Consider the system of equations.

x − 4y = 11,

3x + 5y = −1

Which number should you multiply the first equation by to eliminate the x-variable term?
1
–1
3
–3

If the statements offered as premises are true, and the conclusion follows naturally from those premises, then a deductive argument is considered to be valid

What is Function?

A function is a relationship between a number of inputs and outputs. A function is, to put it simply, an association between inputs where each input is linked to exactly one output. For each function, a domain, codomain, or range exists.

The values that are specified inside a function when the function is called are referred to as a "argument." However, the parameters are the variables that are defined when the function is declared.

true statement : all dogs have hair

true statement : clifford is a dog.

true statement : clifford has hair

Conclusion is true

If the statements offered as premises are true, and the conclusion follows naturally from those premises, then a deductive argument is considered to be valid. Deductive Argument based on logic ie reasoning out to get a valid inference.

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The volume of the solid generated by rotating ΔABC around AB is approximately 23.39 cubic units.

To find the volume of the solid generated by rotating ΔABC around AB, we can use the method of cylindrical shells.

First, we need to find the height of the cylinder that will be generated by the rotation. This height is simply the length of AB, which is 2.

Next, we need to find the circumference of the cylinder at any point along its height. To do this, we can use the fact that the circumference of a circle is given by 2πr, where r is the radius of the circle. In this case, the radius of the circle will be the distance from the axis of rotation (AB) to the edge of the triangle at that height.

Let x be the distance from vertex A to the point on AB directly below it. Then, at any height h, the radius of the circle will be given by:

r = BC - x

To find x, we can use the Pythagorean theorem. Let h be the height above vertex A, so that the distance from A to the base of the triangle is h/2. Then, the distance from vertex A to the point on AB directly below it is:

\(x = \sqrt{AB^2 - \left(\frac{h}{2}\right)^2} = \sqrt{2^2 - \left(\frac{h}{2}\right)^2}\)

Now, we can find the volume of the solid generated by integrating the circumference of the cylinder at each height, multiplied by the height of the cylinder:

\(V = \int_0^2 2\pi\left(BC - \sqrt{2^2 - \left(\frac{h}{2}\right)^2}\right)dh\)

We can simplify this integral using the substitution u = h/2, which gives:

\(V = 4\pi\int_0^1\left(BC - \sqrt{4 - u^2}\right)du\)

Now, we need to plug in the values of BC and evaluate the integral:

\(V = 4\pi\int_0^1\left(5 - \sqrt{4 - u^2}\right)du\)

= \(4\pi\left[\left(5u - \frac{u}{2}\sqrt{4 - u^2} - 2\arcsin\left(\frac{u}{2}\right)\right)\Bigg|_0^1\right]\)

≈ 23.39

Therefore, the volume of the solid generated by rotating ΔABC around AB is approximately 23.39 cubic units.

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If the temperature decreased by 15°F, Pilar would expect to sell 15 fewer cups of hot chocolate.

What is an equation?

An equation is a statement that shows the equality of two expressions by using an equal sign (=). It expresses a mathematical relationship between two or more variables or quantities.

Regarding the second question, to find out how many more cups of hot chocolate Pilar would expect to sell if the temperature decreased by 15°F, we can plug in t = 15 into the equation c = -t + 120 and calculate the difference between the original value of c and the new value.

c(Original) = -15 + 120 = 105

c(New) = -(15+15) + 120 = 90

The difference is:

c(New) - c(Original) = 90 - 105 = -15

Therefore, if the temperature decreased by 15°F, Pilar would expect to sell 15 fewer cups of hot chocolate.

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Answer:

1/12 i hope this is correct i think so i did it in my calculator so i hope it helps

Step-by-step explanation:

Answer:

\(x > 42\)

Step-by-step explanation:

\(\frac{x}{6} > 7\)

Multiply 6 on both sides. \(6(\frac{x}{6}) > 6(7)\).

Simplify it. \(x > 42\)

Therefore, the answer is \(x > 42\).

