6. The third row of a stem-and-leaf chart appears as follows: 21 | 0 1 3 5 7 9. Assume whole
number values.
a. What is the "possible range" of the values in this row?
b. How many data values are in this row?
c. List the actual values in this row of data.

The product of a non-zero rational and an irrational number is always irrational number.

To prove this statement:

Let x be a rational number and y be an irrational number.

Let xy=a.

Let us assume that a is rational.

Since, a is rational it can be expressed as  p/q , where p and q are integers.

Let x= m/n , where m and n are integers.

Now, xy=a

[tex]\frac{my}{n} = \frac{p}{q}[/tex]

On cross multiplying we get,

y = pn/qm​

Now, pn and qm are integers.

Hence, pn/qm is a rational number.

However, y is irrational.

Hence, our assumption is incorrect.

Hence, the product of a non-zero rational and an irrational number is always an Irrational number.

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Using Venn diagram, 49 students participated in only music, 29 students participated in only sports, and 156 students were involved in either music or sports.

Let's use a Venn diagram to represent the information given:

We know that there are 200 students in total, and we can use the information given to fill in the numbers in the Venn diagram.

a.

127 students were involved in music, including 78 who were also involved in sports, so 127 - 78 = 49 students participated in only music.

b.

78 students participated in both music and sports, so 78 - 49 = 29 students participated in only sports.

20 students did not participate in either activity.

c.

The total number of students involved in music or sports is the sum of the number of students in each circle: 49 + 29 + 78 = 156.

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The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3

a. log(2^100) = 100 log(2) ≈ 30.103

b. log(100^2) = 2 log(100) = 2 log(10^2) = 2 × 2 = 4

c. log(3.0862.062) = log(3.086) + log(2.062) ≈ 0.488 + 0.316 = 0.804

(Note: The multiplication of 3.086 and 2.062 can be done using a calculator.)

d. log(55^(-3.1)) = -3.1 log(55) ≈ -3.1 × 1.740 = -5.394

e. log(5/1) = log(5) - log(1) ≈ 0.699 - 0 = 0.699

f. log(1/5) = log(1) - log(5) ≈ 0 - 0.699 = -0.699

g. log(1/81^2) = log(1) - 2 log(81) = -2 log(9^2) = -2 × 2 log(9) ≈ -2 × 0.954 = -1.908

(Note: We can use the property that log(a^b) = b log(a) to simplify the expression.)

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7x² + 48xy - 7y² is the simplified expression

Polynomial is an equation described as the sum of terms in the form of

k[tex]x^n[/tex].

where,

k and n =  positive integers.

Example:

2x³ + 4x² + 3x + 5 is a polynomial.

We have,

(x + 7y) (7x − y)

Distribute the addition over subtraction.

x (7x - y) + 7y (7x - y)

7x² - xy + 49xy - 7y²

Add like terms.

7x² + 48xy - 7y²

We can not further simplify.

So,

7x² + 48xy - 7y² is the final expression.

Thus,

7x² + 48xy - 7y² is the simplified expression

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The complete question.

Find the product (x+7y) (7x−y)

Answer:

(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.

(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.

Answer:

(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.

(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.

The scale factor of dilation is 4/9

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

The triangles

Given that the right is the scaled copy of the left

We have the following representation

Scaled factor = Right/Left

Substitute the known values in the above equation, so, we have the following representation

Scaled factor = 4/9

Hence, the scale factor is 4/9

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The PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths, without having any tickets left over.

We need to find a number that is divisible by at least 3, but less than 10.

We can start by listing out the multiples of 3 and see which one is closest to 1,932:

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

3 × 5 = 15

3 × 6 = 18

3 × 7 = 21

3 × 8 = 24

3 × 9 = 27

We can see that the closest multiple of 3 to 1,932 is 1,932 ÷ 3 = 644. This means that if the PTO split the tickets into 644-ticket batches, they would have 3 equal booths of 644 tickets each.

We can check whether 644 is also divisible by 4, 5, 6, 7, 8, or 9, as those numbers are less than 10. We can see that 644 is not divisible by 4 or 5, but it is divisible by 6, 7, 8, and 9. This means that the PTO could also split the tickets into 6, 7, 8, or 9 ticket booths, with each booth having an equal number of tickets.

Therefore, the PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths.

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The reflected function across the {x} - axis would be -

g(x) = -2/5 (10)ˣ.

If the function f(x) is reflected across the {x} - axis, then the new function g(x) becomes -

g(x) = - f(x)

Given is the function as -

f(x) = 2/5 (10)ˣ

We can write the reflected function as -

g(x) = - f(x)

g(x) = - {2/5 (10)ˣ}

g(x) = -2/5 (10)ˣ

Therefore,  the reflected function across the {x} - axis would be -

g(x) = -2/5 (10)ˣ.

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The student spends x hours tutoring, so y = 15.50x + 35, where x is the number of hours of tutoring and y is the total cost. Therefore, the total cost for a student who receives tutoring for two hours is $66.

