate through wrt t

dx/dt  +  2 dy/dt = 0

so dx/dt -2 dy/dt               (so B)

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Answer:

The correct answer is 8x³y + 5y²x + x² - 14z - 2.

Step-by-step explanation:

This is in standard form because it is a polynomial with the terms arranged in descending order of their exponents, with the coefficient of each term being positive.

The exponent of x is 3, the exponent of y is 2, the exponent of z is 1, and the constant is -2.

For a randomly selected group of 4 adult workers, the probability that no more than 3 drink coffee at least occasionally while on the job is 37.5%.

Probability refers to the chance, odds, or likelihood that an expected outcome is obtained when there are many possible events.

Probability may be 100% certain, depicted as 1, or 100% uncertain, expressed as zero.

Other values of probability lie between one and zero as fractional values that can be depicted as percentages, decimals, or fractions.

The estimated percentage of adults who at least occasionally drink coffee = 50%

Random sample = 4

The number of adult workers from 4 who occasionally drink coffee on the job = 3

The probability of 3 out of 4 workers drinking coffee on the job = 37.5% (3/4 x 50%)

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The set of all x-values at a distance of 15 or less from the number 6 can be represented in interval notation as (-9, 21).

Interval notation is a way of expressing a set of numbers in a concise and easily readable format. In this case, we are looking for all the x-values that are a distance of 15 or less from the number 6. To find these values, we need to consider the range of numbers that are 15 units away from 6 in both the positive and negative directions.

So, in interval notation, the set of all x-values at a distance of 15 or less from 6 is written as (-9, 21) which means all the values between -9 and 21 (not including -9 and 21)

Key points:

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A parabolic tunnel has the shape of a parabola in cross-section, with one axis being symmetric (the width) and the other axis being the height at the center. To find the cross-sectional area of the parabolic tunnel, we can use the formula for the area of a parabola:

Area = (1/2) x Width x Height

Given that the width of the parabolic tunnel is 20 feet and the height at the center is 12 feet, we can substitute these values into the formula:

Area = (1/2) x 20 x 12 = 120 square feet.

So the cross-sectional area of the parabolic tunnel is 120 square feet.

A data set which could be represented by the boxplot shown include the following: A. {6, 6, 8, 8, 9, 12, 13, 13, 14}.

In Mathematics, a boxplot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the given box-and-whisker plot, the five-number summary for the given data set include the following:

By critically observing the box-and-whisker plots or boxplot (see attachment), we can logically deduce that it correctly represents this data set {6, 6, 8, 8, 9, 12, 13, 13, 14}.

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Answer:

D. 15

Step-by-step explanation:

4+5+6=

4+5=9..

9+6=

15.

Thus, Answer is D. 15

Answer:

Your answer is: D)15cm

Step-by-step explanation:

To find the perimeter add all of the side together.

6+4+5=15

It is a structured visual representation of simplified thoughts, ideas, structures, relationships, statistical data, anatomy, etc. It can be used in any part of human activity to clarify a topic or provide an example of a topic.

Mind maps, flowcharts, fishbone diagrams, hierarchy/org charts, and SWOT analysis charts are the most common types of diagrams covered in this article. It is a structured visual representation of simplified thoughts, ideas, structures, relationships, statistical data, anatomy, etc. It can be used in any part of human activity to clarify a topic or provide an example of a topic.

A diagram that shows the parts of an object and their interrelationships is called a diagram.

It is a structured visual representation of thoughts, ideas, structures, relationships, statistical data, anatomy, etc. It's a simplification. It can be used in any part of human activity to clarify a topic or provide an example of a topic.

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A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector.

Unit Vector is represented by the symbol ‘^’, which is called a cap or hat, such as: â. It is given by   â  = a / |a|

Where |a| is for norm or magnitude of vector a.

It can be calculated using a Unit vector formula.

Unit vectors are usually determined to form the base of a vector space. Every vector in the space can be expressed as a linear combination of unit vectors. The dot products of two unit vectors is a scalar quantity whereas the cross product of two arbitrary unit vectors results in third vector orthogonal to both of them. As explained above vectors have both magnitude (Value) and a direction. They are shown with an arrow.

And, â denotes a unit vector. If we want to change any vector in unit vector, divide it by the vector’s magnitude. Usually, xyz coordinates are used to write any vector.

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The height that represents the middle 80 percent of the heights is 64.87 inches and 74.13 inches and this can be determined by using the given data.

Given :

The distribution of heights for adult men in a certain population is approximately normal with a mean of 70 inches and a standard deviation of 4 inches.

The heights that represent the middle 80 percent of the heights are:

P(-z < Z < z) = 0.80

P(Z < z) - P(Z < -z) = 0.80

P(Z < z) - (1 - P(Z < z)) = 0.80

2P(Z < z) = 1.80

P(Z < z) = 0.90

So, the value of z is 1.282.

Now, put the values of height as follows:

x1= 64.87

x2= 75.13

Therefore, the height that represents the middle 80 percent of the heights is 64.87 inches and 74.13 inches.

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The volume of ice in Antarctica can be calculated by first determining the area of the semicircle.

