A die is rolled. Find the probability of the outcome. P( greater than 1 )

1) The mathematical expression that represents this scenario is T = 40/5.

2) The value of T in the equation is $8.

A mathematical expression is a mathematical statement that has two different numbers (known or unknown) and at least one operation.

For instance, an equation is a mathematical equation showing that two variables are equal.

The payment for a subway pass = $55

The number of subway rides = 5

The total amount deducted from the value of the pass = $40

This implies that each subway ride costs = $8 ($40/5)

If T is the cost of a ticket and the total cost incurred for 5 subway rides is $40, therefore T = 40/5.

Thus, the mathematical expression that represents this scenario is T = 40/5.

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27.9 cm≤ perimeter ≤28.5cm

The length of the regular hexagon is 4.7cm to 1 decimal place, i.e.,

4.65≤ length≤4.75

As we know the number of sides of a regular hexagon is 6

So the perimeter for the upper bound of length = 6×4.65

                                                                                = 27.9cm

The lower bound of length perimeter = 6× 4.75

                                                              = 28.5cm

Therefore the interval of the perimeter of a regular hexagon is:

27.9cm ≤ perimeter ≤ 28.5cm

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Classifying an equiangular triangle as an acute equiangular triangle is unnecessary because by definition, all angles are 60°

An equiangular triangle is one with three equal sides and three equal angles, all of which are measured at 60 degrees. Given that the characteristics of both triangles are the same, an equiangular triangle can also be referred to as an equilateral triangle.

This triangle is regarded as a regular polygon because its sides and angles are both equal. Equiangular refers to angles that are all equal.

All triangles have 3 angles that together total 180 degrees. Because an equilateral triangle has equal sides, its angles can only be 60 degrees. This entails that all angles must be acute. It is not required to write that it is intense because of this.

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The total distance traveled by the pendulum when it comes to rest is 10,000 cm.

Because of friction and air resistance, each swing of a pendulum is a little shorter than the previous one. The lengths of the swings form a geometric sequence. Suppose the first swing of a pendulum has a length of 100 cm and the return swing is 99 cm .

Now,

Given,

On the first swing, the distance traveled is 100, and on the second swing, the distance is 99.

The first term of the geometric sequence is, a1 = 100

The second term of the sequence is, a2 = 99

The common ratio r = 99/100

Therefore, the expression for the n-t h term of the sequence is:

a_n = 100*(99/100)^(n-1)

Theoretically, using this formula, it would take an infinite number of trips to come to rest.

Hence we need to find the sum of the series a_n = 100*(99/100)^(n-1) from n=1 to n=infinity.

The sum of an infinite series is given by S = a/(1-r) where a=the first term and r=the common ratio.

Therefore,

the total distance traveled is S = 100/(1-(99/100) = 100/0.01 = 10,000 cm

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Answer:

no it is not because natural numbers are whole numbers :)

hope this was helpful!

The solutions of the given polynomial equation p⁴+32=12 p² is p = {-2√2, 2√2, -2, 2}.

The given polynomial equation is:

p⁴+32=12 p²

Subtract both sides by 12 p²

p⁴ + 32 -12 p² = 12 p² 12 p²

p⁴ -12 p² + 32 = 0     ...... (1)

Let x = p², then equation (1) becomes

x² -12x + 32 = 0  

This is a quadratic equation.

Factorize:

   x² -12x + 32 = 0  

⇔ (x - 8 ) (x - 4) = 0

Take:

x - 8 = 0

x = 8

p² = 8

p = ±√8 = ±2√2

Take:

x - 4 = 0

x = 4

p² = 4

p = ±√4 = ±2

Hence the solution is p = {-2√2, 2√2, -2, 2}

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Inequality is [tex]p + 31 \ge 85[/tex]

Solution is [tex]p \ge 54[/tex]

===============================================

Explanation:

p = number of pages left to read

31 = number of pages already read

p+31 = total number of pages (unread + read)

This total must be 85 or larger, so that's how we end up with [tex]p+31 \ge 85[/tex]

To solve this inequality, we subtract 31 from both sides to end up with [tex]p \ge 54[/tex] which means Jen still needs to read at least 54 pages.

Answer:

The large box weighs 18.75 and the small box weights 15.75

Step-by-step explanation:

We are looking to find 2 variables so we will need two equations.

Let l = the large box weight

Let s = the small box weight

7l + 9s + 273                   5l +3s = 141

I want to add these two equations together and have one of the variables be eliminated.  The way both equations are written now, neither variable will drop out.  I see that 9 is a multiple of 3.  If I multiply the second equation all the way through by - 3, the s variable will be eliminated.

-3(5l +3s) -3(141)  Multiple everything by -3

-15l -9s = -423  Now I will add this to the original equation 7l + 9s = 273

7l + 9s = 273

-8l = -150  Divide both sides by -8

l = 18.75  This is the weight of the large box.

Plug in 18.75 to either of the ordinal equations to find the weight of the small box.

5l + 3s = 141

5(18.75) + 3s = 141  Distribute the 5

93.75 + 3s = 141  Subtract 93.75 from both sides

3s = 47.25  Divide both sides by 3

s = 15.75

Check:

Plug in 15.75 for s and 18.75 for l into both of the original equation to see if they equal.

7l + 9s = 273

7(18.75) + 9(15.75) =273

131.25 + 141.75 = 273  Checks

5l + 3s = 141

5(18.75) + 3(15.75) = 141

93.75 + 47.25 = 141

141 = 141 Checks

The slope of the given points are  (29, 11) and (-3, -7):

= 0.5625.

A line's slope indicates whether sharp it is.. The slope is defined mathematically as "climb overrun" (change in y divided by change in x).

In general, a line's slope indicates its steepness as well as direction. The slope of a straight line connecting two points (x1,y1) and (x2,y2) can be simply calculated by subtracting the coordinates of both the points. The slope is commonly denoted by the letter'm.'

X₁ = 29

Y₁ = 11
X₂ =  -3
Y₂ = -7

The slope is the degree of tilt a line has and it may be positive, negative, zero, or undefined.

slope = (y₂ - y₁) / (x₂ - x₁)

Substituting the value in the given formula:

slope  =  [tex]\frac{(-7 - 11)}{(-3 - 29)}[/tex]

          = -18 / -32

          = -9 / -16

          = 0.5625

The slope of the given points are  (29, 11) and (-3, -7) = 0.5625.

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Answer:

?

Step-by-step explanation:

==================================================

Work Shown:

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

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

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

x+2 = 0 or C-x+2 = 0

x = -2 or x = C+2

If we want one solution only, then we must make C+2 = -2 which solves to C = -4

If C = -4, then x = C+2 = -4+2 = -2 which matches with the first solution mentioned. If C is anything else but -4, then we'd have two different solutions (eg: C = 10 leads to x = C+2 = 12 as the other solution)

Answer: 7.5

Step-by-step explanation: 15 ft * 2 in/ft = 30 in18 ft * 2 in/ft = 36 inso area on plan = 30*36 = 1080 in^2on the real size area = 15*18 = 270 ft^2well to compare them change in^2 to ft^2there are 12 in /ftso 144 in^2 per ft^2so1080 in^2 *1 ft^2/144 in^2 = 7.5 ft^2or you could say30 in = 30/12 ft36 in = 3 ftarea = 90/12 ft^2 = 7.5 ft^2 luckily :)

The angle of elevation of the ramp to the nearest degree is 8°

From the information given, we have the following deductions;

The tangent identity is expressed as;

tan θ = opposite/ adjacent

substitute the values

tan θ = 2/ 15

find the ratio

tan θ = 0. 1333

Find the tangent inverse of the value

θ = [tex]tan^-^1(0. 1333)[/tex]

θ = 7. 79 °

θ = 8° in the nearest degree

Thus, the angle of elevation of the ramp to the nearest degree is 8°

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PS you cant leave out exponents when typing questions without the attached photo. multiplying by 2 is not the dame as a exponent of 2. Use ^2 to show that a number is to the power of 2.

the value of p(2) in this equation is 2.

Answer:

p(2) = 2

Step-by-step explanation:

substitute x = 2 into p(x)

p(2) = - 3(2 - 4)² + 14

      = - 3(- 2)² + 14

      = - 3(4) + 14

      = - 12 + 14

      = 2

Answer:

6,666

Step-by-step explanation:

A four-digit number: 1,234

All digits are the same: 1111, 2222, 3333...

Value in the hundreds place: 0,600

Answer: 6,666

Answer:

y = -1/4 -x/2

Step-by-step explanation:

The solution is attached.

The commutative property [tex]\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex] has been proved.

Commutative property:

The commutative property states that the changes the order or position of two numbers while adding or multiplying them does not change the end result.

The general form of commutative property is

A + B = B + A

For example, while adding the number 4, and 5

4 + 5 = 5 + 4 = 9.

Which means both yields the same result.

Given,

Let

[tex]\overrightarrow{a}= < x_1,y_1 >[/tex]

and

[tex]\overrightarrow{b}= < x_2,y_2 >[/tex]

Now we need to prove the commutative property[tex]\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex].

We know that,

"The vectors are defined as an object containing both magnitude and direction. Vector describes the movement of an object from one point to another."

Based on the commutative property,

We have to to apply the value of [tex]\overrightarrow{a}[/tex]and[tex]\overrightarrow{b}[/tex] to the equation,

Then we get,

[tex]\implies\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex]

=> <x₁, y₁> + <x₂, y₂> = <x₂, y₂> + <x₁, y₁>

While looking at the expression we know that,

Both are equal.

Then the commutative property has been proved.

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Answer: give me the context please

Step-by-step explanation:

The equation is 24.36 = 5.31 + 5 * x  and the cost of each bag of lemon is $3.81

The given parameters are:

The above means that

Total = Cheese + Bags of lemon * 5

This gives

24.36 = 5.31 + 5 * x

Collect the like terms

So, we have

24.36  - 5.31 = 5 * x

Evaluate the like terms

So, we have

19.05 = 5 * x

Divide through by 5

So, we have

x = 3.81

Hence, the equation is 24.36 = 5.31 + 5 * x  and the cost of each bag of lemon is $3.81

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Answer: x<1

Step-by-step explanation:

add 12 to both sides, divide by 2 on both sides.

