Solve the inequality and graph the solution on a number line

Answer:

Sample size is 6, event of rolling an even number is 3/6 (or 1/2)

Step-by-step explanation: When you roll a dice it could be 1, 2, 3, 4, 5, or 6. Count those up and you'll have the sample size. Odds of rolling a 2, 4, or 6 (even number) is 3/6 or 1/2, or 50%

Answer:

11 and 1/3 yards

Step-by-step explanation:

5 yards and 2 feet = 5 and 2/3 yards = 17/3 yards

(17/3 yards)(2) = 34/3 yards = 11 and 1/3 yards

The equivalent value of 5 yards 2 feet × 2 is 11 and 1/3 yards.

Given,

5 yards 2 feet × 2

Here,

Firstly convert feet to yard,

1 yard = 1/3 feet

So,

2 feet = 2/3 yard

So,

5 yards and 2 feet = 5 and 2/3 yards

= 17/3 yards

Now,

(17/3 yards)(2) = 34/3 yards

= 11 and 1/3 yards

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Step-by-step explanation:

Some characteristics of the graph of a square root function are: both the domain and range consist of real numbers greater than and equal to zero, start from origin, etc.

The square root function is the function that is represented by the following:

f(x) = √x

We are asked to give some characteristics of a square root graph.

The characteristics are given below:

The domain of a square root function consists of all real numbers greater than and equal to zero.

The range of a square root function consists of all real numbers greater than and equal to zero.

The graph of the square root function starts at the origin.

The graph of a square root function is an increasing graph.

The graph of the square root function is a one-to-one function. This means each domain value and range value has only one corresponding domain and range value.

Therefore, we have given some characteristics of the graph of a square root function.

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Answer:

29 units

Step-by-step explanation:

The length of a segment of a number line is the difference of the coordinates of the end points:

45 -16 = 29

For this case we have by definition, that an irrational number is a number that can not be expressed as a fraction \ frac {a} {b}, where a and b are integers and b is different from zero.

A) [tex]\sqrt {100} = 10[/tex], it is rational

B)[tex]\frac {1} {8}[/tex], it is rational

C) [tex]-2.2675[/tex], it is rational

D) [tex]\sqrt [3] {16},[/tex] it is not rational.

Answer:

Option D

The only option that represents an irrational number is D) ∛16.

An irrational number is a number that cannot be expressed as a fraction (ratio) of two integers and has an infinite decimal representation without any repeating pattern.

Let's analyze each option:

A) √100:

The square root of 100 is 10, which is a rational number. It can be expressed as the fraction 10/1.

Therefore, option A) is a rational number.

B) 1/8:

The fraction 1/8 can be expressed as a ratio of two integers. It is equal to 0.125 in decimal form.

Since the decimal representation terminates after a finite number of decimal places, option B) is not an irrational number.

C) - 2.2675:

The number -2.2675 is a decimal number, but it is not an irrational number.

It can be expressed as a rational number by writing it as a fraction. Hence, option C) is not an irrational number.

D) ∛16:

The symbol ∛ represents the cube root. The cube root of 16 is approximately 2.5198.

This number is an irrational number because it cannot be expressed as a fraction of two integers, and its decimal representation continues indefinitely without a repeating pattern.

In summary, the only option that represents an irrational number is D) ∛16.

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ANSWER

[tex](8, -1)[/tex]

EXPLANATION

If (8,-4) is on the graph of f(x), then

[tex]f(8) = - 4[/tex]

The corresponding point for the function

[tex]f(x) + 3[/tex]

is

[tex](8,f(8)+3)[/tex]

We substitute to obtain:

[tex](8, - 4+3)[/tex]

We now simplify to get;

[tex](8, -1)[/tex]

The corresponding point on f(x)+3 is therefore

[tex](8, -1)[/tex]

Answer:

14.5 years.

Step-by-step explanation:

Given that you invest $150 at 7% interest compounded annually. Now we need to find about in how many years will you have $400. Then round the  answer ot the nearest tenth of a year.

So plug the given values into compound interest formula.

[tex]A=P\left(1+r\right)^t[/tex]

[tex]400=150\left(1+0.07\right)^t[/tex]

[tex]\frac{400}{150}=\left(1+0.07\right)^t[/tex]

[tex]\ln\left(\frac{400}{150}\right)=\ln\left(1+0.07\right)^t[/tex]

[tex]\ln\left(\frac{400}{150}\right)=\ln\left(1.07\right)^t[/tex]

[tex]\ln\left(\frac{400}{150}\right)=t\cdot\ln\left(1.07\right)[/tex]

[tex]\frac{\ln\left(\frac{400}{150}\right)}{\ln\left(1.07\right)}=t[/tex]

[tex]14.4967313882=t[/tex]

Which is approx 14.5 years.