This can be done by multiplying the radius (2000 km) of the semicircle (2πr2) by half, resulting in a total area of 3,14159265 x (2 x 20002) = 628318530 km2. To calculate the volume of ice, this area must be multiplied by the average thickness of the ice cover (3000 m). This results in a total volume of 18,8547595 x 1012 cm3 of ice in Antarctica. To put this into perspective, this is the equivalent of roughly 6.5 billion Olympic swimming pools of ice.The volume of ice in Antarctica can be calculated by first determining the area of the semicircle.

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(i) 1 quintal = 100 kg

2.5 quintals = 2.5100 = 250 kg

Transportation cost of 250 kg of potatoes = 105(250/35) = Rs 750

we are asked to find the transportation cost of 2.5 quintals (250 kg) of potatoes at the same rate as 35 kg of potatoes. We know that the transportation cost for 35 kg is Rs 105.

To find the cost for 250 kg, we use the proportion of 35/105 = x/750. By cross multiplying we get x= 250*105/35= 750. So the transportation cost for 250 kg of potatoes is Rs 750.

(ii) Transportation cost of 1 quintal of potatoes = 105*(100/35) = Rs 300

Transportation cost of 1 quintal of potatoes = Rs 1500 / Rs 300 = 5 quintals.

we are asked to find how many quintals of potatoes can be transported for Rs 1,500 at the same rate as 35 kg of potatoes. We first find the transportation cost of 1 quintal of potatoes by using the proportion of 35/105 = x/300.

So x = 100, thus the transportation cost of 1 quintal of potatoes is Rs 300. So we can transport 1 quintal of potatoes for Rs 300. Dividing 1500 by 300, we get 5 quintals.

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Answer:

Step-by-step explanation:

f(x) is basically another term for y, and you already have your x values, so you can just plot the points and draw lines through them :)

For drawing graphs we have two points (x-axis and y-axis ) to loacte exact location on the graph.

X-axis point to locate on the graph parallel distance from y-axis.

Y-axis point to locate on the graph parallel distance from x-axis.

Take the y-coordinates as the f(x) and points of x-coordinates as the value of x.

1.Write down the coordinates of x-axis and y-axis

y=-3x+1

(X-axis,Y-axis)=A(-2,7),B(-1,4),C(0,1),D(1,-2),E(2,-5)

2.Write down the coordinates of x-axis and y-axis

y=-x²+5

(X-axis,Y-axis)=A(-2,1),B(-1,4),C(0,5),D(1,4),E(2,1)

3.Write down the coordinates of x-axis and y-axis

y=[tex]2^{x}[/tex]

(X-axis,Y-axis)=A(-2,0.25),B(-1,0.5),C(0,1),D(1,2),E(2,4)

These are the graphs linke images

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The inequality is for the given term 3y + 5 < 10 is y < 5/3.

The term "inequality" refers to a mathematical expression in which the sides are not equal to one another. In essence, an inequality compares any two values and demonstrates that one value is less than, greater than, or equal to the value on the other side of the equation.

Less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠) are the inequality symbols.

Inequalities are used to compare numbers and identify the range (or ranges) of values that satisfy the requirements of a given variable.

Given to solve the inequality

3y + 5 < 10

3y < 10 - 5

3y < 5

y < 5/3

and

y ∈ (−∞, 3/5)

Thus, the inequality is for the given term 3y + 5 < 10 is y < 5/3.

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Material will be required to make six bench legs each 28 1/4 inch is 169.5 inches.

What is Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

What is Decimal?

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

The simple solution is to convert 28 1/4 to a decimal and be cautious about converting it back to a fraction if necessary.

28 1/4=28.25

You need Six of them.

1 leg measures28.25 inches.

6 legs = x

Cross multiply 1/6 = 28.25 / x

x = 6* 28.25

x equals 169.5 inches

How many feet is that exactly? To calculate the amount of feet, divide by 169.5 /6=28.25 feet.

2 by 4s are typically 6 feet long. Unfortunately, you will need two of these for two more for 6 feet.

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To find the number of years it takes for an investment to grow to a certain value at a certain interest rate, you can use the formula:

n = (future value - principal) / (principal * interest rate)

Where:

n = number of years

future value = the final value of the investment

principal = the initial amount invested

interest rate = the annual interest rate as a decimal

Plugging in the given values:

n = (21150 - 5000) / (5000 * 0.17)

n = 16.65

Rounding to the nearest whole number, it would take approximately 17 years for the investment to be worth $21,150.00.

Let x be the total amount of money .

Emily's share =(1/3)x

Given Emily's share = 45000

so (1/3)x = 45000

x = 135000

Eric's share = (2/5)x

Eric puts 75% of his share in bank

= (2/5)*x*0.75

= (2/5)*135000*0.75

= 40500

Cat's share

= 1-([(1/3)*x] + [(2/5)*x])

= (4/15)*x

= (4/15)*135000

= 36000

a. -79, -41, -31, 54, 57

b. -56, -55, -54, -43, -39, -37, 18, 22, 43, 44, 52

In both cases, I have put the integers in order from smallest to greatest by comparing each number and placing them in the correct order. Starting with the smallest number and moving to the largest.