Hope this helped! If not, please let me know! <3

Answer:

2x + 2.9 = 30.6

Step-by-step explanation:

We are to represent the unknown number that Mark thinks of with x

If Mark doubles this unknown number, he multiplies it by 2 and the unknown number becomes - 2x

He then adds 2.9

The equation becomes 2x + 2.9

The answer of the above equation is 30.6

This gives : 2x + 2.9 = 30.6

Answer:

32-8x=y^2 or x=4-y^2/8

Step-by-step explanation:

Refer to the attachment for figure:

The height of the rectangle = 11 inches

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x= height

Width becomes x+49

Diagonal BD=61 inches

By pythagoras theorem,

BD²=BC²+CD²

61²= (x+49)²+x²

3721=x²+98x+2401+x²

On simplification,

x²+49x-660=0

Find the factors

(x+60)(x-11)=0

x=-60, x=11

Consider positive value for height

height = 11 inches

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Answer:

1. 3.

Step-by-step explanation:

The answer to tx2x365 is 730t so when you solve the others you also get 730t

Answer:

y=3x-7

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept

y=3x-7

The new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4),  (-5, 3).

A function, f, that maps to itself are known as a transformation, or f: X → X. The transformation results in the pre-image X becoming the picture X. This transformation can utilize any operation, or a combination of operations, including translation, rotation, reflection, and dilation.

Given, the triangle vertices (-3, 1) (2, 4), and (5, -3).

When the triangle turned 180 degrees counterclockwise, we must determine the new coordinates;

When we rotate 180 degree counterclockwise, the plane changes not the point.

That is,

(-3, 1) becomes (3, -1)

(2, 4) becomes (-2, -4)

(5, -3) becomes (-5, 3)

Therefore, the new coordinates when we rotate the triangle counterclockwise are (3, -1), (-2, -4),  (-5, 3).

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Answer:

C

Step-by-step explanation:

ΔXYZ will also be an equilateral triangle.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean space, an equilateral triangle also is equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It's also referred to it as a regular triangle because it is a regular polygon.

As X,Y,Z are the midpoints of sides of equilateral triangle so when we will join the X,Y,Z we will find that distances XY=YZ=XZ are three are equal because this is proved by similarity of triangles which in itself is a detailed and vast topic

Hence XYZ will also be an equilateral triangle

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Answer: B) -11

Step-by-step explanation:

2 (x+22) + 5 = 27

              -5     -5

2x+44 = 22

   - 44   -44

2x = -22

/2      /2

x = -11

Solution:

To classify the system of equations as no solutions, the lines must be parallel (Not intersect).

First, let's identify the equation forming the line.

We also know that the slope of the equation must be -1.5.

A) 2x + 3y = 0

B) 2x + 3y = 6

C) 2x - 3y = 9

D) y = 3x + 2

Option B is correct.

Answer:

awser 3

Step-by-step explanation:

all the numbers on the x-axis

all the numbers on the y-axis

Answer:

12w + 8d = 100

Step-by-step explanation:

Given:

Price of wall calendars = $12

Price of desk calendars = $8

Total amount pay = $100

Computation:

w = wall calendars

d = desk calendars

So,

Price of wall calendars(w) + Price of desk calendars(d) = Total amount

12w + 8d = 100

Answer:

this can be the answer

because in given question there is no relation between equations

The required annual income is 102,195.6.

a) For a normal distribution, we can compute probabilities using the standard normal distribution, z-score.

For calculating the probability that a household in Maryland has an annual income of 110,000 or more, we can use the standard normal distribution.  We can compute the Z-value using the formula;

Z = (x - μ) / σWhere,x = 110,000,μ = 75,847, andσ = 33,800

Substituting the values, we get;

Z = (110,000 - 75,847) / 33,800Z = 1.019

Probability of Z being greater than 1.019 is P(Z > 1.019). The probability is 0.1525.

Hence, the probability that a household in Maryland has an annual income of 110,000 or more is 0.1525.  (rounded to four decimal places)

Therefore, the probability is 0.1525.

b)  To compute the probability that a household in Maryland has an annual income of 30,000 or less, we can use the standard normal distribution and Z value formula.

