The vertices of quadrilateral PQRS are listed.
P(3,7). Q(6,-2), R(0,-4), S(-3,5)
Which of the following is the strongest classification that identifies quadrilateral PQRS?
O A.
Quadrilateral PQRS IS a parallelogram.
O B.
Quadrilateral PQRS is a rectangle.
• c.
Quadrilateral PQRS is a square.
• D.
Quadrilateral PQRS is a trapezoid.

The value of the function instance h (-3) as required to be determined given the function declaration; h(x) = −3x + 15 is; 24.

It follows from the task content that the value of the function instance h (-3) is to be determined given the function h (x) = -3x + 15.

Since the given function is; h (x) = -3x + 15.

The value of the function instance; h (-3) can be determined by evaluating as follows;

h (-3) = -3 (-3) + 15

h (-3) = 9 + 15

h (-3) = 24.

On this note, the value of the function instance h (-3) as required is; 24.

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The equations that represent a linear function are :

A linear function is a function that represents a straight line on the coordinate plane.  The degree of a linear equation must be 0 or 1 for each of its variables.

A linear function has the following form. y = mx + b.

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

Therefore, linear function can be represented in slope intercept form as follows;

y = mx + b

where

Therefore, the linear function of the equations are as follows;

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Answer: 1264 pounds of garbage in one week

Step-by-step explanation: This problem is a unit rate problem, so, we need to find the unit rate of this word problem. To do that, you would do the amount of garbage produced (189.6) divided by the number of adults (6), which equals 31.6. So, the unit rate is 31.6 pounds of garbage for one adult. Then, you need to do 31.6 times 40 (for the number of adults) which equals 1264.

The probability of drawing two numbers from both jars whose product is even = 5/9.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

Total number of outcomes =9

Favorable cases = (1,2), (2,1), (3,2), (2,3), (2,2)

The probability of drawing two numbers from both the jars whose product is even = 5/9

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The value of the function after evaluation is , f(x)=0 . Hence it is neither a minima nor a maxima.

f(x) =(x + 5)^4; x = - 5

=(-5+5)^4

=(0)^4

=0

The critical value is crucial for accurately portraying a range of properties in statistics. The critical value can be helpful for proving or disproving ideas when they are tested, in addition to validity and accuracy.

If you're taking a statistics course or are just interested in how these concepts work, it is essential to comprehend critical value and how to compute it before analyzing other statistical functions, such as margin of error and significance.

When calculating the margin of error for a set of data, statisticians utilize a measurement known as the critical value.

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As per the cylindrical coordinate, the value of E is (0, 2π/5)

In math, coordinates refers the set of values that show an exact position.

Here we have given that  x² + y² = 9, above the plane z = 0, and below the cone z² = 36x² + 36y²

And we need to find the value of E.

While we looking into the given question, we have identified that in cylindrical coordinates the region E is described by

=> 0 ≤ r ≤ 1, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 2r.

Here the given equation will go through the double integral, then we get,

=> ∫∫∫ₓ x² dV

And it can be rewritten based on the differentiation,

=> ∫₂⁰ ∫¹₀ ∫²₀ (r cos θ)² r dz dr dθ

=>  ∫₂⁰ cos² θ dθ

=> ∫¹₀ 2r⁴ dr = 2π/5

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Maya has a solution that volume is 3.8 liters. She needs more 20.12 liters solution.

What is solution?

A particular kind of homogenous mixture made up of two or more substances is known as a solution. A solute is a substance that has been dissolved in a solvent, which is the other substance in the mixture.

Given that Maya has a solution with volume 3.8 liters.

The symbol is used in mathematics to represent the multiplication operation and the resultant product. It is sometimes referred to as the times sign or the dimension sign.

Times means multiplication.

She requires 4.3 times more than she currently possesses..

She needs = 4.3 × 3.8 = 16.32 liters.

The total amount she needs is 16.32 + 3.8

Addition process:

  1

16.32

+3.80

______

20.12

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The value of the given integral [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] is 2/75.

The given integral is [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex].

We have to evaluate the given integral.

The given integral is definite integral. To evaluate the given integral we firstly solve the integral then we put the value in the solved integral to find the value.