According to the dictionary definition, a tutor is a person who provides one-on-one or occasionally small-group teaching. The goal of tutoring is to enable students to help themselves, or to support or mentor them until they reach the point at which they are self-sufficient learners and no longer require a tutor.

Tutors have the ability to, and frequently do, teach students new things. However, when comparing tutoring with teaching, what is being taught  is the main difference. Teachers are meant to teach students new content, and tutors teach students how to learn new content.

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A situation in which a quadratic equation cannot be solved using the quadratic formula include the following: A. The right-hand side of the equation is 1.

Generally speaking, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

In this context, we can reasonably infer and logically deduce that a quadratic function cannot be solved by using the quadratic formula when the coefficient of the x²-term is equal to zero (0) or when right-hand side of the equation is equal to one (1).

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Answer:

Step-by-step explanation:

hello

The values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:

AC² = 3² + 12² {Pythagoras rule}

AC = √(9 +144)

AC = √153

AC = 12.3693

tanα = 12/3 {opposite/adjacent}

α = tan⁻¹(4) {cross multiplication}

α = 75.9638

tanθ = 3/12 {opposite/adjacent}

θ = tan⁻¹(1/4){cross multiplication}

θ = 75.9638

Therefore, the values for the length AC and the angles of the right-angled triangle ABC are AC = 12.37, α = 75.96 , and θ = 14.04 using the trigonometric ratios of tangent.

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Answer:

Step-by-step explanation:

The correct answer is C: The vertices always lie on the circle.

In Poincaré's system, an equilateral triangle is a unique type of triangle in which all three sides are equal in length and all three angles are equal to 60 degrees. Since the vertices of an equilateral triangle lie on the circumference of a circle, it can be said that the vertices always lie on the circle.

The other options, A and B, are also true for equilateral triangles in Poincaré's system, but option C is the best answer because it directly addresses the question of where the vertices lie.

In Poincaré's system, a geometric model of non-Euclidean geometry, the vertices of an equilateral triangle are points that lie on the circumference of a circle.

Here's how this can be demonstrated step by step:

Draw a circle with a center point and a circumference.

Choose three points on the circumference of the circle and connect them with lines to form an equilateral triangle.

Measure the angles at each vertex using a protractor or by counting the number of degrees along the circumference of the circle. In an equilateral triangle, all three angles will be equal to 60 degrees.

Measure the sides of the triangle. In an equilateral triangle, all three sides will be equal in length.

Since the vertices of the triangle are points on the circumference of the circle, it can be concluded that the vertices always lie on the circle.

It is important to note that in Poincaré's system, the relationships between the vertices, sides, and angles of a triangle are different from those in Euclidean geometry. However, an equilateral triangle in Poincaré's system still follows the basic definition of an equilateral triangle, with all sides equal in length and all angles equal to 60 degrees.

Answer:

Step-by-step explanation:

(-4 - 8)/(5 + 1)= -12/6 = -2

Option C

1,755 cm² icings are needed for one cake.

The correct option is (C).

What is the area of the circle?

The area of a circle is the amount of space enclosed within the circle. It is a measure of the size of the circle, and it is determined by the distance from the center of the circle to its edge (which is the radius). The formula for the area of a circle is:

A = πr²

The surface area of the circular top of the cake can be found using the formula for the area of a circle:

A = πr^2

where A is the area of the circle, and r is the radius. For the red velvet cake, the radius is 13 cm, so the area of the circular top of the cake is:

A = 3.14 x 13^2 = 530.66 cm^2 (rounded to two decimal places)

To find the surface area of the curved side of the cake, we need to find the circumference of the circular base and multiply it by the height of the cake. The circumference can be found using the formula:

C = 2πr

where C is the circumference and r is the radius. For the red velvet cake, the circumference of the circular base is:

C = 2 x 3.14 x 13 = 81.64 cm (rounded to two decimal places)

So, the surface area of the curved side of the cake is:

A = C x h = 81.64 x 15 = 1224.60 cm^2 (rounded to two decimal places)

Therefore, the total surface area of the cake that needs to be iced (excluding the circular bottom) is:

530.66 + 1224.60 = 1755.26 cm^2 (rounded to two decimal places)

Rounding to the nearest square centimeter, we get that approximately 1755 cm^2 of icing is needed for one red velvet cake at the Bisecting Bakery.

Therefore, 1,755 cm² icings are needed for one cake.

The correct option is (C).

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The system of equations defined by the supply and demand models solved for equilibrium price is $9 and equilibrium quantity is 3000 units

Supply:

p=0.003x

x = p/0.003

x = 1/0.003p

Demand:

p= -0.008x+330

-0.008x = p - 330

x = (p - 330)/-0.008

Equilibrium price

Equate supply and demand price

0.003x = -0.008x+330

0.003x + 0.008x = 330

0.011x = 330

x = 330/0.11

x = 3,000

Substitute into

p=0.003x

p = 0.003(3000)

p = $9

Consequently, the equilibrium quantity and price is 3000 units and $9

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Answer:

C) 175.

