Solve for x :

[tex] \sf \: \: \: \: \: \: \: \: \: \: \: 29x + x = 30[/tex]
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \tiny \sf bluh... \: \: so \: \: boring[/tex]
​

The probability of P(20s | Chocolate) and P(chocolate | 30s) x P(vanilla | 30s) will be 0.26 and 0.25, respectively.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Adults were polled to determine whether they preferred vanilla or chocolate ice cream. The survey findings for three age groups are displayed in the table.

There are 127 people who enjoy chocolate, and 33 of them are in their 20s is given as,

P(20s | Chocolate) = 33 / 127 = 0.26

There are 122 persons in their 30s, and 53 of them prefer chocolate 69 others prefer vanilla is given as,

P(chocolate | 30s) x P(vanilla | 30s) = 53/122 x 69/122 = 0.25

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Answer:

The function h(x) = -5√x is decreasing on the interval (–∞, 0) is true, Option A is correct.

A relation is a function if it has only One y-value for each x-value.

The given function h of x equals negative 5 times the square root of x.

h(x) = -5√x

The value of h(x) decreases as the value of x increases.

The function h(x) is a decreasing function over the interval (–∞, 0) because it is a negative function over the interval.

Hence, the function is decreasing on the interval (–∞, 0) is true.

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The expression for P(red) is (x - 5)/x

The given parameters are:

Apple = x

Green = 5

The number of red apples is:

Red = Apple - Green

This gives

Red = x - 5

The expression for P(red) is then calculated as:

P(Red) = Red/Apple

This gives

P(Red) = (x - 5)/x

Hence, the expression for P(red) is (x - 5)/x

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Answer:

the answer is C.64

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

because the

Answer:

$100

Step-by-step explanation:

It appears that each gift card costs $20, so 5 of them would be $20 * 5 gift cards = $100

Answer:

$100

Step-by-step explanation:

From the graph we see that each card costs $20.

In total 180 chairs are ordered for the cost $6000.

The total cost of chairs=$6,000.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Let x be the chairs ordered each at $20 and y be the chairs ordered each at $40.

Then equation will be 20x+40y=6000-------(1)

Given that, twice as many $20 chairs as $40 chairs were ordered.

That is 2x=y⇒2x-y=0--------(2)

Multiply equation (2) by 40.

That is 80x-40y=0--------(3)

By adding equation (2) and (3) we get

20x+40y+80x-40y=6000

⇒100x=6000

⇒x=60

Substitute x=60 in equation (2)

That is, 2x=y

⇒y=120

Total number of chairs=x+y=60+120=180 chairs.

Hence, in total 180 chairs are ordered for the cost $6000.

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Answer:

See below.

Step-by-Step Explanation:

5) 8x+9-6x-7

8x + 2 - 6x (Subtract the numbers)

2x + 2 (Combine like terms)

2 (x + 1)  (Common factor - Factor by grouping twice)

6) 2y-6+5y+9

2y + 3 + 5y (Add the numbers)

7y + 3 (Combine like terms)

7) 3x+8+4x-9

3x - 1 + 4x (Subtract the numbers)

7x - 1      (Combine like terms)

8) 9y+16-12y+24

9y + 40 - 12y (Add the numbers)

-3y + 40 (Combine like terms)

9) 7g-5-8g+12

7g + 7 - 8g (Add the numbers)

-g + 7 (Combine like terms)

10) 11c-8+5c-8

11c - 16 + 5c (Subtract the numbers)

16c - 16 (Combine like terms)

16 (c - 1)   (Common factor - Factor by grouping twice)

11) 5(2x + 3) (This one was a bit blurry, I am assuming that's a addition sign.)

10x + 15 (Distribute)

12) 5(-2x+3)

-10x + 15 (Distribute)

Hope this helps!

Answer: those are the answers its a long time.

Question  5  Answer: 2(x+1)

8x+9−6x−7

Multiply and combine like terms.

2x+2

Factor out 2.

2(x+1)

Questio 6 Answer : 7y + 3

2y−6+5y+9

Combine 2y and 5y to get 7y.

7y−6+9

Add −6 and 9 to get 3.

7y+3

Question 7  Answer: 3x+8+4x−9

Combine 3x and 4x to get 7x.

7x+8−9

Subtract 9 from 8 to get −1.

7x−1

Question 8 Answer: - 3y + 40

9y+16−12y+24

Combine 9y and −12y to get −3y.

−3y+16+24

Add 16 and 24 to get 40.

−3y+40

Question 9 Answer: -g + 7

7g−5−8g+12

Combine 7g and −8g to get −g.

−g−5+12

Add −5 and 12 to get 7.

−g + 7

Question 10 Answer: 16 ( c - 1 )

11c−8+5c−8

Combine 11c and 5c to get 16c.

16c−8−8

Subtract 8 from −8 to get −16.

16c - 16

Question 11 Answer: 10x +15

5(2x+3)

Use the distributive property to multiply 5 by 2x+3.

10x+15

Question 12 Answer: 15 - 10x

5(−2x+3)

Use the distributive property to multiply 5 by −2x+3.