Answer:

The answer is x=9 and/or x = -12

Step-by-step explanation:

This is a quadratic formula meaning that you must take the a value (1) b value (3) and the c value (108) and plug it into the quadratic formula.

[tex]\frac{-3±\sqrt{9+4*1*-108} }{2}[/tex]

which simplifies to -3 add or subtract the sqrt of 441 divided by two.

To solve the equation x² + 3x - 108 = 0, we use the quadratic formula, which gives two solutions: x = 9 and x = -12.

The question asks to solve the quadratic equation x2 + 3x - 108 = 0. To solve this equation, we will use the quadratic formula, which is given by x = (-b ± √(b2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation ax2 + bx + c = 0. In our case, a = 1, b = 3, and c = -108.

Substituting these values into the quadratic formula gives us:

x = (-(3) ± √((3)2 - 4 ×(1) ×(-108))) / (2 ×(1))

x = (-3 ± √(9 + 432)) / 2

x = (-3 ± √441) / 2

x = (-3 ± 21) / 2

This results in two possible values for x:

So, the solutions to the equation x2 + 3x - 108 = 0 are x = 9 and x = -12.

Hello There!

Your answer is In Image Provided.

I have also included steps I made for a question I answered similar to this.

Answer:

lenght = 9

Step-by-step explanation: Area =L×W

Area = 63       7 . x= 63      x=63÷7        x=9               9×7=63

Answer:

(n×4)

Step-by-step explanation:

Divide the 2nd term by the first to find the ratio which is also n.

Answer:

n=5.

Step-by-step explanation:

The given geometric series is

1+ 4 +16 + 64 + 256

In the given G.P.  the number of terms is 5 and n represents the number of terms in a G.P. So, n=5.

Alternate method:

Here the first term is 1 and the common ratio is

[tex]r=\dfrac{a_2}{a_1}=\dfrac{4}{1}=4[/tex]

The nth term of a G.P. is

[tex]a_n=ar^{n-1}[/tex]

where, a is first term and r is common ratio.

Substitute a=1, an=256 and r=4 in the above formula.

[tex]256=(1)(4)^{n-1}[/tex]

[tex]4^4=4^{n-1}[/tex]

On comparing both sides we get

[tex]4=n-1[/tex]

Add 1 on both sides.

[tex]5=n[/tex]

Therefore, the value of n is 5.

ANSWER

(-2,2)

EXPLANATION

The rule for translating a point 'k' units to the right is

[tex](x,y)\to (x+k,y)[/tex]

If the point located at (-5, 2) is translated right 3 units, the coordinates of the image is obtained by adding 3 to the x-coordinate.

This implies that,

[tex]( - 5,2)\to ( - 5+3,2)[/tex]

[tex]( - 5,2)\to ( -2,2)[/tex]

Therefore the image is:

(-2,2)

Answer:

(-2, 2)

Step-by-step explanation:

We are given the following coordinates of a point:

[tex](-5, 2)[/tex]

If this point is translated to the right for 3 units, what will be the coordinates of its image?

Translation towards right side for 3 units means that 3 units are added to its x coordinate so the new point will be:

[tex] ( - 5 , 2 ) [/tex] [tex] \implies [/tex] [tex] ( - 5 + 3 , 2 ) = [/tex] (-2, 2)

Answer:

3a3a3a

3·3·3a^3

Step-by-step explanation:

(3a)^3 = (3a) (3a) (3a)

          = 3*3*3 * a *a *a

          = 3*3*3 * a^3

Answer:

3a3a3a

3·3·3a^3

Step-by-step explanation:

The answere is simple.All yyou have to do is sum up the time required to upload aphoto frim a phone to a website.Then find the time it takes to upload ten photos and multiply it by 2.

Answer:

8 minutes.

Step-by-step explanation:

Time taken to upload 12 photographs from a smartphone to a computer = 3.5 minutes

Time taken to upload that 12 photographs from computer to a website = 1.25 minutes.

∵ The time taken for 12 photographs to upload from smartphone to a computer then to a  website = 3.5 + 1.25 = 4.75 minutes.

∴ The time taken for 1 photograph to upload to a website = [tex]\frac{4.75}{12}[/tex]

∴ Time taken to upload 20 photographs from a smartphone to a computer then to a website =  [tex]\frac{4.75}{12}\times 20[/tex]

                             = 7.916 ≈ 8 minutes.

