which of these steps will eliminate a variable in this system 6x - 3y = 8
23 + 6y = 16

Answer:

0.9475

Hope this Helps!

Answer: 191.3

Step-by-step explanation:

In 2005: x=2005-1998=7

y=123.1(1.065)^7

= 191.3

The area of the entire floor is: C. 140 square feet.

The entire floor of the building given is composed of a trapezoid, rectangle, and a triangle.

Therefore, the area of the entire floor = area of the trapezoid + area of the rectangle + area of the triangle.

The formula are:

Area of entire floor = 1/2(a + b)h + (l × w) + 1/2(b)(h)

The variables are:

Base (a) = 4 ft

Base (b) = 8 ft

Height of trapezoid (h) = 6 ft

Length of rectangle (l) = 10 ft

Width of rectangle (w) = 8 ft

Base of triangle = 6 ft

Height of triangle (h) = 8 ft

Area of entire floor = 1/2(4 + 8)6 + (10 × 8) + 1/2(6)(8)

Area of entire floor = 36 + 80 + 24 = 140 square feet.

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1.35 as a fraction in simplest form is written as 27/20.

A fraction, which is expressed in the form p/q, where p and q are both integers, denotes a portion of a whole.

To convert 1.35 to a fraction, do the following:

Write the decimal number split by 1 first as follows:

1.35/1

Since the numerator has two digits after the decimal point, we must multiply the numerator and denominator by 102 to get 100, removing the decimal point.

1.35 × 100/ 1 × 100 = 135/100

Because 135 and 100 have 5 in common, we may simplify the fraction to show the same amount: 135 5/100 5 = 27/20.

We can also phrase 1.35 as an improper fraction since the numerator exceeds the denominator.

Therefore, 1.35 as a fraction in simplest form is written as 27/20.

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The distance of the ball away from Amaya at Maximum height is; 18 feet

Given the projectile equation as;

y = -0.02(x - 18)² + 12 to model the horizontal distance of a ball from Amaya's position.

We want to find out how far away is the ball from Amaya when it is at its maximum​ height.

The model takes the form of a parabolic equation and as such, the maximum height is obtained at the Vertex :

The general vertex form of the equation of a parabola is;

y = a(x - h)² + k

With maximum height obtained at the Vertex (h, k)

From the model given, we can say that;

Coordinate at the Vertex : (h, k) = (18, 12)

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Complete question is;

Amaya is standing 30 ft from a volleyball net. The net is 8 ft high. Amaya serves the ball. The path of the ball is modeled by the equation y = -0.02(x - 18)² + 12​, where x is the​ ball's horizontal distance in feet from​ Amaya's position and y is the distance in feet from the ground to the ball. a. How far away is the ball from Amaya when it is at its maximum​ height?

using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.

The standard normal distribution table is used to calculate the critical value for this problem.

The critical value at 99% confidence level is 2.576.

The formula for the one-sided confidence interval is given by:

Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n))Therefore, the one-sided 99% Confidence Interval for mu when n = 86, and X_Bar =71 is:

Upper Bound = 71 + (2.576 * 2/sqrt(86))

Upper Bound = 71 + (1.41)

Upper Bound = 72.41

The one-sided 99% Confidence Interval for mu when n = 86 and X_Bar =71 is calculated by using the standard normal distribution table to find the critical value of 2.576, and then using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.

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The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

Given that,

Finding the expression that can be utilised to find

20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98.

From the Latin word "per centum," which means "by the hundred," the word "percentage" was borrowed. The denominator of percents is 100, making them fractions. In other words, it is the relationship between a part and a whole in which the value of the whole is consistently set to 100.

Take

20% of 92

Multiply 20%×92

=18.4

45% of 76

Multiply 45% ×76

=34.2

50% of 62

Multiply 50%×62

=31

60% of 92

Multiply 60%×92

=55.2

12% of 98

Multiply 12%×98

=11.76

Therefore,

The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

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Answer:

it is a 10% increase.

