Two-thirds of a number x is at least 10. Find the smallest possible prime number x.

Answer: x = 15

Step-by-step explanation:

The formula for calculating the sum of the interior angles of a regular polygon is: (n - 2) × 180°. Where n is number of sides.

sum of angles = (n - 2) × 180

sum of angles = (7 - 2) × 180

sum of angles = 5 × 180

sum of angles = 900°

Now to find the value of x, we have to set each of the interior angles, added up, equal to 900°:

7x + 1 + 10x + 6x + 7 + 10x - 9 + 9x + 4 + 8x + 10 + 9x + 2 = 900

Combine like terms:

(7x + 10x + 6x + 10x + 9x + 8x + 9x) + (1 + 7 - 9 + 4 + 10 + 2) = 900

59x + 15 = 900

59x + 15 - 15 = 900 - 15                     subtract 15 from both sides

59x = 885                                  

59x/59 = 885/59                               divide by 59 on both sides

x = 15

Answer:

#3 5(2a+4)

#4 5(a+2+4)

#5 5a+5(2+4)

Step-by-step explanation:

I think so, I am probably wrong

Hi

the trick is to define price by referring only to one item.  

Here the bootle of water is you reference.  

there is 3 gallons  of milk

             6 bottles of water

              6 bags of chips

let's call bottle of water  " X"  

water cost  = X

milk = X+1.7

chips =  X/2

So we have  :  

3 (X+1.7 ) + 6X + 6 ( X/2) = 29.1

3X+ 5.1 + 6X + 6X/2 = 29.1

3X +6X + 3X + 5.1 = 29.1

 12X +5.1 = 29.1

  12X = 29.1 - 5.1

   12 X =  24

        X = 24/12

        X = 2

price of bottle is  2 dollars  

then milk is  2 + 1.7 = 3.7

        chips =  2/2 = 1

let's check =  3*3.7 + 6*2 + 6*1 =   11.1+12+ 6 = 29.1

In around 6.35 years, the population will be 1 million.

The population is modeled by the exponential equation:

[tex]P(t) = 232,012*e^{0.23*t}[/tex]

Then we just need to solve the equation for t:

[tex]P(t) = 232,012*e^{0.23*t} = 1,000,000[/tex]

Let's solve that:

[tex]232,012*e^{0.23*t} = 1,000,000\\\\e^{0.23*t} = 1,000,000/232,012 = 4.31\\[/tex]

If we apply the natural logarithm to both sides:

[tex]ln(e^{0.23*t}) = ln(4.31)\\\\0.23*t = ln(4.31)\\\\t = ln(4.31)/0.23 = 6.35[/tex]

So in around 6.35 years, the population will be 1 million.

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The total amount of the deposit is  $592.92.

The total amount of the deposit can be determined by adding all the money deposited together.

(47 x 1) + (22 x 5) + (9 x 10) + (17 x 20) + (67 x 0.01) + (0.05 x 12) + (9 x 0.1) + (15 x 0.25)

47 + 110 + 90 + 340 + 0.67 + 0.60 + 0.9 + 3.75 = $592.92

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Presumably you mean the equation

[tex]\dfrac{13z}{z+1} = 11-3i[/tex]

Observe that for [tex]z\neq-1[/tex],

[tex]\dfrac{13z}{z+1} = \dfrac{13(z+1) - 13}{z+1} = 13 - \dfrac{13}{z+1}[/tex]

so we can simplify the equation to

[tex]13 - \dfrac{13}{z+1} = 11 - 3i \implies \dfrac{13}{z+1} = 13 - (11 - 3i) = 2+3i[/tex]

Multiply both sides by [tex]\frac{z+1}{2+3i}[/tex].

[tex]\dfrac{13}{z+1}=2+3i \implies \dfrac{13}{2+3i} = z+1 \implies z = \dfrac{13}{2+3i} - 1[/tex]

Rationalize the denominator by introducing its complex conjugate.

[tex]z = \dfrac{13(2-3i)}{(2+3i)(2-3i)} - 1 = \dfrac{26-39i}{2^2+3^2} - 1 = \boxed{1 - 3i}[/tex]

The reason why the expression x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c is because they follow the FOIL Technique

We want to explain why x² + (p + q)x + pq leads to the need to determine integers that add to b and have a product c.

Now, using the FOIL Technique we can say that the factors are;

(x + p)(x + q)

Expanding this gives;

x² + px + qx + pq

⇒ x² + (p + q)x + pq

Now, applying that to the trinomial; x² + 6x + 8, we can say that;    

p + q = 6, and pq = 8

Thus, solving simultaneously gives;

p = 2 and q = 6.