It will take 8 minutes to upload 20 photographs.

Answer:

72π in³

Step-by-step explanation:

Volume of a cylinder is:

V = πr²h

where r is radius (half of diameter) and h is height.

Here, r = d/2 = 3 in, and h = 8 in.

V = π (3 in)² (8 in)

V = 72π in³

[tex]\bf \begin{cases} x=3\implies &x-3=0\\ x=1+3i\implies &x-1-3i=0\\ x=1-3i\implies &x-1+3i=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x-3)(x-1-3i)(x-1+3i)=0 \\\\\\ (x-3)\underset{\textit{difference of squares}}{([x-1]-3i)([x-1]+3i)}=0\implies (x-3)([x-1]^2-[3i]^2)=0 \\\\\\ (x-3)([x^2-2x+1]-[3^2i^2])=0\implies (x-3)([x^2-2x+1]-[9(-1)])=0[/tex]

[ correction added, Thanks to @stef68 ]

[tex]\bf (x-3)([x^2-2x+1]+9)=0\implies (x-3)(x^2-2x+10)=0 \\\\\\ x^3-2x^2+10x-3x^2+6x-30=0\implies x^3-5x^2+16x-30=f(x) \\\\\\ \stackrel{\textit{applying a translation with a -2f(x)}}{-2(x^3-5x^2+16x-30)=f(x)}\implies -2x^3+10x^2-32x+60=f(x)[/tex]

To find the polynomial of degree 3 with real coefficients and specific zeros and y-intercept, we use the fact that complex zeros occur in conjugate pairs. We can express the polynomial as f(x) = a(x-3)(x-(1+3i))(x-(1-3i)), where a is a constant. By plugging in the y-intercept value, we can solve for the constant a.

To find the polynomial with degree 3 and real coefficients that has a y-intercept of 60 and zeros 3 and 1+3i, we can use the fact that complex zeros occur in conjugate pairs. Given that 1+3i is a zero, its conjugate 1-3i is also a zero. Therefore, the polynomial can be expressed as f(x) = a(x-3)(x-(1+3i))(x-(1-3i)), where a is a constant.

Since the polynomial has a y-intercept of 60, we know that f(0) = 60. Plugging in x=0, we can solve for the constant a:

f(0) = a(0-3)(0-(1+3i))(0-(1-3i)) = 60

Since the constant a is the only unknown variable, we can solve for it:

-3*(1+3i)*(1-3i) = 60/a

-3*(1-9i^2) = 60/a

12 = 60/a

a = 5

Therefore, the polynomial f(x) = 5(x-3)(x-(1+3i))(x-(1-3i)) has the desired properties.

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A single chicken lunch will cost $7 so option (C) will be correct.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the cost of chicken = c

cost of ham = h

Given,

Sharon's Deli charged the Business Club $231 for 18 chicken lunches and 14 ham lunches.

So,

18c + 14h = 231

And,

$225.00 for 15 chicken lunches and 16 ham

So,

15c + 16h = 225

By solving both equations

h = 7.5 and c = 7

Hence, a single chicken lunch will cost $7

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Answer:

2

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent of the variable within the expression

y³ is of degree 3

xy² is of degree 1 + 2 = 3 ← sum the exponents of the 2 variables

Thus x²y³ is of degree 2 + 3 = 5

For the expression 5x?y³ + xy² + 8 to be a trinomial with a degree of 5, then the missing exponent of the x term must be 2.

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Polynomials are classified based on degree as linear, quadratic, cubic and so on. A trinomial is a polynomial with three terms.

For the expression 5x?y³ + xy² + 8 to be a trinomial with a degree of 5, then the missing exponent of the x term must be 2.

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The answer is:

The third option is the correct option.

[tex](y+4)^{2}=22=y^{2}+8y-6[/tex]

To find the correct answer, we need to expand the notable product of the given choices, and then, compare it to the given expression.

Also, we must remember how to expand the following notable product:

[tex](a+-b)^{2}=a^{2}+-2*ab+b^{2}[/tex]

We are looking for the following expression:

[tex]y^{2}+8y-6=0[/tex]

So, solving we have:

[tex](y+4)^{2}=10\\\\y^{2}+2*4y+4^{2} =10\\\\y^{2}+8y+16=10\\\\y^{2}+2*4y+16-10=0\\\\y^{2}+2*4y+6=0[/tex]

Hence, we know that the first option is not the correct option.

[tex](y-4)^{2}=10\\\\y^{2}-2*4y+4^{2}=28\\\\y^{2}-8y+16=28\\\\y^{2}-8y+16-28=0\\\\y^{2}-8y-12=0[/tex]

Hence, we know that the second option is not the correct option.

[tex](y+4)^{2}=22\\\\y^{2}+2*4y+4^{2} =22\\\\y^{2}+8y+16=22\\\\y^{2}+2*4y+16-22=0\\\\y^{2}+8y-6=0[/tex]

Hence, we know that the third  option is the correct option.

Have a nice day!

Answer:

M = $22.62

C = $75.38

Step-by-step explanation:

Selling Price = $98

Markup = 30%

Selling Price = 100 + 30 = 130%

130% = $98

1% = 98/130

Markup

= 98/130 x 30  

= $22.62

Cost Price

= 98/130 x 100

= $75.38

Answer:

Around 17.716 inches

Step-by-step explanation:

Answer:

17.7 inches to the nearest tenth

Step-by-step explanation:

Recall that

1 in=2.54 cm

This implies that;

[tex]1cm=\frac{1}{2.54} in.[/tex]

Or

[tex]1cm=\frac{50}{127} in.[/tex]

This implies that;

[tex]45 cm=45\times\frac{50}{127}in[/tex]

[tex]45 cm=45\times\frac{50}{127}in[/tex]

This simplifies to;

[tex]45 cm=17.7 in[/tex] to the nearest tenth.

Answer:

B.  8 in^2.

Step-by-step explanation:

Let the width be x inches, then the length = x + 2 inches.

So by The Pythagoras theorem:

(√20)^2 =  x^2 + (x + 2)^2

x^2 + x^2 + 4x + 4 = 20

2x^2 + 4x - 16 = 0

x^2 + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = 2, -4    (we ignore the negative so x = 2)

So the area = 2 * (2 + 2)

= 8 in^2.

Answer:

B

Step-by-step explanation:

L = W + 2

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

(W + 2)2 + W2 = [tex]\sqrt{20} ^{2[/tex]  

2[tex]w^{2}[/tex] + 4W + 4 = 20

2[tex]w^{2}[/tex] + 4W − 16 = 0

W = 2 or W = −4

And,

L = W + 2

L = 2 + 2

L = 4

Therefore,

A = LW = (4)(2) = 8

Answer:

-9/17 is the answer

Answer:

true

Step-by-step explanation:

numbers divisble by 10 have to be divisible by 5 because the prime factors are 5 and 2

Hello! Based on this problem, 68 is part of a whole. To solve it, we can write and solve a proportion. Set it up like this:

68/x = 85/100

Cross multiply the sections. 68 * 100 is 6,800 and 85 * x is 85x. So you get 6,800 = 85x. Now, divide each side by 85 to isolate the x. 85x/85 cancels out. 6,800/85 is 80. We can check this answer by multiplying 80 by 85%. 80 * 85% (0.85) is 68. There's our answer. 68 is 85% of 80.

The number whose 85 percent gives 68 is 8000.

Given the parameters in the question:

Given Value = 68

Percentage = 85%

To find the number whose 85 percent gives 68, we can use the following formula:

Number = (Given Value / Percentage) × 100

First, convert 85% from percent to decimal:

85% = 85/100 = 0.85

Now, plug these values into the above formula:

Number = (Given Value / Percentage) × 100

Number = ( 68 / 0.85 ) × 100

Number = 80 × 100

Number = 8,000

Therefore, 68 is 85% of the number 8000.

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Answer:

1,12×10^6

Step-by-step explanation:

28 (unit)^2

find the differences in the x (4) and y (7) coordinates

times them together as you normally find the area of rectangle (L×W)

Answer:

0.03

Step-by-step explanation:

fraction = part/whole

= 27/900

= 3/100

=0.03

decimal value = 0.03

ANSWER

[tex]T.S.A = 150\pi[/tex] square inches.

EXPLANATION

The total surface area of a cylinder is given by;

[tex]T.S.A = 2\pi \: r(r + h)[/tex]

The height of the cylinder is , h=10in.

The radius of the cylinder is, r=5in.

We substitute the known values into the formula to obtain;

[tex]T.S.A = 2\pi \times 5(5+ 10)[/tex]

[tex]T.S.A = 10\pi(15)[/tex]

In terms of π, the total surface area is

[tex]T.S.A = 150\pi in^2[/tex]

Answer:

expression

A mathematical symbol, or combination of symbols, representing a value, or relation. Example:  

2

+

2

=

4

Step-by-step explanation:

hope this helps