Consider the given statement. Some shoes on display are new. For each statement below, determine whether it is a negation of the given statement. Yes No

Some shoes on display are not new.
None of the shoes on display are new.
Every shoe on display is new.
Not every shoe on display is new.

7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given inequality is:

x + 8 > 15

Subtracting 8 on both sides of the equation:

x + 8 - 8 > 15 - 8

x > 7

Here, 7 is not included and hence it is depicted using an open dot.

Hence, option B is the correct answer.

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The equation of the polynomial is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2

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

The graph

On the graph, we have the following readings:

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x + 3)(x + 2)(x - 1)(x - 3)^2

The y-intercept is 2

So, we have

a * (0 + 3)(0 + 2)(0 - 1)(0 - 3)^2 = 2

This gives

a = -1/27

Hence, the expression is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2

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Answer:

2

:

5STEP

2

:

Trying to factor as a Difference of Squares:

2.1 Factoring: 5-3x2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 5 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step

2

:

5 - 3x2 = 0

STEP

3

:

Solving a Single Variable Equation:

3.1 Solve : -3x2+5 = 0

Subtract 5 from both sides of the equation :

-3x2 = -5

Multiply both sides of the equation by (-1) : 3x2 = 5

Divide both sides of the equation by 3:

x2 = 5/3 = 1.667

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 5/3

The equation has two real solutions

These solutions are x = ±√ 1.667 = ± 1.29099

Two solutions were found :

x = ±√ 1.667 = ± 1.29099

f is increasing on (-infty, -4) and (2,infty) since that's where you'd be walking uphill.

f is never decreasing.

f is constant on (-4,2), since that's where it's completely flat.

a)

The total number of possible 3​-card poker hands is 22100

b)

The number of possible black flushes is 2600

c)

The probability of being dealt a black flush is 0.1176

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of cards = 52

Number of cards in hand = 3

Combination formula.

[tex]^nC_r[/tex] = n! / r! (n -r)!

a)

The total number of possible 3​-card poker hands.

= [tex]^{52}C_3[/tex]

= (52 x 51 x 50) / (3 x 2)

= 22100

b.

Number of black cards (spades and clubs) = 13 + 13 = 26

The number of possible black flushes.

= [tex]^{26}C_3[/tex]

= (26 x 25 x 24) / (3 x 2)

= 2600

c.

The probability of being dealt a black flush.

From (a) and (b)

= 2600/22100

= 0.1176

Thus,

The total number of possible 3​-card poker hands = 22100

The number of possible black flushes = 2600

The probability of being dealt a black flush = 0.1176

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The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

Domain: The domain of the function is the set of all real numbers greater than -8, since the argument of the logarithm, x + 8, must be positive.

Range: The range of the function is all real numbers.

Asymptotes: The function does not have any vertical asymptotes.

Transformation: The function is a reflection of the standard logarithmic function over the x-axis, with a vertical scaling factor of -2. This means that the function will start from the origin and increase without bound.

Behavior near x = -8: As x approaches -8 from the right, the value of the function approaches negative infinity. As x approaches -8 from the left, the value of the function approaches positive infinity.

The domain of the function is set of all real numbers except 8. Range of the function is set of all real numbers. The given function does not have asymptotes.

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Answer:8

Step-by-step explanation:

Because Angle GJH is 90 degrees, Angle HJZ is also 90 degrees. (Because all right angles are 90 degrees)

Now, find Angle WJZ

90 - 18 = 72 degrees

By the Vertical Angles Theorem, Angle GJL is congruent to Angle ZJW

Now solve for x

72 = 9x

x = 8

Answer:

29 feet by 40 feet to get a viable dimension for the goats pen

The first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20

An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.

Given is an arithmetic sequence, [tex]a_{k+1} = a_k-20[/tex] and [tex]a_1 = 300[/tex],

we need to find the first five terms,

a₂ = a₁-20

a₂ = 300-20

a₂ = 280

a₃ = a₂-20

a₃ = 260

a₄ = a₃ - 20

a₄ = 240

a₅ = a₄ - 20

a₅ = 220

aₙ = aₙ₊₁ - 20

d = 20

Hence, the first five terms of the arithmetic sequence are 300, 280, 260, 240, 220 and the common difference d is 20

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Answer:

yes

Step-by-step explanation:

2*(4+7) = ( 2 * 4 ) + ( 2 * 7 )

The solution of the inequality is -4≤x<7. Therefore, option D is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -12≤2x-4<10.

Here, -12≤2x-4

Add 4 on both the sides of an inequality, we get

-8≤2x

Divide 2 on both the sides of an inequality, we get

-4≤x

Now, 2x-4<10

Add 4 on both the sides of an inequality, we get

2x<14

Divide 2 on both the sides of an inequality, we get

x<7

So, the solution of the inequality is -4≤x<7

Therefore, option D is the correct answer.