Thus;

x² + 6x + 8 = (x + 2)(x + 6)

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The adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]

The matrix is given as:

[tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex]

For a matrix A be represented as:

[tex]A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

The adjoint is:

[tex]Adj = \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]

Using the above format, we have:

[tex]Adj = \left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]

Hence, the adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]

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8. The length of the support is 7. 9 m

9. The length of the conveyer is 12m

3. a = 59m

A = 44°

B = 52°

4. c = 88. 6 mm

b = 49. 1 m

B = 34°

8. We have the angle to be 20 degrees

Opposite side = x

hypotenuse = 23m

Using the sine ratio

sin θ = opposite/ hypotenuse

[tex]sin 20 = \frac{x}{23}[/tex]

Cross multiply

[tex]sin 20[/tex] × [tex]23 = x[/tex]

[tex]x = 0. 3420[/tex] × [tex]23[/tex]

x = 7. 9 m

The length of the support is 7. 9 m

9. The angle of elevation is 37. 3 degrees

Hypotenuse = 19 . 0m

Opposite = x

Using the sine ratio

sin θ = opposite/ hypotenuse

[tex]sin 37. 3 = \frac{x}{19}[/tex]

cross multiply

[tex]x = 0. 6059[/tex] × [tex]19[/tex]

x = 11.5

x = 12 m in 2 significant figures

The length of the conveyer is 12m

3. To determine the sides and angles, we use the sine rule;

[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]

For side a, we use the Pythagorean theorem

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

[tex]85^2 = a^2 + 67^2[/tex]

[tex]a = \sqrt{89^2-67^2}[/tex]

[tex]a = \sqrt{3432}[/tex]

a = 58. 58, a = 59m

To find angle A and B, use the sine rule

[tex]\frac{59}{sin A } = \frac{85}{sin 90}[/tex]

cross multiply

[tex]sin A[/tex] × [tex]85[/tex] = [tex]sin 90[/tex] × [tex]59[/tex]

make sin A subject of formula

[tex]sin A = \frac{59}{85}[/tex]

[tex]sin A = 0. 6941[/tex]

A = [tex]sin^-^1(0. 6941)[/tex]

A = 44°

[tex]\frac{67}{sin B} = \frac{85}{sin 90}[/tex]

cross multiply

[tex]sin B[/tex] × [tex]85[/tex] = [tex]sin 90[/tex] × [tex]67[/tex]

make sin b subject of formula

[tex]sin B = \frac{67}{85}[/tex]

[tex]sin B = 0. 7882[/tex]

B = [tex]sin^-^1( 0. 7882)[/tex]

B = 52°

4. To find the sides, we use the sine rule;

[tex]\frac{74. 0}{sin 56. 6} = \frac{c}{sin 90}[/tex]

Cross multiply

[tex]sin 56. 6[/tex] × [tex]c = sin 90[/tex] × [tex]74[/tex]

make 'c' subject of formula

[tex]c = \frac{74}{0. 8348}[/tex]

c = 88. 6 mm

To find length b, we use the Pythagorean theorem

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

[tex]b^2 = c^2 - a^2[/tex]

[tex]b^2 = 88. 8^2 - 74^2[/tex]

[tex]b = \sqrt{7885. 44 - 5476}\\\\ b = \sqrt{2409. 44}[/tex]

b = 49. 1 m

[tex]\frac{74. 0}{sin 56. 6} = \frac{49. 1}{sin B}[/tex]

cross multiply

[tex]sin B = \frac{40. 99}{74. 0}[/tex]

B = [tex]sin^-^1(0. 5539)[/tex]

B = 34°

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Simply put, cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.

Cultural identity can be defined as the self-perception of an individual which gives them a sense of belonging to an identical group that shares same qualities which may included music, food, traditions, social class, beliefs, ethnicity, among others.

In summary, we can say that cultural identity is what identifies one with a group of shared identities such as music, traditions, among others.

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The pieces of information that is provided by the box plots are the median and first quartile.

The piece of information that is not provided by the box plots is the mean.

The interquartile range is 22.50.

An outlier would distort the values of the median and the quartiles.

A box plot is used to study the distribution and level of a set of scores. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median.  The third line on the box represents the upper (third) quartile. The difference between the quartiles is the interquartile range.

Interquartile range = 60 - 37.50 = 22.50

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The value of x such that the vertices 3x + 10 and x + 60 are equal is 25

Vertices are the endpoints or corners of a shape (such as triangle, square, rectangle and related shapes)

The two vertices are given as:

3x + 10 and x + 60

The condition on the two vertices are not given.

So, we assume that the vertices are equal (as in the base angles of an isosceles triangle)

So, we have the following equation

3x + 10 = x + 60

Subtract x from both sides of the equation

2x + 10 = 60

Subtract 10 from both sides of the equation

2x = 50

Divide both sides of the equation by 2

x = 50/2

Evaluate the quotient

x = 25

Hence, the value of x such that the vertices 3x + 10 and x + 60 are equal is 25

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Answer:

(-∞, -1) U (0, ∞)

Step-by-step explanation:

To figure out which parts of the function are decreasing, we need to read the graph left to right.

Given this information, we can figure out that the first part of the graph is decreasing, starts to go up a little bit, and then starts to decrease again.