−10x+15

The constant of proportionality is 0.1

Find the constant of proportionality (r)in the equation y=rx.

r =

x    y

14  1.4

16  1.6

21  2.1

The equation is given as:

y = rx

When x = 14 and y = 1.4, we have:

1.4 = r * 14

Divide both sides by 14

r = 0.1

Hence, the constant of proportionality is 0.1

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The surface area of the cylinder is 5969.03 cm²

The internal volume is 23156.68 cm³

Given:

A gas tank consists of a cylinder with a hemisphere on top.
The thickness of the metal is 1 cm
The overall height is 90 cm
The external diameter is 20 cm

To Find
a) the surface area of the tank

We will add the area of the bottom circle of radius 10 cm (counting the 1 cm thickness in), the external surface area of cylinder of height (90 - 10) cm =80 cm and radius 10 cm, and the surface area of the hemisphere of radius 10 cm.

So, the surface area of the cylinder is

[tex]\pi\times(10)^2+2\times\pi\times 10\times 80+ 2\times \pi \times (10)^2[/tex]
= π×(100+1600+200)

= π×(1900)

= 5969.03 cm²

b) To find the internal volume of the tank we find the internal volume of the hemisphere with an internal radius (10-1)=9 cm,
the internal volume of the cylinder of radius 9 cm and height (80-1) cm

= [tex]\frac{4}{3}\times \pi \times 9^3[/tex]+[tex]\pi\times 9^2\times 79[/tex]

= 23156.68 cm³

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A figure can be graphed on a coordinate plane as a set of points located on specific places, specified by  their coordinates.

The cartesian coordinate plane is an infinite 2 dimensional plane and each point of a cartesian plane is tracked by a location.

Now, the perpendicular distance of point from the horizontal axis and vertical axis are respectively usually named x-axis and y-axis. The location is then written as (a,b) where;

a is that point's shortest distance from the y-axis and called x-coordinate of that point.

b is that point's shortest distance from the x-axis, and called y-coordinate of that point.

Thus, those given geometric figures can be graphed on a coordinate plane as a set of points located on specific places, specified by  their coordinates.

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The maximum number of songs she can download while still remaining within her budget is x <= 21

The given parameters are:

One-time fee = $12.99

Rate = $0.65 per song

Budget = $27

The inequality is then represented as:

One-time fee + Rate * x <= Budget

So, we have:

12.99 + 0.65x <= 27

Subtract 12.99 from both sides

0.65x <= 14.01

Divide both sides by 0.65

x <= 21.55

Round down

x <= 21

Hence, the maximum number of songs she can download while still remaining within her budget is x <= 21

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Step-by-step explanation:

2y+9= 4

2y=-5

y=-5/2

y= -2and 1/2

Based on the calculations, the length of side AB is equal to 13.93 units.

Since the points of tangency are at A and B, we would determine the side length of the point lying between side A and D as follows:

AM = AD - BC

AM = 7 - 2

AM = 5 units.

Now, we can determine the length of side AB by applying Pythagorean's Theorem:

AB² = BM² + AM²

AB² = 13² + 5²

AB² = 169 + 25

AB = √194

AB = 13.93 units.

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Answer:

A) y = 1 - 2x

Step-by-step explanation:

Substitute the points given into all of the equations

Let's take point (1, -1)

A) y = 1 - 2x

-1 = 1 - 2(1)

-1 = 1 - 2

-1 = -1 ✓

B) y = -x - 1

-1 = -1 - 1

-1 =  -2 ✘

C) y = x - 2

-1 = 1 - 2

-1 = -1 ✓

D) y = 2x - 1

-1 = 2(1) - 1

-1 = 2 - 1

-1 = 1 ✘

So far, lines A and C can be possible solutions. Let's try point (2, -3)

A) y = 1 - 2x

-3 = 1 - 2(2)

-3 = 1 - 4

-3 = -3 ✓

C) y = x - 2

-3 = 2 - 2

-3 = 0 ✘

Thus, line A is the correct answer

Answer:

This point is not on the line, NOT TRUE

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

           b represents the y-intercept

where the format of a point is (x, y)

Given: y = 7x (6/7, -1/4)

we can plug in the point (6/7, -1/4)

-1/4 = 7(6/7)

-1/4 = 6

-1/4 does not equal 6 so this point is not on the line

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definetly not a

Step-by-step explanation:

because it is an incompetent answer

Answer:

A ≈ 22.2 ft²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{50}{360}[/tex]

   = π × 7.13² × [tex]\frac{5}{36}[/tex]

    = 50.8369π × [tex]\frac{5}{36}[/tex]

    ≈ 22.2 ft² ( to the nearest tenth )

72

x varies directly as y

hence x=k y

k=6

y=12

x=6×12

x=72

Answer:

45

Step-by-step explanation:

Solution :-

Here we have been given with two equations :

¤ From Equation No.1 :

>> x = -5y

¤ In Equation No.2 :

Substituting the value of x which we got above as -5y here.

