solve the equation for x in simplest form
2 / 3x = 1/6
A x= 1/4
B x= 3/5
C x=1/2
D= x=4/5

Answer:

404 inches

Step-by-step explanation:

Since a room of 2cm is to be left of either side of the TV, thus, the permissible required length of the TV is 136-2 = 134cm

Use Pythagoras Theorem,

h² = 134² + 86² = 17956 + 7396 = 25352

h = √25352 = 159.22 ≈ 159cm = 404.41 inches ≈ 404 inches.

The answers are as follows:

a. There are 6 ways of tossing a coin and then drawing a marble from the bag. (Tree diagram is shown in the diagram below) The probability is 1/12.

b. These are independent events since tossing a coin does not affect the drawing of marble from the bag.

c. From the tree diagram, the probability of tossing a head and drawing a red marble is 1/6(since they are independent events).

d. The probability of drawing two blue marbles if the first marble is not replaced is 1/5(since they are dependent events).

It is given that a bag contains,

Number of white marbles(W) = 1

Number of Blue marbles (B) = 3

Number of Red marbles (R) = 2

Thus, there are 6 marbles in the bag. So, the sample space for drawing a marble = 6

a. Finding all the possible outcomes using a tree diagram:

The possible outcomes from the tree diagram are

(H, W), (H, B), (H, R), (T, W), (T, B),  and (T, R)

The probability of tossing head or tail = 1/2

The probability of drawing a marble from the bag = 1/6

So, the compound probability = (1/2)(1/6) = (1/12)

The sample space for this is 12.

b. Independent or dependent events:

These are independent events since the tossing of a coin does not affect the drawing of marble from the bag.

c. Finding the probability of tossing a head and drawing a red marble:

The probability of tossing a head = 1/2

The probability of drawing a red marble = 2/6 = 1/2

Since they are independent events,

The required probability = (1/2)(1/2) = 1/4

d. Finding the probability of drawing two blue marbles if the first marble is not replaced:

The probability of drawing a blue marble from the bag(1st attempt) = 3/6

The probability of drawing another blue marble from the bag (2nd attempt) = 2/5 (From the leftover marbles after the first attempt)

Since they are dependent events, the probability of the 2nd event is calculated only after the first event is calculated.

So, the required probability = (3/6)(2/5) = 1/5

Thus, all the probabilities are calculated.

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Answer:

8.4 meters tall   ( one decimal place)

Step-by-step explanation:

See diagram below:

find distance 'd'   as     tan 68 = opp / adj = d/6

   then   d = 6 tan 68       =  14.85 m

Then find   h   as   tan 9  = h / d

                               d tan 9 = h

                              14.85  tan 9 = h = 2.35 m tall

                                      add the 6 m height of the house    8.4  m tall

The equation that will produce the given graph is; 6x² + 6y² = 144

The standard equation of a circle can be expressed as:

(x + a)² + (y - b)² = r²

where;

(a, b) is the center of the circle

r is the radius of the circle.

From the diagram, we can see that the radius of the circle is between 4 and 5.  Thus, the correct equation must have a radius between these values.

From the option, we can see that the only equation that will have a radius between 4 and 5 is;

6x² + 6y² = 144

Divide through by 6 to get;

x² + y² = 24

x² + y² = √24

Thus r = √24 which is greater than 5

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The area of the logo is 136. 14 cm²

First, let's find the area of the semicircle

Area of semicircle = 1/2(πr²)

radius = 8/2 = 4cm

Substitute into the formula

Area of semicircle = [tex]\frac{1}{2} * 3. 142 * 4 * 4[/tex] = 25. 135 cm²

Now, let's find area of trapezium

Area of trapezium = [tex]\frac{a + b}{2} * h[/tex]

Area =  [tex]\frac{12 + 10. 2}{2} * 10[/tex]

Area = [tex]11. 1 * 10[/tex]

Area = 111 cm²

Area of logo = Area of trapezium + area of semicircle

Area of logo = 111 +  25. 135

Area of logo = 136. 14 cm²

Thus, the area of the logo is 136. 14 cm²

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Answer:

-7, 8.

Step-by-step explanation:

x^2 - x - 56 = 0

Let's see if we can factor this function:

We need 2 numbers whose product is -56 and whose sum is -1 ( which is the coefficient of x).

They are  -8 and 7 , so the factors are:

(x - 8)(x + 7) = 0

x - 8 = 0 giving x =  8 and

x + 7 = 0 giving x = -7.