Step-by-step explanation:

Sure, here's a step-by-step solution:

Let's call the number of employees at the agency "x".

If 80% of the employees have more than 12 days of unused sick leave, that means 0.8 * x employees have more than 12 days of unused sick leave.

We know that 0.8 * x = 140, so we can solve for x by dividing both sides of the equation by 0.8:

x = 140 / 0.8

Simplifying, we get:

x = 175

So there are 175 employees who work at the agency, and the answer is C) 175.

The required value of the given expression which satisfy it is b = 3/5.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

We have,

3 - 2(b - 2) = 2 - 7b

= 3 - 2b - 4 = 2 - 7b

= 5b = 3

= b = 3/5

Thus, required value of the b for the given function is b = 3/5.

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The f -intercepts and r -intercepts of the function are (0, 180) and (6, 0), (-6, 0),(5, 0)

The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.

Assume that we've got: y = f(x)

At y-axis, we've got x = 0, so putting it will give us the y-intercept.

Thus, y-intercept of y = f(x) is y = f(0)

We are given that;

The function is  f ( r ) = ( r − 6 ) ( r + 3 ) ( r − 1 )

Now,

Substituting r=0 for f -intercept

f(0) = (0-6)(0+6)(0-5)

f(0) = 180

The f-intercept is (0, 180);

Solving for the r-intercepts;

Set the function equal to 0.

0 = (r-6)(r+6)(r-5)

(r-6) = 0

r = 6

(r+6) = 0

r = -6

(r-5) = 0

r = 5

Therefore, the r-intercepts will be (6, 0), (-6, 0), and (5, 0)

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Answer: no

Step-by-step explanation:

If the r-value, or correlation coefficient, of a data set is 0.934, the

coefficient of determination to three decimal places is:  A. 0.872.

The coefficient of determination (R-squared) is the square of the correlation coefficient (r) and represents the proportion of the variance in the dependent variable (y) that can be explained by the independent variable (x).

So, to find the coefficient of determination, we need to square the correlation coefficient:

R-squared = r^2

= 0.934^2

= 0.872 (Rounded to three decimal places)

Therefore, the answer is (A) 0.872.

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The graph of the quadratic function y = x² - 5 is given by the image presented at the end of the answer.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function is given as follows:

y = x².

Which is concave up with vertex at the origin.

The translated function is given as follows:

y = x² - 5.

Meaning that the function was translated 5 units down, hence the vertex is at (0,-5) and the roots are plus/minus square root of 5.

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The domain of the relation include the following: C. {-5, -2, 0, 1, 4}.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain:

Domain = {-5, -2, 0, 1, 4}.

In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {-5, -2, 0, 1, 4}.

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Answer:

Step-by-step explanation:

1. YES

2. NO

3.NO

4. YES

1. This is because only some shoes are new not all of them.\

2. There are some new shoes so it is wrong.

3. Not all of them are new

4. Not every shoe is new because there are some old shoes.

The correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, a transformation that maps polygon ABCD to polygon A'B'C'D',

We are asked to select the correct composition of similarity transformations,

According to the graph, there is a scale factor of 1/2 which is smaller than 1,

Also, the polygon is dilating and then reflected.

Hence, the correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

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Answer:

1

Step-by-step explanation:

f(x) = 3x^3+kx+9, and the remainder when f(x) is divided by x+2 is -17, then what is the value of k=1

x = 415.

Check attached image 1.

So at this point, we know the measures of the angles, in terms of "x", which is a variable. We may use the implicit information in the drawing to find more information. Such as the total measure of the sum of angles DBE and CBE. This total measure equals 90°, we know this because there's a square drawn on the base of both angles. Whenever you see a square drawn at the base of an angle, it means the measure of that angle is 90°, a right angle.

Check attached image 2.

We know that the sum of angles DBE and CBE equal 90°. Hence:

[tex]DBE+CBE=90[/tex]

In terms of variable "x", this is:

[tex](0.1x-22)+(0.3x-54)=90[/tex]

[tex]0.1x-22+0.3x-54=90[/tex]

[tex]0.1x+0.3x-54-22=90\\ \\0.4x-76=90[/tex]

[tex]0.4x-76+76=90+76\\ \\0.4x=166[/tex]

[tex]\frac{0.4x}{0.4} =\frac{166}{0.4} \\ \\x=415[/tex]

To see if "x = 415" is the correct answer, take the original equation, substitute "x" by "415" and, if the same number appears on both sides of the equal (=) sign, then we've found our answer!

[tex](0.1x-22)+(0.3x-54)=90\\ \\(41.5-22)+(124.5-54)=90\\ \\(19.5)+(70.5)=90\\ \\90=90[/tex]

x = 415.