>> 3y + 2(-5y) = -21

>> 3y + 2 × (-5y) = -21

>> 3y - 10y = -21

>> -7y = -21

>> 7y = 21

>> y = 21 / 7

>> y = 3

¤ Finding out value of x :

>> x = -5y

>> x = -5(3)

>> x = -15

Answer:

135

Step-by-step explanation:

Depending on where you start, the protractor can read in different ways. Since the measure of this angle started from the left, you read the numbers at the top. If the measure would have started from the right, you read the numbers below.

A good rule of thumb is that if the angle appears to be greater than 90 degrees, or an obtuse angle, you would choose the only answer choice that is above 90 degrees.

Hope this helps!

Answer:

Step-by-step explanation:

m∠5 + m∠6 = 180° - This is true because the exterior angle and interior angle form a linear pair, and are thus supplementary.

m∠2 + m∠3 = m∠6 - This is true by the exterior angle theorem.

m∠2 + m∠3 + m∠5 = 180° - This is true because the interior angles of a triangle add to 180 degrees.

The three right options are:

m∠5 ₊ m∠6 = 180° which represents a linear pair.

∠2 ₊ ∠3 = ∠6 showing the exterior angle property of triangle.

m∠2  m∠3  m∠5 = 180° as the sum-triangle

sum-triangleproperty.

Given,

the interior angles of the triangle are 2,3,5

the exterior angle at ∠2 is ∠1.

the exterior angle at ∠3 is ∠4.

the exterior angle at ∠5 is ∠6.

Now, take into account a triangle with external angles as ∠1 , ∠4 and ∠6.

Apply the exterior angle property of a triangle.

The sum of the opposing internal angles determines the outer angle of a triangle.

For exterior ∠1 we get

∠1 = ∠5 ₊ ∠3

Similarly, for exterior ∠4 we get

∠4 = ∠5 ₊ ∠2

Then for exterior ∠6 we get

∠6 = ∠2 ₊ ∠3

∴ through the exterior angle property we get the correct option as

m∠6 = m∠2 ₊ m∠3

Now we know the sum-triangle property that sum of the angles in triangle is equal to 180°

∴ m∠2 ₊ m∠3 ₊ m∠5 = 180°

We know the linear pair property i.e, If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.,

∴ m∠5 ₊ m∠6 = 180°

Hence we get the statements which match the diagram are:

m∠5 ₊ m∠6 = 180°

m∠2 ₊ m∠3 ₊ m∠5 = 180°

m∠6 = m∠2 ₊ m∠3

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Range is the set of all values which the given function can output. The correct option is A.

Since y is the output for the given function, and the only outputs that can be seen for the function are 0, 2, and 4. Therefore, the range of the function is {0,2,4}.

Hence, the correct option is A.

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Answer:

See below

Step-by-step explanation:

4(x + 5) = 9x + 4x − 34

4x + 20 = 9x + 4x − 34   [Distributive]

4x + 20 =  13x − 34         {Combine Like Terms]

4x - 13x + 20 = 13x - 13x − 34  [Subtractive:  -13x both sides]

-5x + 20 = - 34            [Combine Like Terms]

-5x + 20 - 20 = -34 - 20     [Subtractive:  - 20 both sides]

-5x  = -54               [Combine Like Terms]

x = -54/-5             [Division Property:  divide both sides by -5]

x =  - 10 4/5            

An expression can either be an equation or an inequality.

The correct classification of the terms are:

Expression; 4x+20

Inequality: 4x+20>40

Equation: 4x+20=40

We have given that,

{20,18,8,18,10,8,4}

{12,14,16,20,4,8,10}

{12,16,4,20,8,6,8}

To determine the correct classification, we make use of the following highlights

When an expression has the =, then the expression is an equation.

When an expression has any of the following signs>, <, >=, <= or != , then the expression is an inequality.

When the expression is neither an equation nor an inequality, then it is just an expression.

Hence, the correct classifications are:

Expression; 4x+20

Inequality: 4x+20>40

Equation: 4x+20=40

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Answer:

  (a)  Horizontal line test

Step-by-step explanation:

A relation that is a function already passes the vertical line test. If it has an inverse function, that function must also pass the vertical line test.

The inverse relation will be the same graph reflected across the line y=x. That is, points that are horizontally aligned on the relation graph become vertically aligned on the inverse relation graph.

If the inverse relation is to be a function, then there must be no points on its graph that are vertically aligned. This requirement translates to the requirement that there be no horizontally-aligned points on the graph of the original relation. The "horizontal line test" checks for horizontally aligned points. If there are none, the test is said to pass.

A function will have an inverse function if it passes the Horizontal Line Test.

__

Additional comment

The attached graph shows a function (red curve) that does not pass the horizontal line test. Its inverse relation is the green curve, which you can see is not a function. It does not pass the vertical line test.

The line y=x is shown (dashed orange) so you can see the symmetry of the function and its inverse.

Answer:

r = 5

Step-by-step explanation:

The zeroes ( where the function intersects the x - axis) are equi-distant from the vertex line of symmetry

vertex 2,4      to  get to  -1 , 0    you have to go three units in the negative x direction .....  the other zero is on the OTHER side of the vertex 3 units which would be    5,0       so   r  = 5

Here is a graph to look at: