The experiment is to roll a six-sided did with the dots

In the given geometric series, the common ratio is 5. The value of n, which indicates the term number, is found to be 4 by setting up and solving an equation based on the general formula for the nth term in a geometric series.

The series presented is a geometric series. In a geometric series, each term is multiplied by a common ratio to get the next term. In this case, the common ratio is 5 because each term is obtained by multiplying the previous term by 5.

In a geometric series, the general formula for the nth term is a * r^(n-1), where a is the first term and r is the common ratio. Hence, let's set up the nth term equation and solve for n.

500 = 4 * 5^(n-1)

When we solve the equation, we find that the value of n is 4.

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Answer:

[tex]x_1=4.158[/tex]

[tex]x_2=0.8416[/tex]

Step-by-step explanation:

For an equation of the form [tex]ax^2 +bx +c[/tex]

The quadratic formula is

[tex]\frac{-b\±\sqrt{b^2 -4ac}}{2a}[/tex]

In this case the equation is:

[tex]2x^2 - 10x + 7 = 0[/tex]

Then

[tex]a= 2\\b= -10\\c= 7[/tex]

Therefore, using the quadratic formula we have:

[tex]x=\frac{-(-10)\±\sqrt{(-10)^2 -4(2(7)}}{2(2)}[/tex]

[tex]x=\frac{5\±\sqrt{11}}{2}[/tex]

[tex]x_1=4.158[/tex]

[tex]x_2=0.8416[/tex]

ANSWER

[tex]x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2} [/tex]

EXPLANATION

The given quadratic equation is:

[tex] 2{x}^{2} - 10x + 7 = 0[/tex]

Comparing this equation to

[tex] a{x}^{2} + bx + c = 0[/tex]

we have

a=2, b=-10 and c=7.

The solution is given by the quadratic formula;

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

We plug in the values to get,

[tex]x = \frac{ - - 10 \pm \sqrt{ {( - 10)}^{2} - 4(2)(7) } }{2(2)} [/tex]

This implies that

[tex]x = \frac{ 10 \pm \sqrt{ {100} - 56 } }{4} [/tex]

[tex]x = \frac{ 10 \pm \sqrt {44 } }{4} [/tex]

[tex]x = \frac{ 10 \pm 2\sqrt {11 } }{4} [/tex]

[tex]x = \frac{ 5 \pm \sqrt {11 } }{2}[/tex]

[tex]x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2} [/tex]

answer : (A) q>p , where p= jacks pet is a pig and q= jacks pet cannot fly

The converse of an implication reverses the order of the original statement. Therefore, the converse of 'If Jack’s pet is a pig then Jack’s pet cannot fly' is 'If Jack's pet cannot fly, then Jack's pet is a pig'.

In this problem, we're dealing with a form of logical statement known as an implication, which can be symbolized as p → q. In the original statement, 'If Jack’s pet is a pig (p) then Jack’s pet cannot fly (q)', the implication is that being a pig causes or results in the inability to fly. The converse of an implication reverses the order of the original statement, so 'if q then p'. Therefore, the converse of the given statement would be 'If Jack's pet cannot fly, then Jack's pet is a pig', or symbolically represented as q → p.

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Answer:

13.2 ft.

Step-by-step explanation:

In the given ΔABC

tanA = [tex]\frac{Height}{Base}[/tex] = [tex]\frac{BC}{AB}[/tex]

tan 31° =[tex]\frac{x}{22}[/tex]

x = 22 tan 31°

  = 22 × (0.6009)

  = 13.22 ≈ 13.2 ft.

Answer:

On the left is a 30 60 90 triangle so the height = 10 / 2 = 5 feet

Area of triangle = (5 * 8.7) / 2 = 21.75 sq feet

Area of Rectangle = 12 * 5 = 60 sq feet

TOTAL Area = 21.75 + 60 = 81.75 square feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

Final answer:

The sum 42 + 24 can be expressed as 24 + 42 using the commutative property of addition, or by decomposing into tens and units for easier mental calculation.

Explanation:

The student is asking for another way to express the sum 42 + 24. One way to approach this is by performing a common mathematical technique known as commutation (or the commutative property of addition), which states that numbers can be added in any order and the sum will remain the same.

So, another way to express 42 + 24 would be 24 + 42. You can also decompose the numbers into tens and units to simplify mental calculation: (40 + 20) + (2 + 4) = 60 + 6 = 66. This demonstrates that there are multiple ways to approach addition, making it easier to perform in my head. Thus, we affirm that mathematics indeed offers many paths to the same answer.

Answer:

110

Step-by-step explanation:

2=80 and 3=30

2+3=ac=110

Answer:

Option B. 110°

Step-by-step explanation:

In the given circle m ∠1 = 100°

m BC = 30°

Then we have to find the measure of m AC

Since ∠1 = 100°

and ∠1 + ∠2 = 180° [supplementary angles]

100 + ∠2 = 180°

∠2 = 180° - 100°

∠2 = 80°

Now we know ∠3 = 15°

and m AC = ∠2 + ∠3

m AC = 80 + 30 = 110°

Therefore, Option B. 110° will be he answer.

Answer:

Third Option

[tex]f(x) = 4x,\ g(x)=\frac{1}{4}x[/tex]

Step-by-step explanation:

For a function f(x) it is satisfied that the range of f(x) is equal to the domain of its inverse function. In the same way the domain of f(x) is equal to the range of its inverse.

Therefore, to verify which pair of functions are inverse to each other, perform the composition of both functions and you must obtain

[tex]f(g(x)) = x[/tex]  and   [tex]g(f(x)) = x[/tex]

For the first option we have:

[tex]f(x) = x,\ g(x)=-x[/tex]

Then

[tex]f(g(x)) = (-x) = -x[/tex]  They are not inverse functions

For the second option we have:

[tex]f(x) = 2x,\ g(x)=-\frac{1}{2}x[/tex]

Then

[tex]f(g(x)) = 2(-\frac{1}{2}x) = -x[/tex]  They are not inverse functions

For the third option we have:

[tex]f(x) = 4x,\ g(x)=\frac{1}{4}x[/tex]

Then

[tex]f(g(x)) = 4(\frac{1}{4}x) = x[/tex]

[tex]g(f(x)) = \frac{1}{4}(4x) = x[/tex] They are inverse functions

For the fourth option we have:

[tex]f(x) = -8x,\ g(x)=8x[/tex]

Then

[tex]f(g(x)) = -8(8x) = -64x[/tex]  They are not inverse functions

Answer:

x=.5x

25 miles

Step-by-step explanation:

Answer:

17.6 ounces per 500 g

Step-by-step explanation:

Knowing one ounce equals 28.34 g, all we have to do is divide half a kilo (500 g) by the equivalent of an ounce to get the number of ounces in a kg.  So,

O = 500 g / 28.34g/ounce = 17.64 ounces

We round that to the nearest tenth... to get 17.6 ounces per 500 g

Converting between metric and imperial/US system is always complicated.

Answer:

0.5 kilograms (kg) is equal to 17.6 ounces

Step-by-step explanation:

We have

                    1 kg = 35.274 ounces

                   0.5 kg = 0.5 x 35.274 = 17.637 ounces

Rounding to nearest tenth

              0.5 kg = 17.637 ounces   = 17.64 ounces = 17.6 ounces

So we have 0.5 kilograms (kg) is equal to 17.6 ounces    

Hello There!

The correct answer would be "B" this is because we are taking 6 and multiply it by our x column which is the "in" column and adding 1 to what we get.

Answer:

The Correct answer is (B) or option 2.

Answer:

d.

Step-by-step explanation

it is a random variable but is continuos as it doesn't change.

Answer:

Height of 10 years olds

Step-by-step explanation:

A p e x

Answer:

The answer is C.

Step-by-step explanation:

The integer form is 60 as the answer

Kwan would have 6.75 crayons in each box

Answer:

the answer is 8 because...

Step-by-step explanation:

You forgot to put in that he LOST 5 crayons. He has 27 AFTER he lost the five. using inverse operations we would add 5 to 27 to get 32, and then we divide that by the number of boxes he had, we get 8.

Answer:

[tex]\large\boxed{-8x^2-(8x-6x^2-8x)-[7-(-8x-7)]=-2x^2-8x-14}[/tex]

Step-by-step explanation:

[tex]-8x^2-(8x-6x^2-8x)-[7-(-8x-7)]\\\\=-8x^2-8x-(-6x^2)-(-8x)-[7-(-8x)-(-7)]\\\\=-8x^2-8x+6x^2+8x-(7+8x+7)\\\\=-8x^2-8x+6x^2+8x-7-8x-7\qquad\text{combine like terms}\\\\=(-8x^2+6x^2)+(-8x+8x-8x)+(-7-7)\\\\=-2x^2-8x-14[/tex]

B) dilation

this transformation changes the shape's size (making it smaller/larger) whilst the others keep the shape congruent (same shape, same size)

When two shapes are similar but not congruent, it means the transformations performed on the shapes is non-rigid. The transformation that Michael can use to obtain a non-congruent triangle for is (b) dilation.

A non-rigid transformation is such that changes the side lengths of a shape. An example is dilation.

Because the resulting triangle [tex]\triangle A'B'C'[/tex] must not be congruent, then, Michael can dilate the original [tex]\triangle ABC[/tex] to give the new triangle [tex]\triangle A'B'C'[/tex]

See attachment for an illustration of dilation

Hence, (b) is correct

Read more about transformations at:

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Answer:

The equation would be:

(X+1)^2 + (y-1)^2 = 9

This is the equation of the circle in general form.  

[tex]\[ x^2 + y^2 + 2x - 2y - 7 = 0 \][/tex]

or

[tex]\[ (x + 1)^2 + (y - 1)^2 = 9 \][/tex]

To write the equation of a circle in general form, you start with the standard form of the circle's equation, which is:

[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]

where \( (h, k) \) is the center of the circle and \( r \) is the radius.

From the information provided:

- The center of the circle is \( (-1, 1) \)

- The radius of the circle is \( 3 \) units

Let's substitute these values into the standard form:

[tex]\[ (x - (-1))^2 + (y - 1)^2 = 3^2 \][/tex]

[tex]\[ (x + 1)^2 + (y - 1)^2 = 9 \][/tex]

Now, to write it in general form, you'll expand the equation and combine like terms:

Step 1: Expand the squares

[tex]\[ (x + 1)^2 = x^2 + 2x(1) + 1^2 \][/tex]

[tex]\[ (y - 1)^2 = y^2 - 2y(1) + 1^2 \][/tex]

Step 2: Write the expanded form

[tex]\[ x^2 + 2x + 1 + y^2 - 2y + 1 = 9 \][/tex]

Step 3: Combine like terms

[tex]\[ x^2 + y^2 + 2x - 2y + 1 + 1 = 9 \][/tex]

Step 4: Move the constant to the right side

[tex]\[ x^2 + y^2 + 2x - 2y = 9 - 2 \][/tex]

Step 5: Final general form

[tex]\[ x^2 + y^2 + 2x - 2y - 7 = 0 \][/tex]

This is the equation of the circle in general form.

Both triangles have 2 side lengths labeled and a common angle ( shown by the curved lines).

You could use the SAS Similarity theorem.

Answer:

Step-by-step explanation:

This was the answer that was right for me, I just did this question :) Hope this helps!

ANSWER

c.

[tex]5{e}^{i \frac{5\pi}{3} }[/tex]

EXPLANATION

The exponential form of complex numbers is given by;

[tex]z =r {e}^{i \theta} [/tex]

The given complex number in polar form is:

[tex]5( \cos( \frac{5\pi}{3} + i \sin( \frac{5\pi}{3}) ) [/tex]

We have r=5 from the question and

[tex] \theta = \frac{5\pi}{3} [/tex]

We substitute these values to obtain the exponential form:

[tex]z =5{e}^{i \frac{5\pi}{3} }[/tex]

The correct answer is C

Answer: the first answer

| 2 1/5 - 4.35 |

Step-by-step explanation:

this is the integer of the answer. not a negative of it.