For the given set of inequality, the value of x is 8.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Given, the equation is -

x+ 3 > 19 = 3x

⇒ x + 3 > 19 - 3x

Subtracting 3 from bot sides

⇒ x > 16 - 3x

subtracting x from both sides

⇒ 16 - 2x > 0

⇒ x = 8

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The eighth term of the given geometric sequence is 256/6561.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 2/3, 4/9, 8/27...

As we can observe, each successive term of the geometric sequence is 2/3 of the previous one.

Thus, r = 2/3  and a₁ = 2/3.

The formula used to find the nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 8, [tex]a_8=\frac{2}{3}(\frac{2}{3})^7=\frac{2}{3}^8=\frac{256}{6561}[/tex]

Thus, the eighth term of the given geometric sequence is 256/6561.

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Answer:

13/6

Step-by-step explanation:

1 Simplify  \sqrt{8}

8

​

  to  2\sqrt{2}2

2

​

.

\frac{2}{6\times 2\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})

6×2

2

​

2

​

2

​

−(−

81

​

18

​

)

2 Simplify  6\times 2\sqrt{2}6×2

2

​

  to  12\sqrt{2}12

2

​

.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{\sqrt{81}})

12

2

​

2

​

2

​

−(−

81

​

18

​

)

3 Since 9\times 9=819×9=81, the square root of 8181 is 99.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-\frac{18}{9})

12

2

​

2

​

2

​

−(−

9

18

​

)

4 Simplify  \frac{18}{9}

9

18

​

  to  22.

\frac{2}{12\sqrt{2}}\sqrt{2}-(-2)

12

2

​

2

​

2

​

−(−2)

5 Rationalize the denominator: \frac{2}{12\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{2\sqrt{2}}{12\times 2}

12

2

​

2

​

⋅

2

​

2

​

​

=

12×2

2

2

​

​

.

\frac{2\sqrt{2}}{12\times 2}\sqrt{2}-(-2)

12×2

2

2

​

​

2

​

−(−2)

6 Simplify  12\times 212×2  to  2424.

\frac{2\sqrt{2}}{24}\sqrt{2}-(-2)

24

2

2

​

​

2

​

−(−2)

7 Simplify  \frac{2\sqrt{2}}{24}

24

2

2

​

​

  to  \frac{\sqrt{2}}{12}

12

2

​

​

.

\frac{\sqrt{2}}{12}\sqrt{2}-(-2)

12

2

​

​

2

​

−(−2)

8 Use this rule: \frac{a}{b} \times c=\frac{ac}{b}

b

a

​

×c=

b

ac

​

.

\frac{\sqrt{2}\sqrt{2}}{12}-(-2)

12

2

​

2

​

​

−(−2)

9 Simplify  \sqrt{2}\sqrt{2}

2

​

2

​

  to  \sqrt{4}

4

​

.

\frac{\sqrt{4}}{12}-(-2)

12

4

​

​

−(−2)

10 Since 2\times 2=42×2=4, the square root of 44 is 22.

\frac{2}{12}-(-2)

12

2

​

−(−2)

11 Simplify  \frac{2}{12}

12

2

​

  to  \frac{1}{6}

6

1

​

.

\frac{1}{6}-(-2)

6

1

​

−(−2)

12 Remove parentheses.

\frac{1}{6}+2

6

1

​

+2

13 Simplify.

\frac{13}{6}

6

13

​

Done

Answer: If (4, y ) is an ordered pair of the function, then y = 1

Step-by-step explanation:

The known x coordinate for the position (4,y) is 4.

We'll just refer to it as y since we don't know the y coordinate just yet.

On the x axis, trace a vertical line through 4 (see related remark below).

Thus in red (see attached image).

The red line crosses the graph at the point (4,1)

so this tells us that,

                                          y = 1

Although it's helpful to see how it turns out, you are not need to draw a vertical red line.

You will be able to visually perceive the solution without these extra lines after you become accustomed to these kinds of situations.

Therefore,

If (4, y ) is an ordered pair of the function, then y = 1

                               y = 1

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Answer:

3

Step-by-step explanation:

if m is the number of months

Beckett: 90 + 25m

Lakota Hills 45 + 40m

so 90 + 25m = 45 + 40m

40m - 25 = 90 - 45

15m = 45

m = 45/15 = 3

Answer:

Step-by-step explanation:

triangles are similar so:

[tex]\frac{10}{10+14} = \frac{x}{36}[/tex]

24x=360

x=15

Answer: Options 3, 4, 6

Step-by-step explanation:

[tex]4x-y=6 \\\\-4x+y=-6\\\\y=4x-6[/tex]

This means are looking for lines with a slope of 4 (since parallel lines have the same slope).

Answer:

Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6

Step-by-step explanation:

Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6