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The fraction of Mrs. Stanford's class that came late and brought notes that day was 1 / 4

To find the fraction of Mrs. Stanford's class that came late and brought notes that day, the relevant formula would be:

= Fraction of students who came late x Fraction of late students who brought notes

Fraction of students who came late = 3 / 4

Fraction of students who were late and brought notes = 1 / 3

The fraction of total students who were late and brought notes were ;

= 3 / 4 x 1 / 3

= 3 / 12

= 1 / 4

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56.7 cubic feet of acetylene gas will be needed to make 27 brackets.

What is Total price?

In order to calculate the total price of something is by using this formula. Purchase Price = Cost Price + Margin.

To find out how much gas will be needed to make 27 brackets, we need to multiply the amount of gas required for making one bracket by the number of brackets to be made.

So, the total amount of gas needed to make 27 brackets would be:

2.1 cu ft * 27 = 56.7 cu ft

Therefore, 56.7 cubic feet of acetylene gas will be needed to make 27 brackets.

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The length and width of the rectangular wall of a barn given the area is 22 feet and 5 feet respectively.

Area of the rectangular wall of a barn = 110 square feet

Width of the barn = w

Length of the barn= 2w + 12

Area of a rectangle = length × width

110 = (2w + 12) × w

110 = 2w² + 12w

equate to 0

2w² + 12w - 110 = 0

w² + 6w - 55 = 0

using factorization method of solving quadratic equation

w² + 11w - 5w - 55 = 0

w(w + 11) - 5(w + 11) = 0

(w - 5) (w + 11) = 0

w = 5 or w = -11

The width of the rectangular barn cannot be negative

Therefore,

Width of the barn = w

= 5 feet

Length of the barn= 2w + 12

= 2(5) + 12

= 10 + 12

= 22 feet

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The inequality is |x-9| ≥ 4, and its solution set is (5,13).

An Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality of the form |x-a| ≥ k means that the distance between x and a is greater than or equal to a certain value, k.

If the solution set is (5,13), it means that x is a number between 5 and 13, but not including 5 or 13. In other words, 5 < x < 13.

To find the value of a and k, we need to look for the midpoint of the solution set, which is (5+13)/2 = 9.

The distance between 9 and either endpoint (5 or 13) is 4, which is the value of k.

Thus, the inequality is |x-9| ≥ 4, and its solution set is (5,13).

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To fill a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden, you will need 79.33 cubic yards.

The volume is the product of the multiplication of the thickness, length, and width.

The thickness of the topsoil = 6 inches

12 Inches = 1 Feet

6 inches = 0.5 Feet (6/12)

The length of the garden = 28 feet

The width of the garden = 17 feet

The thickness of the soil = 0.5 feet

Volume of the topsoil = 28 x 17 x 0.5

= 238 ft³

3 Feet to 1 Yard

238 ft³ = 238/3 yards

= 79.33 cubic yards

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Answer:

PR and SQ have the same midpoint.

Step-by-step explanation:

PR and SQ have the same midpoint.

Answer:

The [tex]66[/tex]th term is [tex]363[/tex].

Step-by-step explanation:

To find the [tex]n[/tex]th term, the formula is [tex]7n - 99[/tex]. Since we want to find the [tex]66[/tex]th term, we can plug [tex]n[/tex] for [tex]66[/tex]. So our expression is now [tex]7 \cdot 66 - 99 =[/tex] [tex]66[/tex]th term. Solving this we have

[tex]462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\[/tex]. Therefore, the [tex]66[/tex]th term is [tex]\boxed{363}[/tex].

Answer:

a₆₆ = 363

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then

a₆₆ = - 92 + (65 × 7)

      = - 92 + 455

     = 363

Opposite sides JK and ML are equal and parallel (with slopes of -1/5 and 1/5, respectively), and opposite sides KL and MJ are equal and parallel (with slopes of 7/3 or 7). /3) We can conclude that JKLM is a parallelogram. 

To determine if JKLM is a parallelogram, we need to check if its opposite sides are parallel and equal in length.

First, we can find the lengths of the sides using the distance formula:

JK = [tex]\sqrt{(1 - (-4))^2 + (3 - 2)^2} = \sqrt{25} = 5[/tex]

KL = [tex]\sqrt{(-4 - (-1))^2 + (2 - (-5))^2} = \sqrt{58}[/tex]

LM = [tex]\sqrt{(-1 - 4)^2 + (-5 - (-4))^2} = \sqrt{26}[/tex]

MJ = [tex]\sqrt{(4 - 1)^2 + (-4 - 3)^2} = \sqrt{50}[/tex]

Next, we can find the slopes of the sides using the slope formula:

Slope of JK = (2 - 3)/(-4 - 1) = -1/5

Slope of KL = (-5 - 2)/(-1 - (-4)) = 7/3

Slope of LM = (-4 - (-5))/(4 - (-1)) = 1/5

Slope of MJ = (3 - (-4))/(1 - 4) = 7/3

Since opposite sides, JK and ML have the same length and are parallel (they have slopes of -1/5 and 1/5, respectively), and opposite sides KL and MJ have the same length and are parallel (they have slopes of 7/3 and 7/3, respectively), we can conclude that JKLM is a parallelogram.

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The location of the points for quadrilateral KLMN have been plotted in the graph shown in the image attached below.

In Geometry, there are different types of quadrilateral and these include the following:

Next, we would use an online graphing calculator to construct (plot) quadrilateral KLMN on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral KLMN on the x-coordinate and y-coordinate respectively as shown in the table.

By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a parallelogram.

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Answer:46

Step-by-step explanation:

180=104+30+x

134+x=180

x=46

According to the information, it can be inferred that the option that the quote explains is: The outcome... is situational irony because the opposite of what was expected is what happening.

To identify the correct option that explains the quote we must read the text carefully and the options. Once we have read and understood this information, we can infer which option explains the quote.

In accordance with the above, option A would be the one that explains the quote because options B and C by discarding are fragments of the quote. So these fragments could not explain the same quote that is being used in the text. On the contrary, the paragraph of option A does explain the situation clearly.

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We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is  [tex]\mathrm{\dfrac{1}{m^4}}[/tex] .

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

It is possible to compare expressions to phrases. In language, a phrase by itself may contain an action, but it does not constitute a complete sentence.

The following are some examples of expressions and word phrases that they relate to:

Expression: 3 + 7

Given

⇒ [tex]\mathrm{(m)^6^{(-2/3)}}[/tex]

⇒ [tex]\mathrm{(m)^{(-12/3)}}[/tex]

⇒ [tex]\mathrm{(m)^{(-4)}}[/tex]

⇒ [tex]\mathrm{\dfrac{1}{m^4}}[/tex]

We have simplified the expression [tex]\mathrm{(m)^6^{(-2/3)}}[/tex] and written answer using a positive exponent that is  [tex]\mathrm{\dfrac{1}{m^4}}[/tex]

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Answer:

384 cm

Step-by-step explanation:

The proofing will be illustrated thus:

1.  Seg. AC bisects ∠BAD                                 1.  Given

2.  (m=measure) m∠BAC=∠CAD                      2.  Definition of angle bisector

   Therefore, m∠BAC≅∠CAD.

3.  AC=AC                                                      3.  reflexive property

4.  ∠ABC =∠ADC                                            4.  Given

5.  Triangle ABC≅Triangle ADC                        5.  Angle-Angle-Side (AAS postulate).

6.  Therefore, BC=DC                                     6. CPCTC

It should be noted that AAS stands for Angle-Angle-Side. In this case, ehen two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

Corresponding parts of congruent triangles are congruent.

Here, the two pairs of angles correspond, but there is a shared side that is not between the angles.

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Given: AC bisects \angle BAD

Given: AC bisects \angle BAD

\angle ABC=\angle ADC

Write a two-column proof to prove= BC=DC

The number of bags of sand that has to be used would be 92

diameter = 30 yards

width of path = 5 yards

diameter with path

30 + 2 * 5

= 40 Yd

area of path = area of garden with path - ara of garden

= 3.14 * 40² / 4 - 3.14 * 30² / 4

= 1256 - 706.5

= 549.5

area covered by bag = 549.5 / 6

= 91.58

= 92 bags

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Answer:

Below

Step-by-step explanation:

So you have this:

4x + 16 = 35       subtract 16 from both sides of the equation

4x = 19   Divide by 4

x = 19/4

Answer:

The value of x is

[tex]x = 4.75[/tex]

Step-by-step explanation:

Greetings!!!

Thus, the value of y is given as 35, substitute known value of y in expression and solve for x.

[tex]4x + 16 = 35[/tex]

Move the constant to the right

[tex]4x = 35 - 16 \\ 4x = 19[/tex]

Divide both sides of the expression by 4

[tex] \frac{4x}{4} = \frac{19}{4} [/tex]

solve

[tex]x = \frac{19}{4} [/tex]

or

[tex]x = 4 \frac{3}{4} [/tex]

or

[tex]x = 4.75[/tex]

Hope it helps!!!

The exact value of cosine is 4/5

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

(8,-6) be a point on the terminal side of an angle

Using the above as a guide, we have the following:

Cos(angle) = x/(√x² + y²)

In this case

x = 8 and y = -6

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

Cos(angle) = 8/(√8² + (-6)²)

So, we have

Cos(angle) = 8/10

Simplify

Cos(angle) = 4/5

Hence, the value is 4/5

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The another example that supports Hilary's conjecture are, 26² - 21²

In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.

For example, if we take 4 pencils out of 10 then remaining pencils are 6

so this process is called subtraction.

Given that,

Hilary was examining the differences between perfect squares of numbers separated by 5.
The differences always have the digit 5 in the ones place.

Another example that supports Hilary's conjecture is:

= 26² - 21²

= 676 - 441

= 235

As we can see, the difference between the perfect squares of 26 and 21 is 235,

which ends in the digit 5 in the ones place, confirming Hilary's conjecture that the differences between perfect squares of numbers separated by 5 always have the digit 5 in the ones place.

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