The length of a rectangular part is 20 feet longer than the width of the park is the length of the park is 36 feet what is the width of the park

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.

The correct option for an adjoining situation in which liquid is flowing through a pipe of variable cross-section representing pressure is  (a) V1>V2 if L1>L2.

This is because, in a pipe of variable cross-section, the velocity of the liquid (V) is directly proportional to the cross-sectional area of the pipe (L). Therefore, if the cross-sectional area of one section of the pipe (L1) is greater than that of another section (L2), then the velocity of the liquid flowing through the first section (V1) will be greater than that of the second section (V2). This is due to the fact that in the area of the pipe where the cross-sectional area is greater, the liquid will have more space to flow and thus will have a higher velocity.

The other options are incorrect because these situations are not possible.

In fluid mechanics, The pressure drop is directly proportional to the fluid velocity, as well as the density of the fluid and the length of the pipe. The pressure drop is inversely proportional to the cross-sectional area of the pipe. So if the cross-sectional area of the pipe is increasing, the pressure is decreasing. And if the cross-sectional area of the pipe is decreasing, the pressure is increasing.

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The complete question is:

Select the correct option for the adjoining situation in which liquid is flowing through a pipe of variable cross-section (P1, P2 represent pressure(a) V1>V2 if L1>L2 (b) V1<V2 for all values of L1 and L2 (c) P1<P2 for all values of L1 and L2 (d) P1>P2 values of L1 and L2

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:

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 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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If the sample size is large (typically n > 30), then it is generally appropriate to use the standard normal distribution (z-distribution) to approximate the sampling distribution of the sample mean.

What are the standard's mean and variance?

Standard deviation is the square root of the number, while variance is equal to the average squared deviations from the mean. Additionally, the variance's square root is the standard deviation.

This is because as the sample size increases, the Central Limit Theorem states that the sample mean will become more normally distributed, regardless of the underlying distribution of the population.

This is due to the fact that the standard error of the sample mean, which is the standard deviation of the sampling distribution of the mean, decreases as the sample size increases. When the sample size is large, the sample mean will be approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

However, it is important to note that in order to use the z-distribution to approximate the sampling distribution of the sample mean, it is necessary to know the population mean and population standard deviation. If these values are not known, it is appropriate to use the t-distribution, which does not require knowledge of the population parameters.

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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?

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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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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The weights (in pounds) of a sample of 13 male eleventh graders ,so the median weight of these students is 159.

Calculate the mean by summing the centre values and dividing them by the number. From there, you may obtain the median.

To arrange the data points in ascending order for a small data set, count the number of data points (n). To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.

148, 140, 159, 141, 151, 156, 173, 167, 160, 159, 146, 174, 170

140 , 141 , 146 , 148, 151 ,156,  159 ,159, 160, 167 , 170, 173, 174.

The median weight of these students is 159.

The weights (in pounds) of a sample of 13 male eleventh graders ,so the median weight of these students is 159.

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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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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!

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.

Answer:

21x+35y=?

Step-by-step explanation:

multiply 3 by 7

multiply 5 by 7

you can't add different variables together

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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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 radioactive substance cesium-137 has a half-life of 30 years.  For the given compound, Initial amount is 647 grams and Amount after 100 years is 64 grams.

A sample's half-life is the amount of time it takes for half of its unstable nuclei to decay, for its activity to halve, or for its count rate to decrease by half. The number of decays that a detector, like the Geiger-Muller tube, records each second is known as the count-rate.

For radioactive compounds, a general exponential function is provided by

Ao(1/2)t/t1/2 = A(t)

Where,

A(t) is the sum that is left after t years.

Ao is the radioactive substance's initial concentration.

The time it takes for a radioactive substance to degrade to A is measured in years.

The radioactive substance's half-life is represented by t1/2.

A(t) = 523(1/2)t/30 in comparison to the general exponential function

A starting point (Ao) of 523 grams

A(t) = 647(1/2)^t/30

t = 100

A(100) equals [647 × (1/2) × 100] /30

=647 × 0.53.333

=647 × 0.0992

=64.182

=64 grams (to the nearest gram)

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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

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.

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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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

square side ²= area

s =√81

S = 9

perimeter= 9×4 = 36

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

Answer:

m = 2/3

Step-by-step explanation:

Take two random points, I personally picked (-2, 0) and (1, 2)

Slope = rise/run = [tex]\frac{2-0}{1-(-2)} = \frac{2}{3}[/tex]

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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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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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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