We solving the integral [tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]

Let u = 2e^{5t}+3

Now differentiating

du/dt = 10e^{5t}

e^{5t}dt = du/10

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int\frac{1}{u^2}dt[/tex]

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int{u^{-2}}dt[/tex]

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-2+1}/(-2+1)]+C

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-1}/(-1)]+C

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/u)+C

[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/2e^{5t}+3)+C

Now;

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5t}+3}\right]^{\text{In}3/5}_{0}[/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5({\text{In}3/5})}+3}-\frac{1}{2e^{5(0)}+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{({\text{In}3})}+3}-\frac{1}{2e^{0}+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2\cdot3+3}-\frac{1}{2+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{6+3}-\frac{1}{2+3}\right][/tex]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[1/9 - 1/5]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[5-9/45]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[-4/45]

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 2/75

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The right question is:

Problem 3: Integration via the Substitution Method ( 16 points) Evaluate each of the following. Explain and show your work. You do not need to simplify your final answer.

[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]

Using ratios we know that the total number of sweet Debs and Jamie has is 50.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

Two quantities are compared to form a ratio.

An equality of two ratios is a proportion.

How to format a ratio Analyze the ratio to see whether it is part to part or part to whole.

Calculate the whole and the pieces as necessary.

So, we have a ratio of 3:7.

Debs has 20 fewer sweets than Jamie.

Let, Jamie have x sweets and Debs has x - 20.

Now, we get the equation:

3/x - 20 = 7/x

Now, solve as follows:

3/x - 20 = 7/x

3x = 7(x - 20)

3x - 7x - 140

7x - 3x = 140

4x = 140

x = 140/4

x = 35

x - 20 = 35 - 20 = 15

Total: 35 + 15 = 50

Therefore, using ratios we know that the total number of sweet Debs and Jamie has is 50.

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The correct statement is: the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are congruent.

The correct answer is an option (c)

In this question we have been given a statement 'the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are______'

We need to select a correct choice to complete the given statement.

Also, we need to give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles.

We know that by Alternate Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent.

Consider the following figure.

A pair of alternate interior angles: ∠4 and ∠6

a pair of corresponding angles:  ∠2 and ∠6

and a pair of alternate exterior angles: ∠2 and ∠8

Therefore, the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are congruent.

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The total cost of painting and carpeting the 4 walls and the floor is C = ₹(720x² + 1324.8x).

Given is that a room three times as long as it is broad and its height is 4.6 m. The cost of carpeting its floor at Rs. 240 per square meter be  the cost of painting the 4 walls at Rs. 24 per sq. m.​

Assume that the breadth to be equivalent to [x] meters. Then its length will be [3x] meters.

Area of floor = {3x} x {x} = 3x² sq. m.​

The cost of carpeting the floor = Rs. 240 per sq. m.

For 1 sq. m., the cost is 240 sq. m.

For {3x² sq. m}, the cost will be -

C{f} = 240 x 3x² = 720x²

C{f} = 720x²

The total area of the 4 walls = 4 × (3x) × 4.6 = 55.2x sq. m.

The cost of carpeting the walls = Rs. 24 per sq. m.

For {55.2x sq. m}, the cost will be -

C{w} = 24 x 55.2x = 1324.8x

C{w} = 1324.8x

The total cost of painting and carpeting -

C = C{w} + C{f} = 720x² + 1324.8x

C = ₹(720x² + 1324.8x)

Therefore, the total cost of painting and carpeting the 4 walls and the floor is C = ₹(720x² + 1324.8x).

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The probability that the product of the two two-digit numbers is less than 200 is given as follows:

43/8010.

A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes.

There are 90 different two-digit numbers, hence the number of total outcomes for the product is of:

90 x 89 = 8010.

(the numbers have to be different)

The desired outcomes which result in a product of less than 200 are of given as follows:

Hence the number of desired outcomes is given as follows:

9 + 8 + 6 + 5 + 4 + 4 + 3 + 2 + 2 = 43.

Meaning that the probability is of:

43/8010.

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The answer of the limit is -3

Hi, To convert a temperature from degrees Fahrenheit to degrees Celsius, you can use the following formula:

C = (F - 32) / 1.8

Substituting the value of F and solving for C, we find that:

C = (284 - 32) / 1.8

= 252 / 1.8

= 140

Therefore, 284 °F is equivalent to 140 °C.

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The calculation of  el valor de "x, y, and z" is "2, 3, 1"

Equation [1] must be solved for the variable z.

[1] z = -x - y + 6

/ Replace this in equation [2]'s variable z.

[2] 2x - y + 3•(-x -y +6) = 3

[2] -x - 4y = -13

Add this to the equation [3]'s variable z.