Step-by-step explanation:

3,036 - 2,760 = 276

276/2,760 · 100 = 10%

The Ratio of Julia’s frogs to Rimma’s frogs will be 9:5

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

For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

Ratio = [tex]\frac{1^{st} element}{2^{nd} d element}[/tex]

Let Rimma’s frog = x

So, Julia's frog =  [tex]\frac{2x}{5}[/tex]

Rimma gives  [tex]\frac{1}{2}[/tex] of her frog to Julia

Therefore, rimma left with  [tex]\frac{x}{2}[/tex]

Ratio = [tex]\frac{Julia's frog}{Rimma's frog}[/tex]

[tex]=\frac{\frac{2x}{5} +\frac{x}{2} }{\frac{x}{2} } \\=\frac{\frac{9x}{10} }{\frac{x}{2} }\\=\frac{9}{5}[/tex]

Therefore, ratio will be 9:5

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The example of the commutative property of addition is option (D) 4 + 3 = 3 + 4

The commutative property of the addition states that changing the order of the numbers or the variable does not affect the result of sum

The commutative property of addition is

A + B = B + A

Here the position of the variable A and B are changed but still the result is same

From the given option

The example that shows the commutative property of  addition is

4 + 3 = 3 + 4

Here the position of the 3 and 4 changed, but the result will be

7 = 7

Therefore, the correct example is option D) 4 + 3 = 3 + 4

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The angle with a positive sine and negative cosine among the options is [tex]\frac{3\pi }{4}[/tex]

What is an obtuse angle?

Obtuse angle is any angle greater than 90°: Straight angle is an angle measured equal to 180°: Zero angle is an angle measured equal to 0°: Complementary angles are angles whose measures have a sum equal to 90°:

All obtuse angles usually have positive sine and negative cosine.

Amongst all the options  [tex]\frac{3\pi }{4}[/tex] is the only obtuse angle . which if you convert to degrees

using π rad = 180 degrees, 3/4 x 180  you get  135°

In conclusion  [tex]\frac{3\pi }{4}[/tex] is the angle with a positive sine and negative cosine.

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The integer in the solution set that will make the equation true is (c) 3

From the question, we have the following parameters that can be used in our computation:

3p + 13 = 22

Subtract 13 from both sides of the expression

So, we have the following representation

3p = 9

Divide both sides of the equation by 3

p = 3

Hence, the solution is p = 3

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a) The line belongs to the plane.

b) The line does not belong to the plane.

The equation of a line has the format given as follows:

[tex]\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}[/tex]

The equation of a plane has the format given as follows:

Ax + By + Cz + D = 0.

The line will belong to the plane if these two conditions are satisfied:

In standard format, the line for item a is given as follows:

[tex]\frac{x - 1}{4} = \frac{y + 2}{9.5} = \frac{z - 3}{1}[/tex]

Then the conditions are tested as follows:

The two conditions are satisfied, hence the line belongs to the plane.

For item b, we have that:

(-2)(-6) + 1(8) - 5(-3) + 1 = 36.

First condition already not satisfied, hence the second does not need to be tested, meaning that the line does not belong to the plane.

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Answer:

25

Step-by-step explanation:

[tex]5^{2}[/tex] = 5x5 = 25

The ways the assignments can be assigned to the students with the condition is 66 ways

From the question, we have the following parameters that can be used in our computation:

Total number of questions, n = 12

Total numbers of students, r = 2

The number of ways the assignments can be assigned to the students is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 12 and r = 2

Substitute the known values in the above equation

Total = ¹²C₂

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 12!/10! * 2!

Evaluate

Total = 66

Hence, the number of ways is 66

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Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.

"Information available from the question",

In the question:

In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars.

Five of the points are labeled A, B, C, D, and E, respectively.

E $6,500+ А $6,000 B $5,500+ $5,000+ $4,500+ Value $4,000 + + 50 60 70 80 90 100 Miles Driven

To find the which point is the most influential with respect to a regression of trade-in value versus miles driven?

Now, According to the question:

According to the points of labeled:

The correct answer is :

To see the figure.

Hence, Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.

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if a decimal number is divisible by 3 if and only if the sum of its digits is divisible by three is evident and proved below.

Let n be a decimal number.

Assume n is divisible by 3.

lets consider n in terms of its digits as

n = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0

where m is the number of digits in n and d_1, d_2, ..., d_m are its digits.

Substituting n = 3k into the above equation, we get

3k = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0

Subtracting 3k from both sides of the equation, we get

0 = d_1 * 10^(m-1) + d_2 * 10^(m-2) + ... + d_m * 10^0 - 3k

Adding 3k to both sides of the equation, we get

3k = d_1 * 10^(m-1) + d

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A function is a rule that for each input has at most one output.

Describe a function. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (the domain) and their outputs (the codomain), where each input has exactly one output and the output can be traced back to the original input.

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The probability density function will be expressed as f_M(x) = n * x^(n-1) and cumulative density function is f_Z(z) = n * (1-z)^(n-1).

To find the probability density function of M, we need to find the probability that M takes on a particular value x, which is equal to the probability that all of the random variables U1, ..., Un are less than or equal to x. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is less than or equal to x. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is less than or equal to x is simply x. Therefore, the probability that M takes on a particular value x is equal to x^n.

This means that the probability density function of M is given by:

f_M(x) = n * x^(n-1)

for x in the range [0, 1].

For the second part of the question, we want to find the cumulative distribution function (c.d.f.) and probability density function (p.d.f.) of Z = min(U1, ..., Un). We can find the c.d.f. of Z by finding the probability that Z is less than or equal to a particular value z. This is equal to the probability that all of the random variables U1, ..., Un are greater than or equal to z. Since the Ui are independent, this probability is equal to the product of the individual probabilities that each Ui is greater than or equal to z. Since each Ui has a uniform distribution over [0, 1], the probability that Ui is greater than or equal to z is simply 1-z. Therefore, the probability that Z is less than or equal to z is equal to (1-z)^n.

This means that the cumulative distribution function of Z is given by:

F_Z(z) = (1-z)^n

for z in the range [0, 1].

To find the probability density function of Z, we can differentiate the cumulative distribution function with respect to z. This gives us:

f_Z(z) = n * (1-z)^(n-1)

for z in the range [0, 1].

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Answer:

Side h and side

The volume of cylinder is 84.82 cubic feet

In this question, we have been given for a cylinder the diameter equals 3 feet and the length equals 12 feet.

We need to find  the volume of a cylinder.

From given data,

diameter d = 3 feet

So, radius r = d/2

                r = 1.5 ft

length of cylinder (h) = 12 ft

The formula for the  volume of a cylinder is,

V = π * r² * h

V = π * 1.5² * 12

V = π * 2.25 * 12

V = 84.82 cubic feet

Therefore, the volume of cylinder with the diameter equals 3 feet and the length equals 12 feet is 84.82 cubic feet

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Answer: D.) None of these

Step-by-step explanation: A polygon is regular when all angles are equal and all sides are equal (otherwise it is "irregular").

The best estimate for the marginal cost in dollars, to produce the 57th unit of the product is C'(57) - C'(56). This is also known as the difference in cost between producing the 57th unit and the 56th unit, and is represented by the expression C'(57) - C'(56).

The marginal cost of producing a particular unit of a product is the cost of producing that unit minus the cost of producing the previous unit. So to find the marginal cost of producing the 57th unit of the product, you can subtract the cost of producing the 56th unit from the cost of producing the 57th unit.

This means that the best estimate for the marginal cost of producing the 57th unit of the product is given by:

M(57) = C(57) - C(56)

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Answer:

[tex]\begin{aligned}\textsf{1.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{2.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{3.} \quad \textsf{As}\;\; &x \rightarrow - \infty,\;\;f(x) \rightarrow - \infty\\ \textsf{As}\;\; &x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty \end{aligned}[/tex]

Step-by-step explanation:

Root Multiplicity

Odd multiplicity → the graph will cross the x-axis at the root.