[tex]\bf x^2=0.0025\qquad \textit{let's convert the decimal to a fraction} \\\\[-0.35em] ~\dotfill\\\\ 0.\underline{0025}\implies \cfrac{00025}{1\underline{0000}}\implies \cfrac{25}{10000} \\\\[-0.35em] ~\dotfill\\\\ x^2=0.0025\implies x^2=\cfrac{25}{10000}\implies x=\sqrt{\cfrac{25}{10000}}\implies x=\cfrac{\sqrt{25}}{\sqrt{10000}} \\\\\\ x=\cfrac{5}{100}\implies x=\cfrac{1}{20}[/tex]

The expression -4x^2(3x - 7) simplifies to -12x^3 + 28x^2 after distributing -4x^2 across the parentheses and performing the necessary multiplications.

The expression to be simplified is -4x^2(3x - 7).

To simplify the expression, you need to distribute the term -4x^2 across the parentheses. This involves two multiplication steps:

Multiply -4x^2 by -7 to get +28x^2.

After performing these multiplications, the expression simplifies to -12x^3 + 28x^2.

Answer:

The area of the walls is [tex]2,160\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of the walls is equal to the perimeter of the conference room multiplied by the height of the ceiling

so

[tex]A=2[40+50](12)=2,160\ ft^{2}[/tex]

ANSWER

D.

[tex]x = \frac{ - ( - 9 )\pm \sqrt{ {( - 9)}^{2} - 4(2)(4)} }{2(2)} [/tex]

EXPLANATION

The given equation is

[tex]2 {x}^{2} - 9x + 4 = 0[/tex]

When we compare this to:

[tex]a{x}^{2} + bx + c = 0[/tex]

we have a=2, b=-9, and c=4.

The quadratic formula is given by,

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

We substitute the values into the formula to get,

[tex]x = \frac{ - ( - 9 )\pm \sqrt{ {( - 9)}^{2} - 4(2)(4)} }{2(2)} [/tex]

The correct choice is D

Answer:

A rigid transformation includes only rotation and translation.

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

5/4 can only be greater than 1.

Answer:

Point D is located at 5/4 on the number line. Hope this helps

Answer:

x = 14

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value of sin45°

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex]

Hence

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7\sqrt{2} }{x}[/tex]

Multiply both sides by x

x × sin45° = 7[tex]\sqrt{2}[/tex] ( divide both sides by sin45° )

x = [tex]\frac{7\sqrt{2} }{sin45}[/tex]

  = [tex]\frac{7\sqrt{2} }{\frac{\sqrt{2} }{2} }[/tex]

  = 7[tex]\sqrt{2}[/tex] × [tex]\frac{2}{\sqrt{2} }[/tex] = 7 × 2 = 14

Answer is: 213, 278 , 108, 213, 157

213 is repeated 2 times; more than any other number.

A number that appears most often is the mode.

Answer:

213, 278, 108, 213, 157

Step-by-step explanation:

The mode is the number with the highest frequency in a given list of data. Simply, it is the number with most occurrence.

Now, let us chart the frequency of each numbers in the list provided:

1........ 111, 108, 213, 198, 205

Arrange in ascending order

108, 111, 198, 205 and 213

Numbers Frequency

108 1

111 1

198 1

205 1

213 1

No modal value

2..... 212, 215, 213, 211, 220

Arranging in ascending order:

211, 212, 213, 215 and 220

Numbers Frequency

211 1

212 1

213 1

215 1

220 1

No modal value

3......213, 278, 108, 213, 157

Arranging in ascending order:

108, 157, 213 and 278

Numbers Frequency

108 1

157 1

213 2

278 1

The mode here is 213. It has a frequency of 2 compared to other numbers whose mode is 1

4........ 210, 200, 213, 221, 221

Arranging in ascending order:

200, 210, 213, 221

Numbers Frequency

200 1

210 1

213 1

221 2

The mode here is 221