How many solutions are in 18+6x=20+6x

Answer:

P(A) = 13/18

P(B) = 7/18

Step-by-step explanation:

A) Sum greater than 5

If the sum needs to be >5, then it can be 6, 7, 8, 9, 10, 11, and 12.

There are 26 out of 36 events where the sum is >5, thus P(A) = 26/36 = 13/18.

B) Sum divisible by 4 or 6

The sum ranges from 2 to 12, there are two methods to calculate this:

B1) Method 1: Calculate the frequency one by one

The sums divisible by 4 or 6 are S = {4, 6, 8, 12}. There are 9 of them, n(S) = 14. Thus P(B) = 14/36 = 7/18.

B2) Method 2: Use the rule of not mutually exclusive events

Not mutually exclusive events (might also be called mutually inclusive) happens when two events can happen together at the same time. In this problem, the sum might be divisible by 4 and 6 at the same time, i.e. the number 12.

The common formula for not mutually exclusive events is P(A∪B) = P(A) + P(B) - P(A∩B). Nb: P(A) isn't talking about the previous problem, nor does P(B) talk about the second section as a whole; the terms P(A) and P(B) will be utilized next, explained with their uses.

P(A) = probability of the sum being divisible by 4, i.e. the number 4, 8 and 12

P(A) = (3+5+1) / 36 = 9/36 = 1/4

P(B) = probability of the sum being divisible by 6, i.e. the number 6 and 12

P(B) = (5+1) / 36 = 6/36 = 1/6

P(A∩B) = probability of the sum being divisible both by 4 and 6, i.e. the number 12

P(A) = 1 / 36 = 1/36

Here comes the use of formula P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 1/4 + 1/6 - 1/36 = 7/18

Nb: As you can see, both method B1 and B2 give the same answer. Method B1 is usually easier to use when facing simpler problems like this. I'd recommend using method B2 for more complex and difficult questions, such as when you can't visualize the problem with a table because there are too much sets of variables.

Image of table for reference: https://qph.fs.quoracdn.net/main-qimg-1283a98bd649f522986e2f91a592ffd3

Answer:

B

Step-by-step explanation:

Slope is change of y over change of x

Y is going up by 8 and x is going over by 1

Therefore, $8/1 lb

Answer:

Always in the range zero to one

Step-by-step explanation:

Option c is the answer

The amount of paint needed to cover all parts of the table will be 3703 square inches. Then the correct option is B.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The top of the table can be modeled with a cylinder, and the legs can be modeled with rectangular prisms.

The table is shown below.

The surface area of the cylinder will be

SA of cylinder = 2πr² + 2πrh

SA of cylinder = 2π (18² + 18 × 3)

SA of cylinder = 2375 square inches

Then the surface area of the prism will be

SA of prism = 4 [WL + 2(WH + LH)]

SA of prism = 4 [2 x 6 + 2 (2 x 20 + 6 x 20)]

SA of prism = 4 [12 + 2 x 160]

SA of prism = 4 [12 + 320]

SA of prism = 1328 square inches

Then the total surface area of the table will be

Total surface area = SA of prism + SA of cylinder

Total surface area = 1328 + 2375

Total surface area = 3703 square inches

Thus, the amount of paint needed to cover all parts of the table will be 3703 square inches.

Then the correct option is B.

More about the geometry link is given below.

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Answer:

D

Step-by-step explanation:

13x16=208

208/3= 69 reapeated.

Answer:

[tex]\sf X=\dfrac{2345}{9999}[/tex]

Step-by-step explanation:

Given:

[tex]\sf X=0.234523452345...[/tex]

Therefore, X is a recurring decimal (the decimal numbers 2345 repeat forever).