Z = (x - μ) / σ

Where,x = 30,000,μ = 75,847, andσ = 33,800

Substituting the values, we get;

Z = (30,000 - 75,847) / 33,800Z = -1.348

Probability of Z being less than -1.348 is P(Z < -1.348).

The probability is 0.0885.

Hence, the probability that a household in Maryland has an annual income of 30,000 or less is 0.0885.  (rounded to four decimal places)

Therefore, the probability is 0.0885.

c) To compute the probability that a household in Maryland has an annual income between 60,000 and 70,000.

We will have to convert both the values of income to their respective Z values.Z1 = (60,000 - 75,847) / 33,800Z1 = -0.467Z2 = (70,000 - 75,847) / 33,800Z2 = -0.172

The required probability is the difference between the probability of two Z values;

P(Z1 < Z < Z2) = P(Z < Z2) - P(Z < Z1) = 0.5675 - 0.3226 = 0.2449

Hence, the probability that a household in Maryland has an annual income between 60,000 and 70,000 is 0.2449. (rounded to four decimal places)

Therefore, the probability is 0.2449.

d) We can find the annual income of a household in the 80th percentile of annual household income in Maryland using the standard normal distribution.

Z80 = invNorm(0.80) = 0.84The Z value for the 80th percentile is 0.84.

Now, we can use the Z-score formula to calculate the annual household income.x = Zσ + μ

Substituting the values, we get;

x = 0.84 × 33,800 + 75,847x = 102,195.6

Hence, the annual income of a household in the eighty-fifth percentile of annual household income in Maryland is 102,195.6. (rounded to the nearest cent)Therefore, the required annual income is 102,195.6.

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The exchange rate in 2010 should be $0.66/riyal. To determine the adjusted exchange rate in 2010 based on purchasing power parity, we need to calculate the relative rate of inflation between the United States and Saudi Arabia and multiply it by the 1981$/riyal exchange rate of $0.42.

The formula for calculating the relative rate of inflation is:

Relative Rate of Inflation = (Saudi Arabian Price Level / U.S. Price Level) - 1

Given that the Saudi Arabian price level in 2010 is 240 and the U.S. price level in 2010 is 100, we can calculate the relative rate of inflation as follows:

Relative Rate of Inflation = (240 / 100) - 1 = 1.4 - 1 = 0.4

Next, we multiply the relative rate of inflation by the 1981$/riyal exchange rate:

Adjusted Exchange Rate = 0.4 * $0.42 = $0.168

Finally, we add the adjusted exchange rate to the original exchange rate to obtain the exchange rate in 2010:

Exchange Rate in 2010 = $0.42 + $0.168 = $0.588

Rounding the exchange rate to 2 decimal places, we get $0.59/riyal.

Based on purchasing power parity and considering the relative rate of inflation between the United States and Saudi Arabia, the exchange rate in 2010 should be $0.66/riyal. This adjusted exchange rate accounts for the changes in price levels between the two countries over the period.

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A fraction is a way to describe a part of a whole. The total number of hours for which the team practiced this week is 6 2/3 hours.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

A mixed fraction is a fraction that contains a whole number and a fraction whose denominator is greater than the numerator. A mixed fraction can be converted as,

2 1/2

= (2×2 + 1)/2

= 5/2

= 2.5

To calculate the number of hours for which the team practiced, we need to convert the mixed fraction to fractions. Therefore, the fraction can be converted as,

Practice hours on Wednesday = 2 1/6 = (6×2 + 1)/6 = 13/6

Practice hours on Saturday = 4 1/2 = (4×2 + 1)/6 = 9/2

Now, the total hours of practice is,

Total hours of practice = 13/6 + 9/2

                                      = 13/6 + 27/6

                                      = 40/6

                                      = 20/3

                                      = 6 2/3

Hence, the total number of hours for which the team practiced this week is 6 2/3 hours.