Even multiplicity → the graph will touch the x-axis at the root (but will not cross the x-axis).

Given function:

[tex]p(x)= \dfrac{2}{3}(3x - 6)(x + 2)(x - 3)^2[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow + \infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The x-intercepts of a function are when f(x)=0.  

Therefore, the x-intercepts are:

Therefore, the graph of the given function has 3 turning points.

Given function:

[tex]p(x)=(x - 3)^2 (x + 2) (2x + 7)^2[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The x-intercepts of a function are when f(x)=0.  Therefore, the x-intercepts are:

Therefore, the graph of the given function has 4 turning points.

Given function:

[tex]p(x)=(x - 5)(x + 2)(x - 1)-30[/tex]

Therefore:

End behaviors:

[tex]\textsf{As}\;\; x \rightarrow - \infty,\;\;f(x) \rightarrow -\infty[/tex]

[tex]\textsf{As}\;\; x \rightarrow +\infty,\;\;f(x) \rightarrow + \infty[/tex]

The graph has 2 turning points.

Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

The correct option is (B).

Now, According to the question:

Stratified sampling design divides the given population into small sub-groups called strata. The members of each strata share some common features and at any particular time, a sample is randomly selected from each stratum which is then compared to the entire population. During random sampling, a number proportional to the stratum size is selected from all strata. The randomly selected samples from each strata are then combined to form a common random sample.

Considering that the editor wants to adopt stratified sampling, option B fits (Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.)

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The complete question is this:

A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design?

(A) Send a survey to all city residents and use the first 500 returned surveys for the sample.

(B) Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

(C) Select one voting district at random, and then select a random sample of 500 from the selected voting district.

(D) Alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district.

(E) Select the first 500 city residents who attend the next high school football game.

The value of x for the given trigonometric function is (15/18)π.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right angle.

As per the given,

secx = (-2√3)/3

1/cosx = -2/√3

cosx = -√3/2

x  = 150° = (15/18)π

Thus, x goes into the second quadrant as shown below.

Hence"The value of x for the given trigonometric function is (15/18)π".

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The equation to solve the width of rectangle created by John from 48 square centimetre tiles is w(w+2) = 48

and the greatest width in centimetres use for mosaic is 6 cm.

We have given that

John wants to create a mosaic of rectangular shape.

total area of tile(A) = 48 square centimetre

let l and w be length and width of rectangle

length of rectangle is 2 cm longer than width then length of rectangle (l) =( w+2) cm

Area oa rectangle (A) = l × w

=> (w+2) × w = 48

=> w²+ 2w = 48

which is quadratic equation , solve it

w² + 2w - 48 = 0

=> w² - 6w + 8w - 48 = 0

=> (w-6) (w+8) = 0

=> w = 6, -8

Hence, the required equation is w(w+2) = 48 and width of rectangle is 6cm.

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If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

Given that,

The combined length and girth of a priority mail package cannot exceed 171 inches, according to postal standards.

We have to find calculate the size of the largest volume, cylindrical container that can be sent via priority mail.

We know that,

Let

Length= Breadth =x

Height=y

Volume can be written as

V=x²y

Now,

Combined length and girth is

7x+y=171

y=171-7x

V(x)=x²(171-7x)

V(x)=171x²-7x³

Differentiating with respect to x.

V'(x)=343x-21x²

The maximum value

V'(x)=0

343x-21x²=0

7x(49-3x)=0

x=0

and

49-3x=0

3x=49

x=49/3

Once again differentiating with respect to x.

V''(x)=343-42x

V''(x)=343-42(0)=343>0(min)

V''(x)=343-42(49/3)=-343<0(max)

The maximum volume is

Vmax=V(49/3)=(49/3)(171-7(49/3))

Vmax=925

Therefore, If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

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