Converting a recurring decimal to a fraction

Let X equal the recurring decimal:

[tex]\implies \sf X=0.234523452345...[/tex]

Create another number with recurring 2345s by multiplying the above expression by 10000:

[tex]\implies \sf 10000X=2345.23452345...[/tex]

To solve these two equations and write X as a fraction, take away X from 10000X to remove all the recurring decimal places:

[tex]\large\begin{array}{r r l}& \sf 10000X & = \sf 2345.23452345... \\- & \sf X & = \sf \quad \:\:\:0.23452345.... \\\cline{2-3} & \sf 9999X & = \sf 2345\end{array}[/tex]

[tex]\implies \sf 9999X=2345[/tex]

Divide both sides by 9999:

[tex]\implies \sf X=\dfrac{2345}{9999}[/tex]

Therefore, 0.23452345... as a fraction is [tex]\sf \dfrac{2345}{9999}[/tex]

Answer:

D' : (2, 1)

E' : (2, 3)

A' : (5, 3)

Step-by-step explanation:

Answer:

D' = (2, -3)

E' = (2, -1)

A' = (5, -3)

Step-by-step explanation:

Coordinates are :

The transformation rule is :

Point D'

Point E'

Point A'

Step-by-step explanation:

Select all of the following that are quadratic equations.

x² + 3x - 5 = 0 ✓

x² - x = 3x + 7 ✓

5x - 7 = 0 X

7x² + 14x = 0 ✓

x³ - 3x² + 1 = 0 X

x - 5 = 9x + 7 X

What is quadratic equations?

Quadratic equations is a equation that has a general form like "ax² + bx = c"

For example :

x² + 3x - 5 = 0

x² + 3x = 5

x² → ax²

3x → bx

5 → c

Answer:

x = 3

Step-by-step explanation:

x / 4 = 6 / 8

4 time    2   = 8

4a = 8    divided both side by 4    4a / 4 = 8 / 4      a = 2

so

x time    2   = 6

2a = 6    divided both side by 2    2a / 2 = 6 / 2      a = 3

Answer:

I think it is a bit not for shore

If the trigonometric expression is sin θ = -√2/2. Then the value of angle θ will be 5π/4, 7π/4, and 13π/4.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The trigonometric expression is given below.

sin θ = -√2/2

The expression can be written as

sin θ = -1/√2

Then the value of angle θ will be

θ = sin⁻¹ (-1/√2)

θ = 5π/4, 7π/4, and 13π/4.

Thus, the correct options are B, C, and E.

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Answer:

B,C,E

Step-by-step explanation:

Answer:

g(x) = 2ˣ⁻¹ + 3

Step-by-step explanation:

f(x) = 2ˣ

Translated 1 unit right

Translated 3 units up

Answer:

Well if its a translation on the x-axis  the formula would be g(x) = -2×

Although Functions are not my strong suit

I hope i got this right!

Answer:

See below

Step-by-step explanation:

2 ^(5+x) = 2^8            (because 256 = 2^8)

 equate the exponents    5+x = 8     then x = 3

1/3 ^(2+x) = 1 / 3^ 6        (because 729 = 3^6 )

  equate the exponents  2+ x = 6    then x = 4

Answer:

a) x = 3

b) x = 4

Step-by-step explanation:

Use the Exponential Power Rule.

[tex]a^x \times a^y = a^{x+y}[/tex]

Also covert the term on the right to the same base as on the left.

If you are allowed to have calculator do [tex]\log_{\text{base}} (\text{number})[/tex] to get the exponent. For example [tex]\log_{2} (256) = 8[/tex], that means [tex]256 = 2^8.[/tex]

Without calculator you can divide with base untill you have it fully factored, then count. For example:

256/2 = 128
128/2 = 64
64/2 = 32
32/2 = 16
16/2 = 8
8/2 = 4
4/2 = 2
2/2 = 1

We had to divide with base two 8 times so 256 = 2⁸.

a)

[tex]2^5 \cdot 2^x = 256\\2^{5+x} = 2^8[/tex]

Now that we have same base we can equate the exponents!

[tex]5 + x = 8\\x = 8 - 5\\x = 3[/tex]

b)

[tex](\frac{1}{3})^2 \cdot (\frac{1}{3})^x = \frac{1}{729}\\\\(\frac{1}{3})^{2+x} = \frac{1}{3^6}\\\\(\frac{1}{3})^{2+x} = (\frac{1}{3})^6[/tex]

[tex]2 + x = 6\\x = 6 - 2\\x = 4[/tex]

5 (12 + x)

Step-by-step explanation:

Answer:

5(12+X)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The values of the temperature in degree Celsius (12 and 24) converted to degree Fahrenheit are 53.6°F and 75.2°F respectively.

