Complete the fraction to make a true inequality, and explain your reasoning


4 × < 4
3




I know this because the fraction I made

The solution of the inequality will be;

⇒ 5.5 ≤ x

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 10 ≤ 2x - 1

Now,

Since, The inequality is,

⇒ 10 ≤ 2x - 1

Hence, Solve the inequality as;

⇒ 10 + 1 ≤ 2x - 1 + 1

⇒ 11 ≤ 2x

⇒ 5.5 ≤ x

Thus, The solution of the inequality will be;

⇒ 5.5 ≤ x

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The polynomial with given roots is,  

y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.

What is factor of polynomial?

In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.

Given:

The polynomial y(x) that has roots at x = -0.7, x = 0.5, x = 3.4 and x = 5.8.

Since if 'a' is a root of the polynomial then (x - a) is the factor of the polynomial.

So, the factors of the polynomial are, (x + 0.7), (x - 0.5), (x - 3.4), (x - 5.8).

⇒ y(x) = (x + 0.7)(x - 0.5)(x - 3.4)(x - 5.8)

          = (x^2 - 0.5x + 0.7x - 0.35)(x^2 - 5.8x - 3.4x + 19.72)

          = (x^2 + 0.2x - 0.35)(x^2 - 9.2x + 19.72)

   y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902

The graph of the polynomial on the domain -1 ≤ x ≤ 6 is attached below.

Hence, the polynomial with given roots is,  

y(x) = x^4 - 9x^3 + 17.53x^2 + 7.164x - 6.902.

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The number of tennis matches that she could have won before the weekend began is 0.

Before the weekend, the player had a win ratio of 0.500, which indicates that she had won exactly as many games as she had lost. Call this number x for now. She has so lost x matches in addition to the x matches she won before to the weekend.

She competes in three matches during the course of the weekend and loses one, bringing her overall win total (after the weekend) to x + 3 and her overall loss total (after the weekend) to x + 1. Consequently, her weekend victory ratio is

[tex]\frac{(x + 3)}{(x + 1)}[/tex]

= [tex]\frac{(3x + 3)}{(x + 1) }[/tex]

= [tex]\frac{3x }{x + 1 }[/tex]

= [tex]\frac{3}{\frac{1}{x+1} }[/tex]

given that this value is greater than 0.503,

Thus,

[tex]\frac{3}{\frac{1}{x+1} }[/tex] > 0.503

Simplifying,

[tex]\frac{3}{\frac{1}{x+1} }[/tex]> 0.503 - 1

= -0.497

Further,

[tex]\frac{3}{\frac{1}{x+1} }[/tex] > -0.497

[tex]\frac{3}{\frac{1}{x+1} }[/tex] is equivalent to 3x

This inequality can be written as

3x > -0.497

3x is positive, dividing on both sides by 3 we get

x > -0.497 / 3

Simplifying,

x > -0.166

The least value of x that meets this inequality is 0, as x, the number of matches won, must be a positive integer. Thus, the maximum number of games the player might have won prior to the start of the weekend is x = 0, and the response is 0.

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Answer:

164

Step-by-step explanation:

Let n be the number of matches she won, and m be the number of matches she played. Then, n/m = 1/2 and (n + 3) / (m + 4) > 0.503. By the first equation, 2n = m. Substituting m = 2n into the second equation/inequality, we get (n + 3) / (2n + 4) > 0.503. Because n cannot be negative in this context, we can multiply both sides by (2n + 4). We get n + 3 > 0.503 (2n + 4). Distributing the right-hand side, we get n + 3 > 1.006n + 2.012. Solving this inequality gives us 0.006n < 0.988, or n < 164.666667. n must be a whole number, so the greatest n you can achieve is 164.

On an actual test, you can also check using answer choices if given them. 164 gives around 0.50301, so it is 164, or cannot be determined. Then it is a 50/50 guess, and 164 is most likely the correct answer, which in this case, is the correct answer.

Answer:

(0, 139) and (139/35, 0)

Step-by-step explanation:

Answer:

Point slope: y - 115 = 2(x -30)

Slope intercept: y = 2x + 55

Step-by-step explanation:

I choice the first point to write the equation in the point slope form of a line.

(30,115)

Slope is the change in y over the change in x.  I see that the y's are increasing by 10, while the x's are increasing by 5

10/5 = 2

The slope is 2

y = y = m( x + x)

y - 115 = 2(x - 30)

Slope intercept form of a line

We already found the slope to be 2.  Use the slope and the point (30,115) to find x

y = mx + b

115 = 2(30) + b

115 = 30 + b    Subtract 30 from both sides

55 = b

y = 2x + 55

It is possible for the the two different non-isomorphic graphs can have same number of vertices and edges , and the two such graphs are drawn below .

Two graphs are said to be isomorphic if they contain same number of vertices connected in the same way.

So, Yes the two non-isomorphic graphs can have the same number of vertices and the same number of edges.

The two such graphs are drawn below

If the degrees of vertices in two graph are same then the graph will become isomorphic it will no longer be Non-Isomorphic.

Therefore, No two graphs that are non isomorphic can have same number of edges, vertices and degrees of vertices all at once.

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Answer: 4x

Step-by-step explanation:

Combine like terms

3x + x

4x

Hope this helps!

Answer:

  4x

Step-by-step explanation:

You want to "solve" 3x +x.

Start by understanding the meaning of 3x. The coefficient of 3 tells you how many instances of x you have. The term 3x is a representation of repeated addition:

  3x = x + x + x . . . . . . . . x is included in the sum 3 times

The sum 3x + x can be written out as ...

  3x + x = (x + x + x) + x

This is fully equivalent to ...

  3x + x = x + x + x + x

We recognize the sum on the right includes 4 instances of x, so can be written using a coefficient as ...

  x + x + x + x = 4x

This means ...

  3x + x = 4x

If we use the distributive property, we can also get there this way:

  3x + x = 3x + 1x = (3 +1)x = 4x

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you are examining the data with a stem-and-leaf plot. here is the start of the plot. finish the plot. 3|6

3| 0 2 4 5 6 8 9

A stem-and-leaf plot is a type of data display that shows the frequency of data items in a set. The plot consists of two columns, a stem column and a leaf column. The stem column contains the leading digit or digits of each data item, and the leaf column contains the remaining digits.

In this case, the stem is 3 and the leaf column is 6. To finish the plot, we need to add other data items to the leaf column which have the same stem (3). So, the completed plot would look like this:

3| 0 2 4 5 6 8 9

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The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ.

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 triangle.

It is known that,

Cos(A + B) = cosAcosB - sinAsinB

Cost(A - B) = cosAcosB + sinAsinB

As per the given,

cos(θ + π/4) - cos(θ - π/4)

(cosθ cos π/4 - sinθ sin π/4) - (cosθ cos π/4 + sinθ sin π/4)

-2 sinθ sin π/4

-2 sinθ (1/√2)

-√2 sinθ

Hence "The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ".

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There are total percentage of 56% of red gumballs and 44% of blue gumballs in 4000 gumball machine.

Percentage is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given,

Total gumballs in the machine = 4000

Red gumballs in the machine = 2240

Blue gumballs in the machine = 1760

Percentage of each gumballs,

Percentage of red gumballs,

Value/Total × 100%

2240/4000 × 100

0.56 × 100

56%

Percentage of blue gumballs,

1760/4000 × 100%

0.44 × 100%

44%

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The Method of Cylindrical Shells will be used to assist.

As previously, we construct a region R that is enclosed on the top by the graph of the function y = f (x), on the bottom by the x axis, and on the left and right by the lines x = a and x = b, respectively (a).

As seen in Figure 1, we then rotate this region around the y-axis (b). Be aware that this is distinct from what we have previously done..

Previously, areas that were described in terms of x-functions were centered on the x-axis or a line that ran parallel to it.

Since the shell is a cylinder, its volume equals the cross-sectional area times the cylinder's height. The cross-sections are annuli, which are essentially circles with holes in the middle and are formed like rings.

According to our question-

V= 2π ∫025/2 x [ 5 - √(2x) ] d x = 625π/ 4 cubic units

USING THE WASHER METHOD

V = ∫05 π (1/4) y4 d y = 625π/ 4 cubic units

Hence, The Method of Cylindrical Shells will be used to assist.

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The family  can spend 1 hour on the trampoline and 2 hours in the pool and the inequalities are 10t + 5p ≤ 25  and t + p < 4.

a ) Let the time on the trampolines  = t  

           10t + 5p ≤ 25

            t + p < 4

b )No, the family cannot  spend 1 hour in the trampoline and 3 hours in the pool.

c ) No, the family cannot  spend 2 hours in the trampoline and 1.5 hours in the pool.

         10t + 5p ≤ 25

         10(2)+ 5(1.5) = 27.5

d ) Yes, the  family  can spend 1 hour on the trampoline and 2 hours in the pool.

        10t + 5p ≤ 25

        10(1)+ 5(2) = 20

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Answer:

r=8, r=9, r=10

Step-by-step explanation:

5(7)≤6(7)-8

35≤42-8

35≤34

not true.

5(8)≤6(8)-8

40≤48-8

40≤40

true.

5(9)≤6(9)-8

45≤54-8

45≤46

true.

5(10)≤6(10)-8

50≤60-8

50≤52

true.

have a great day!

The probabilities for each case in this problem are given as follows:

a) A and B disjoint -> P(B and not A) = 1/2.

b) A is contained in B -> P(B and not A) = 1/6.

c) P(A and B) = 1/8 ->  P(B and not A) = 3/8.

The probability that we want to obtain in this problem is given as follows:

P(B ∩ Ac).

Which is the probability of B and the complement of A, that is:

P(B and not A).

If A and B are disjoint, it means that their intersection is of 0, hence:

P(B and not A) = P(B) = 1/2.

If A is contained in B, all elements of A are contained in B, hence the proportion of elements that are in B but not A is given as follows:

P(B and not A) = 1/2 - 1/3 = 1/6.

If the probability of the intersection is of 1/8, the proportion of elements that are in B but not A is given as follows:

P(B and not A) = 1/2 - 1/8 = 4/8 - 1/8 = 3/8.

(as 1/8 of them belong to both B and A, hence they do not belong to the complement of A).

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R ≥75 will be the inequality to symbolize the need that each individual bring home at least one rose, and for the cost requirement, it will be, 1.45R + 0.65C ≤ 200.

A connection that compares two numbers or other mathematical expressions unequally is known as an inequality in mathematics. Most frequently applied when comparing two numbers on the number line that differ in size.

Given:

Jada has $200 she can use to buy flowers. Each carnation costs $0.65 and a rose costs $1.45, so 75 guests may leave with at least one rose.

Jada has a total of $200.

Let R be the number of roses Jada bought.

There will be 75 persons in all present at the event.

As a result, the cost of R roses at $1.45 each is 1.45R.

Combined with roses C: Jada bought carnations.

Currently, each carnation costs $0.65.

Cost of C carnations at $0.65 per flower, then, equals 0.65C.

Inequality will serve as a restraint that requires everyone to bring home at least one rose,

[tex]R \geq 75[/tex]

There will be inequality that represents the cost limitation.

[tex]1.45R + 0.65C \leq 200[/tex]

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Step-by-step explanation:

of the following is the correct arrangement of the following atoms in order of DECREASING first ionization energy?

O>Te>Se>Po

Po>Te>Se>O

O>Se>Te>Po

Po>Se>Te>O

The statement is true for parallelogram is a square is a) All the rhombuses are squares.

In a rhombus, the opposing sides are parallel. In a rhombus, the opposing angles are equal. Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals.

Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals. One of the most significant characteristics of rhombus diagonals is this. Two adjacent angles added together equal 180°.

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Answer:

Step-by-step explanation:

The correlation coefficient is a measure of the strength and direction of the relationship between two variables. It ranges from -1 to 1, with -1 indicating a strong negative relationship, 0 indicating no relationship, and 1 indicating a strong positive relationship.

To find the correlation coefficient in this case, you can use the formula:

correlation coefficient = (slope * standard deviation of Y) / standard deviation of X

Plugging in the values you provided, we have:

correlation coefficient = (1.25 * standard deviation of Y) / standard deviation of X

The value of the correlation coefficient depends on the standard deviations of Y and X, which you have not provided. Without these values, it is not possible to calculate the correlation coefficient.

The ratio of outputs for any two inputs that are one value apart 2 .

A ratio is an ordered pair of numbers a and b, written a / b. where b is not zero. A ratio is an equation that equates two ratios. For example, if you have one boy and her three girls, the ratio can be written as: 1:3 (3 girls for 1 boy). A ratio is the  comparison of the  two numbers by division.

Taking the first two outputs, or the  -1/8 and -1/4, we can divide not the second one by the first one to find the

ratio:

-1/4-1/8

When dividing fractions, we multiply by the reciprocal:

-1/4x-8/1

To multiply fractions, multiply straight across:

(-1x-8)/(4x1) 8/4=2

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(1 , -5) satisfy the inequality y ≤ 3x + 2  but not to y > –2x – 3

According to the question,

It is Given : y ≤ 3x + 2  

y > –2x – 3

We have to find the relationship between the point (1, –5) and the given system of inequalities.

Substituting the point (1,5) in our inequality y ≤ 3x + 2  

=> x = 1

=> y ≤ 3(1) + 2  

=> y ≤  5

=> - 5 ≤ 5

Which is true

Hence point (1, –5)  satisfy y ≤ 3x + 2  

Substituting the point (1,5) in our inequality  y > –2x – 3

x = 1

=> y > -2(1) - 3

=> y > - 5

but - 5 = -5

Hence  point (1, –5)   does not satisfy y > –2x – 3

I've answered the question in general as the given question is incomplete

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The relationship shows a ratio.

What is a relationship?

A relation in mathematics describes the connection between two sets of values for ordered pairs. The set of items in the first set are referred to as domain, and they are connected to the set of elements in the second set, referred to as range.

How can one tell whether a relationship is a function?

A function is described as having one and only one output for each input value. In this case, the output values are referred to as the range and the input values as the domain.

In the rate the unit of two variables are different. In the ratio the unit of the variable is the same.

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Answer:

70.73%

29/41 = 0.7073...

Move the decimal over 2 places and get: 70.73

The maximum volume of the box is 40√(10/27) cu in.

Here we see that volume is to be maximized

The surface area of the box is 40 sq in

Since the top lid is open, the surface area will be

lb + 2lh + 2bh = 40

Now, the length is equal to the breadth.

Let them be x in

Hence,

x² + 2xh + 2xh = 40

or, 4xh = 40 - x²

or, h = 10/x - x/4

Let f(x) = volume of the box

= lbh

Hence,

f(x) = x²(10/x - x/4)

= 10x - x³/4

differentiating with respect to x and equating it to 0 gives us

f'(x) = 10 - 3x²/4 = 0

or, 3x²/4 = 10

or, x² = 40/3

Hence x will be equal to 2√(10/3)

Now to check whether this value of x will give us the max volume, we will find

f"(2√(10/3))

f"(x) = -3x/2

hence,

f"(2√(10/3)) = -3√(10/3)

Since the above value is negative, volume is maximum for x = 2√(10/3)

Hence volume

= 10 X 2√(10/3)  -  [2√(10/3)]³/4

= 2√(10/3) [10 - 10/3]

= 2√(10/3) X 20/3

= 40√(10/27) cu in

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Complete Question

(Image Attached)

The value of k will be 7 by using conditions slope of the graph.

What is slope?

Slope of a line measures its steepness . Slope is calculated as "rise over run" (change in x divided by change in y).

Two ways to find the slope :

1. Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates

(rise/run or slope).