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Answer:

The correct options are;

A. Construct a perpendicular bisector of the diameter AB

D. Use the compass to draw a circle centered at point C

E. Use the compass to draw two arcs of the same radius centered at point C

F. Use the straightedge to draw diameter AB of the circle

G. Use the straightedge to draw lines connecting the endpoints of the two diameters

Step-by-step explanation:

To draw an inscribed square of a circle, the circle is first constructed. The diameter of the circle is drawn with a straight edge to find the first two vertices of the intended inscribed square. The perpendicular bisector of the diameter is then drawn intersecting the circumference to provide the other two vertices of the square.

The straightedge is then used to draw lines that connect the endpoints of the two diameters to form the inscribed square of the circle.

If g ◦ f = IX and f ◦ g = IY, then f and g are both one-to-one and onto, and g = f⁻¹.

A function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

The statement is true. Let's prove it.

To prove that f is one-to-one, suppose we have two elements a, b ∈ X such that f(a) = f(b). We need to show that a = b.

Using the composition property, we have (g ◦ f)(a) = (g ◦ f)(b). Since g ◦ f = IX, we can simplify this to IX(a) = IX(b), which gives g(f(a)) = g(f(b)).

Since g ◦ f = IX, we can apply the property of the identity function to get f(a) = f(b). Since f is one-to-one, this implies that a = b. Therefore, f is one-to-one.

To prove that f is onto, let y be an arbitrary element in Y. We need to show that there exists an element x in X such that f(x) = y.

Since g ◦ f = IX, for any y ∈ Y, we have (g ◦ f)(y) = IX(y). Simplifying, we get g(f(y)) = y.

This shows that for any y ∈ Y, there exists an x = f(y) in X such that f(x) = y. Therefore, f is onto.

Now, to prove that g = f⁻¹, we need to show that for every x ∈ X, g(x) = f⁻¹(x).

Using the composition property, we have (f ◦ g)(x) = (f ◦ g)(x) = IY(x) = x.

Since f ◦ g = IY, this implies that f(g(x)) = x.

Therefore, for every x ∈ X, we have f(g(x)) = x, which means that g(x) = f⁻¹(x). Hence, g = f⁻¹.

In conclusion, if g ◦ f = IX and f ◦ g = IY, then f and g are both one-to-one and onto, and g = f⁻¹.

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Answer:

yes

Step-by-step explanation:

Answer:

a) 8 apples

b) 5 oranges

c) 2 oranges and 6 apples

Step-by-step explanation:

a) 8 apples × 1$ = 8$ < 10$

b) 5 oranges × 2$ = 10$

c) 2 oranges × 2$ = 4$

6 apples × 1$ = 6$ (4+6=10)

Answer:

Step-by-step explanation:

The problem scenario gives rise to two equations. One describes the total number of fruit. It is plotted in blue. The other describes the total cost. It is plotted in red.

The total number of fruit will be 8 at any blue dot. (It will not cost $10 if that dot is not also red.) One such total is (4 apples, 4 oranges)

__

The total cost will be $10 at any red dot. (The fruit count will not be 8 if that dot is not also blue.) One such cost is (4 apples, 3 oranges)

__

The cost for 8 pieces of fruit will be $10 where the blue and red dots are plotted at the same point: (6 apples, 2 oranges)

Answer: its number two

Answer:

The answer is -285

Step-by-step explanation:

Step-by-step explanation:

In this problem, it is given that, the number shown by the calculator is 0.6222....

(a) We need to find the number as a fraction

Let x = 0.6222....  ...(1)(it is a recurring decimal at the digit '2')

Muliply both sides of equation (1) by 10.

10x=0.6222.. × 10

10x = 6.222..

Multiply both sides of equation (1) by 100.

100x = 0.6222.. × 100

100x = 62.222.. ...(2)

Subtract equation (2) by (1).

100x-10x = 62.2222... - 6.2222...

90x=56

x=(56/90)

⇒\(x=\dfrac{28}{45}\)

This is the required fractional form of the given no i.e. "28/45"

(b) The fraction has 28 at numerator and 45 at denominator. Numerator shows the part of a denominator.

It would mean that 28 students vote for Brianna.