In this exercise, you're required to convert the value of temperature in degree Celsius to degree Fahrenheit. Thus, we would use the following mathematical expression to do the conversion:

F(t) = 9/5C(t) + 32

When t = 12, we have:

F(t) = (9/5 × 12) + 32

F(t) = 21.6 + 32

F(t) = 53.6°F.

When t = 24, we have:

F(t) = (9⁄5 × 24) + 32

F(t) = 43.2 + 32

F(t) = 75.2°F.

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Answer:

Step-by-step explanation:

a) the thickness of one ream of paper :

= 0.1 × 500

= 50 mm

b) 12 cm = 12 × 10 = 120 mm

Then

the number of sheets that exist in a pile of papers that has a thickness of 12 cm :

= 120 ÷ 0.1

= 1 200 sheet of paper

A mean is an arithmetic average of a set of observations. The increase in the mean for the second week compared to the first is 0.4.

A mean is an arithmetic average of a set of observations. it is given by the formula,

[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]

Given the spending in the first week is $12.99, $10.50, $9.89, $6.90, and $7.58, therefore, the mean will be,

[tex]\rm (Mean)_1 = \dfrac{\$12.99 + \$10.50 + \$9.89 + \$6.90 + \$7.58 }{5} = \$9.57[/tex]

Also, the spending in the second week is $2 more than the total of the first week, therefore, the mean will be

[tex]\rm (Mean)_2 = \dfrac{\$12.99 + \$10.50 + \$9.89 + \$6.90 + \$7.58 + \$2}{5} = \$9.97[/tex]

Hence, the increase in the mean for the second week compared to the first is 0.4.

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Answer:

its C

Step-by-step explanation:

I used something else for it for it

Answer:

41 degrees

Step-by-step explanation:

All of the angles must add up to 360 degrees to form a circle. So we have 22 + b + 297 = 360. Solving for b, we get b = 41.

Answer:

least to greatest: 149,156,161,164,165,165,165,168,169,172,172,172,178,178,178,180,182,184,184,184,187,189,190,190,215

Greatest to least: 215,190,190,189,187,184,184,184,182,180,178,178,178,172,172,172,169,168,165,165,165,164,161,156,149

Step-by-step explanation:

The volume of the cylindrical jar, considering it's radius and height, is of 923 in³.

The volume of a cylinder of radius r and height h is given by:

[tex]V = \pi r^2h[/tex].

In which problem, we have that r = 4.7 in, h = 13.3 in, hence the volume in cubic inches is given by:

[tex]V = \pi \times 4.7^2 \times 13.3 = 923[/tex]

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Answer:

  83 m

Step-by-step explanation:

The missing dimension can be found by using the area formula. Fill in the given values, and solve for the remaining unknown value.

__

  A = LW . . . . . area of a rectangle of length L and width W

  3403 m² = L(41 m) . . . . with given values filled in

  L = (3403 m²)/(41 m) = 83 m . . . . . . divide by the coefficient of L

The length of the gym is 83 meters.

Answer:

A. 25/33

B. 1/3

C. 1/33

D. 25/9

Answer:

Step-by-step explanation:

Answer:

Find the radius.

Step-by-step explanation:

The task is to solve for area of a circle, and you are given the diameter.

The formula for area is :

Area of a circle = π × (radius)²

In this formula, there is only one input value, and that is the radius.

To find the radius, you must know the relation :

Radius x 2 = Diameter

Hence, the radius must be computed first and foremost.

Answer:

6.28

Step-by-step explanation:

2×3.14 because this is just simple multiple

Answer:

28

Step-by-step explanation:

DI is a radius

CJ is a diameter

The diameter is twice the radius

CJ = 2 * DI

CJ = 2 * 14

CJ = 28

Answer:

Angle 1 = 63.3

Angle 2 = 37.3

Angle 3 = 63.3

Angle 4 = 142.7

Step-by-step explanation:

When a line intersects two parallel lines the interior angles are equal. So angle 2 = 37.3

Angle 3 = 180 - (79.4 + 37.3) = 63.3 since the sum of the angles on a straight line must be 180

Ange 1 = Angle 3 = 63.3

Angle 4 = 180-37.3 = 142.7