[3] 4x + 5y - 10•(-x -y +6) = 13

[3] 13x + 14y = 72  Equation [2] must be solved for x.

[2] x = -4y + 13

/ Replace the value of x in equation [3] with this.

[3] 14•(-4y+14) + 15y = 73  [3] - 41y = -122

Equation [3] must be solved for the variable y.

[3] 41y = 122

[3] y = 3  We already know the following:

y = 3, z = -x-y+6, and x = -4y+14 To find x, use the value of y.

x = -4+3 = 1  To find z, use the x and y values.

z = -(2)-(3)+6 = 1

Answer: "x, y, and z" = "2, 3, 1"

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. To find the distance between two points, use the distance formula.

It will be the square root of (x2-x1)squared + (y2-y1)squared.

Use (3,-4) as x1, y1. Use (5,1) as x2, y2.

We get the square root of (5-3)squared + (1- -4)squared.

That gives us the square root of 2 squared + 5 squared.

Now we have the square root of 4 + 25, = the square root of 29.

That is the distance between the two points.

Answer:

1/2

Step-by-step explanation:

(5/3-7/4)+√1/16+√1/9

= {(5x4-7x3)/12} + 1/4 + 1/3

= -1/12 + (3+4)/12

= (-1+7)/12

= 6/12

= 1/2

The factor that produces the corresponding dimensions of cylinder B is: 3/2.

Similar solids have the same shape but different sizes, and which means the ratio of their corresponding linear measurements are the same.

To find the scale factor of similar solids, you can use the formula:

scale factor = (size of the similar solid) / (size of the original solid)

For example, if you have two similar solids, one with a volume of 64 cubic units and the other with a volume of 16 cubic units, the scale factor would be:

scale factor = (16 cubic units) / (64 cubic units) = 1/4

This means that the smaller solid is 1/4 the size of the larger solid.

Given the following:

Circumference of the base of cylinder A = 4π units [the radius = 2 units]

Area of the base of cylinder B = 9π units² [the radius = 3 units]

Scale factor = radius of the base of cylinder B / radius of the base of cylinder A

Scale factor = 3/2

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Complete Question:

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units. The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?

The best reason to prefer the least-squares regression line that uses to predict is the Standard Deviation of the residuals is smaller.

Least Squares Regression:

Least squares is a mathematical technique that allows analysts to determine the best way to fit a curve to a graph of data points. It is commonly used to make scatterplots easier to interpret and is associated with regression analysis. Least squares is now available as part of most statistical software programs.

There are two least-squares regression lines, one to predict log(y) using x and the other to use for prediction.

a. A small value of means that the variance is explained poorly compared to the model that predicts instead, and thus the model is a poorer model. Therefore, there is no compelling reason to choose a model that predicts logic in.

b. If the standard deviation of the residuals is not too high, there will be less variability between the actual and predicted values, and thus the model will be more accurate. Therefore, there are compelling reasons to favor a model that predicts.

C. The magnitude of the slope has no effect on whether a model is good or bad, so it's not the best reason to favor a model that expects log y and  x.

d. The presence of more random variation in the number of residuals does not necessarily indicate a superior model. The reason for this is that the variation between the expected and actual values ​​is large, which can lead to large variability. This means that there is no compelling reason to prefer a model that uses to predict log y. It is normal that the distribution of residuals of residuals does not affect model quality. As a result, this is not the best reason.

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The possible formula for P(x) is x⁵-x⁴-21x³+45x²

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). Based on the number of terms present in the expression, it is categorised as monomial, binomial, and trinomial.

P(x) has roots of multiplicity 2 at x=3 and x=0.

The equation stands, P(x) = x²(x-3)²

P(x) has a root of multiplicity 1 at x=-5

The equation stands, P(x) = x²(x-3)²(x+5)

Simplifying the equation,

P(x) = x²(x²+9-6x)(x+5)

⇒ P(x) = (x⁴+9x²-6x³)(x+5)

⇒ P(x) = x⁵+5x⁴-6x⁴-30x³+9x³+45x²

⇒ P(x) = x⁵-x⁴-21x³+45x²

The possible formula for P(x) is x⁵-x⁴-21x³+45x²

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C(n) = min(αn, βn) then gcd(0,b) = p(1)^(c1)∙p(2)^(c2)..................p(n)^(cn). So for all other a, b have gcd exist.

The integer a=0 and b=0 does not have any greatest common divisor.

Suppose n = gcd(0,r)

Then 12|0 and 12|0 also n is the greatest divides both (a=0), (b=0).