2. Differentiate the line's equation and value of dy/dx that will be value of slope .

Mathematically ,

to find slope we differentiate the graph equation :

2dy/dx = 1/7k

dy/dx = 1/14k

Given slope = 1/2

so, 1/14k = 1/2

k = 7.

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The triangle is an isosceles trianlge. Then the value of the variable 'x' will be 19.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The two triangular legs and their opposing angles are congruent in an isosceles triangle.

In the event that the air conditioner is harmonious to CB, the proportion of point A = (3x + 18), and the proportion of point C = (2x - 8)

Then the equation is given as,

∠A + ∠B + ∠C = 180°

3x + 18 + 3x + 18 + 2x - 8 = 180

8x + 28 = 180

8x = 152

x = 19

The triangle is an isosceles trianlge. Then the value of the variable 'x' will be 19.

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0.6 gives the value of green cars 120 that is not possible in the problem,  0.6 can not be the probability of selected green car.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

total cars= 200

white cars= 100

red cars = 30

silver cars = 20

occupied space = 50+30+20 = 100

remaining space= 200- 100= 100

let number of green car in parking lot is 'x'

check every given probability of selecting a green car with x

according to question x <=(less than or equals to)100

p(prob. of green car) = x/200

a) 0.2

p=0.2

x/200= 0.2

x=0.2*200 = 40

b) 0

p=0

x/200=0

x= 0*200= 0

c) 0.1

p= 0.1

x/200 = 0.1

x= 0.1*200 = 20

d) 0.6

p = 0.6

x/200 = 0.6

x =0.6 * 200 =120

e) 0.5

p  = 0.5

x/200 = 0.5

x= 0.5*200 = 100

Hence,  0.6 gives the value of green cars 120 that is not possible in the problem,  0.6 can not be the probability of selected green car.

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The nth term of the given sequence is 8(3)ⁿ⁻¹. The given sequence is a geometric series and its common ratio is r = 3.

The nth term of a geometric series is calculated by the formula

tₙ = arⁿ⁻¹

Here a is the first term of the sequence and r is the common ratio of the sequence.

The common ratio is calculated by r = aⁿ⁺¹/aⁿ

The given sequence is 8, 24, 72, 216

Here, the first term in the given sequence is a = 8;

The ratios of the terms of the sequence are:

24/8 = 3

72/24 = 3

216/72 = 3

Since the ratios are the same, then the given sequence is geometric.

Thus, the common ratio is r = 3.

And the nth term of the given geometric sequence is

tₙ = arⁿ⁻¹ = (8)(3)ⁿ⁻¹

Therefore, the nth term of the given geometric sequence is 8(3)ⁿ⁻¹.

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the predicted interval of time between eruptions would be 53.16 minutes with regression equation.

The equation of the regression line is y = 33.35 + 13.29x.

Plugging in x = 4, we get y = 33.35 + 13.29(4) = 53.16 minutes.

The equation of the regression line is y = 33.35 + 13.29x. This equation is used to predict the interval of time between eruptions based on the duration of the previous eruption. By plugging in the value of x (4) into the equation, the predicted y value is 53.16 minutes. This means that if the previous eruption lasted 4 minutes, the predicted interval of time between eruptions would be 53.16 minutes.

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Answer:

a) 191.3 students

b) 433.8 students

Step-by-step explanation:

a) Since x represents years since 1998, on the graph, the number of student in 2005 is represented at x = 7.

So, to solve for the number of students studying abroad in 2005, find the approximate y-coordinate of the point on the graph at x = 2005 - 1998 = 7:

(7, 191.296)

         ↓

   191.296

Finally, round this to the nearest tenth.

192.296 ≈ 191.3 students

See the attached images for a graph and an algebraic solution for the coordinate.

b) Since x represents years since 1998, on the graph, the number of student in 2018 is represented at x = 2018 - 1998 = 20.

So, to solve for the number of students studying abroad in 2018, find the approximate y-coordinate of the point on the graph at x = 20:

(20, 433.761)

         ↓

   433.761

Finally, round this to the nearest tenth.

433.761 ≈ 433.8 students