How do we write this in mathematical terms, however? We simply take the x-values for which parts it decreases.

The graph started on negative infinity, and kept decreasing until -1 on the x-axis. We can write this as (-∞, -1). The graph starts to increase, which is not relevant to the question. As it starts to decrease again, it starts on 0, and slowly decreases to the right, meaning that it is going towards positive infinity. We can write this as (0,∞).

Now that we have both parts of the decreasing function, we can combine them using the union symbol (∪).

Therefore, our final answer is (-∞, -1) U (0, ∞).  

The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.

The graph represents a parabola.

The graph can be a function if it passes the vertical line test.

The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.

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Since the x-coordinates are equal, hence the equation of the line will be x =4

The equation of a line in slope-intercept form is expressed as:

y = mx + b

where

m is the slope

b is the intercept

From the given coordinate points (four, three) and (four, negative two), we can see that the x-coordinates are equal, hence the equation of the line will be x =4

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Answer:

6 x 2 x 2 x 1

Step-by-step explanation:

6 x 2 = 12

12 x 2 = 24

24 x 1 = 24

The sum of the given expression is 6b^2+8b-15

Given the following expression

(6b^2+5)+(8b-20)

We are to take the sum. On expansion;

6b^2+5 + 8b-20

Collect the like terms

6b^2+8b +5 - 20

6b^2+8b-15

Hence the sum of the given expression is 6b^2+8b-15

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El valor del número A es 692.31.

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:

[tex]\frac{50}{100} =0.5*100=50%[/tex]

The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks  etc.

The exercise asks you the value of A and it gives you the value (900) that represents 130%A. Thus, you should write an equality between the division the percentage and the variable A by 100 with the value 900.

You should follow the steps below.

[tex]\frac{130*A}{100}=900\\ \\ 130A=90000\\ \\ A=\frac{90000}{130} =692.31[/tex]

You can check the result : [tex]\frac{692.31*130}{100} =\frac{90000.3}{100} =900.003=900[/tex]

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Answer:

$22 * (20) + $18 * (48) = $1304

Step-by-step explanation:

There are 20 reserved seats so it would be: $22 * 20 = $440 for all reserved seats

There are 28 general admission tickets more than reserved seats ticket so number of general admission tickets is: 20 + 28 = 48 (tickets)

Each general admission tickets cost $18, so: $18 * 48 = $864  for all general admission tickets

So the total money was paid for all of the tickets is: $440 + $864 = $1304

The standard deviation of the number of defective candles in the group is 0.9277.

When a random variable X follows a binomial distribution, with the sample size n, and the proportion of success is p, then the standard deviation is calculated as:

σ = √{np(1-p)}.

In the question, we are given that off the production line, there is a 2.2% chance that a candle is defective.

We are asked if the company selected 40 candles off the line, then what is the standard deviation of the number of defective candles in the group.

Assuming the occurrence of a defective bulb as success, we get the proportion of success, p = 2.2% or 0.022, and the sample size, n = 40.

Thus, we can calculate the standard deviation of the number of defective candles in the group as:

σ = √{np(1-p),

or, σ = √{40*0.022*(1 - 0.022)} = √0.86064 = 0.9277.

Thus, the standard deviation of the number of defective candles in the group is 0.9277.

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The expressions are illustrated below.

3x = 12

x = 12/3

x = 4

x + 4 = 17

x = 17 - 4

x = 13

9y + 3 = 21

9y = 21 - 3

9y = 18

y = 18/9

y = 2

x ÷ 2 = 4

x = 4 × 2

x = 8

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Using slopes, the table that could represent Relationship B is the second table.

The slope of a relationship is given by the change in y divided by the change in x.

For relationship A, we have points (2,3) and (4,6), hence the slope is:

mA = (6 - 3)/(4 - 2) = 3/2 = 1.5.

Then, the slopes in the table are given as follows:

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The measure of the indicated angle to the nearest degrees is 23 degrees.

The angle of a right angle triangle can be found as follows:

Therefore, the angle can be found using trigonometric ratios as follows;

cos ∅ = adjacent / hypotenuse

Therefore,

adjacent side = 35 units

hypotenuse side = 38 units

Hence,

cos ∅ = 35 / 38

∅ = cos⁻¹ 0.92105263157

∅ = 22.9272842944

∅ ≈ 23 degrees.

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[tex]\large\displaystyle\text{$\begin{gathered}\sf 5(3+6)x^{2} -6x^{2} \end{gathered}$}[/tex]

Add 3 and 6 to get 9.

Multiply 5 and 9 to get 45.

Combine 45x² and −6x² to get 39x².

Answer:

Step-by-step explanation: 23000 milligrams

The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of children and y represent the number of adult, hence:

5.2x + 9.9y = 1303.5     (1)

Also:

x + y = 163    (2)

From both equations:

x = 66, y = 97

The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.

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Answer:

Step-by-step explanation:

B :10/(x+1)  +5