But n+1|0, n+1|0 as (n+1)*0 = 0 which is a contradiction to n = gcd(0, r).

Hence, gcd(0, r) does not exist.

But if a≠0 or b≠0.

It has a unique prime factorization that is;

a= p(1)^(α1)∙p(2)^(α2)∙p(3)^(α3)......................p(n)^(αn),

b= p(1)^(β1)∙p(2)^(β2)∙p(3)^(β3)......................p(n)^(βn).

Let C(n) = min(αn, βn) then gcd(0,b) = p(1)^(c1)∙p(2)^(c2)..................p(n)^(cn).

So for all other a, b have gcd exist.

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Slope-intercept form: [tex]y=mx+b[/tex]

Parallel lines always have the same slopes and different y-intercepts.

We're given:

Because parallel lines have the same slopes, this line therefore has a slope of -3.

[tex]y=-3x+b[/tex]

Now, plug in the given point to solve for b:

[tex]3=-3(-1)+b\\3=3+b\\b=0[/tex]

Therefore:

[tex]y=-3x[/tex]

[tex]y=-3x[/tex]

Answer:

100

Step-by-step explanation:

0 20 40 60 100

5. l

10. l

15. l

20. l

Answer: y=2(x+1)^2 +7

Step-by-step explanation:

The equation for a parabola is y=a(x-h)^2+k

(h,k) would be the vertex but when writing the equation, the sign in front of the h has to be the opposite of the x-value in the vertex (note: the minus sign in front of the h just means opposite of, not always negative) So in this situation since the 1 is negative, it would be positive in the equation

The a represents the distance from the vertex to the focus.

In order to solve this problem you just sub in the opposite of h and the normal value of k and then the a would be two since that is the distance between the focus and the vertex.

This would make your answer 2(x+1)^2 +7

The value of y is 16.

When one quantity's value increases compared to another's decrease or vice versa, it is said that the two are inversely proportionate.

It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between time and speed is inverse.

Inverse proportionality will be represented by the symbol '∝'. When two values x and y are Inverse proportional to each other then

             x ∝ 1/y

Here we have

y varies inversely with the square root of x

=>  [tex]y\propto\frac{1}{\sqrt{x} }[/tex]

=>  [tex]y\ = \frac{k}{\sqrt{x} }[/tex]  

=> [tex]\sqrt{x} y = k[/tex] ----- (1)

At x = 64, and y = 12  

=> √64 × 12 = k

=> k = (8) × 12

=> k = 96  

Thus the proportionality constant k = 96

Now Take x = 36 and k = 96 in equation (1)

=> √36 × y = 96

=>  6 × y = 96

=>  y = 16

Therefore,

The value of y is 16.

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Answer:

Step-by-step explanation:

c

The square root representing in the statement is 25.

In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4²= 16.

A square root of a number is a value that, when multiplied by itself, gives the number or a factor of a number that, when multiplied by itself, gives the original number.

Given that, if I have 5 fishes and 25 fishermen what would be the square root

We need to identify the squared number in the statement, in between 5 and 25 we know 25 = 5²

Which means, 25 is the square of 5

Or, 5x5 = 25

Hence, the answer square root number is 25

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Answer:

Step-by-step explanation:

because there is no change in slope. The graph will always be strait in this

A constant term in mathematics is a term in an algebraic equation whose meaning is constant or cannot change because it has no modifiable variables. For example, in the quadratic polynomial x² + 2x + 3 = 0, the term 3 is a constant.

The critical values for the function are t = 6 , -5.667 where t = 6 makes sense . At t = 6 , y is increasing

According to the question,

After t hours of production, a plant produces an average of y units per hour, according to analysis of its daily output is

y = 102t + 0.5t² - t³ , 0 ≤ t ≤ 10

(a) To calculate critical values for the given function

We have to differentiate it w.r.t time and then have to put y'=0

=> y = 102t + 0.5t² - t³

Derivating w.r.t time

=> y' = 102 + t - 3t²

Equating to zero,

=>  102 + t - 3t² = 0

Solving quadratic equation,

=> t = 6 , -5.667 are critical values

(b) t = 6 makes sense in particular problem because time cannot be negative.

(c) To check increasing value

Derivate y' w.r.t time again

=> y" = 1 - 6t

Putting critical value,

At t = 6

y" < 0 , Therefore at t = 6 function is increasing

Hence , For t = 6 y is increasing

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