The zeros are -7, 8

Answer:

[tex]y=7x[/tex]

I hope this helps and that you can give a brainliest!

Step-by-step explanation:

If x and y vary directly, that means that y is directly proportional to x. So, the parent function is y = kx.

So, by plugging in the given y=42 when x=6 into this parent function, we get:

42=6k

If we solve for k, we end up with 7.

Now if we plug in the value of k back into the parent function of this scenario, we get:
[tex]y=7x[/tex]

The relation in option B is a function.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are 4 relations, A, B, C, D.

From the definition of function, it is clear that, no input value have more than one output value.

A : The value of x = -2 is mapping to 2, 1, 0, -1.

That is, an input value is having more than one output values.

So this is not a function.

B : Here the input values, 0, 1, 2 and 3 maps to -2.

Here the input values are distinct. No input values are mapping to more than one output value.

So this is a function.

C : Here 1 is mapping to -2 and 3. So not a function.

D : For x = 0, there are two y values, 3 and -3.

So this is not a function.

Hence option B is a function.

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Answer:

a₅ = 80 , [tex]a_{n}[/tex] = 5[tex](2)^{n-1}[/tex]

Step-by-step explanation:

to find a term in the geometric sequence multiply the previous term by r

a₁ = 5

a₂ = a₁ × 2 = 5 × 2 = 10

a₃ = a₂ × 2 = 10 × 2 = 20

a₄ = a₃ × 2 = 20 × 2 = 40

a₅ = a₄ × 2 = 40 × 2 = 80

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

here a₁ = 5 and r = 2 , then

[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]

Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

According to the statement

we have given that the Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal.

and we have to find that the expected value of the difference between the number of days.

So, the total number of days in a year is 365 days.

Chance to get a prime number on a die = 3/6

Chance to get a prime number on a die = 1/2.

and chances to get a composite number = 2/6

chances to get a composite number = 1/3

and chances to get a 1 on a die = 1/6.

Then the expected value =

so, expected value = 365(1/6) + 365(1/3) + 365(1/2)

then after calculating

Expected value = 1+2+1

then the value become is 4

and by this way he eat 171 days sweet cereal and other days he eat unsweetened.

So, Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

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If the marriage licenses  issued in 2001,2003,2006,2010 were 141000,133000,121000,141000 then by solving arithmetic progression we will get that the marriage licenses issued in 2008 were 113000.

Given that the marriage licenses issued in 2001,2003,2006,2010 were 141000,133000,121000,141000.

We are required to find how many marriage licenses were issued in 2008.

Average difference between licenses issued from 2001 to 2003=

=133000-141000)/2

=-4000

Average difference between licenses issued from 2003 to 2006=

=(121000-133000)/3

=-12000/3

=-4000

Average difference between licenses issued from 2006 to 2010=

=(105000-121000)/4

=-16000/4

=-4000

It is an arithmetic progression because the difference between marriage issued from one year to another is equal.

An arithmetic progression is a sequence in which each terms are having equal difference between them.

Nth term=a+(n-1)d

8th term=141000+(8-1)*(-4000)

=141000+7*(-4000)

=141000-28000

=113000

Hence the marriage licenses issued in 2008 were 113000 which is

option A.

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The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

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

Given the equation:

x/3 - 3/4 = 5/12

Hence:

x/3 = 5/12 + 3/4

x/3 = 7/6

x = 7/2

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

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The tiles to match the descriptions are;

Hull house - Neighbourhood assistance.

Muckrakers - Investigative journalists.

Protestants - Temperance movement.

Women's suffrage - Nineteenth amendment.

The Progressive Era, which encompassed the years between the 1890s and the 1920s in US history, was one of intense social and political reform with the goal of advancing the creation of a better society.

Case 1: The settlement home that welcomed newly arrived European immigrants to the United States in 1889 is known as Hull House. There were also social, educational, and artistic initiatives for immigrants in this building.

Case 2: Muckrakers A name used to describe a group of North American journalists in the early 20th century who made public criticisms of: government corruption, abuse of labor is destructive to society and is committed by influential people or institutions of the time.

Case 3: Third, the term "Protestantism" is used to describe a variety of 16th-century religious movements. Because the Catholic Church had a different understanding of the Bible's holy texts, this movement was distinguished by its break with it.

Case 4: The 19th Amendment to the United States Constitution, which was adopted in June 1919, guaranteed every American woman the right to vote.

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The complete question is-

Think about what you learned about the events during the Progressive time period. Drag and drop the tiles to match the

descriptions                        

Tiles;

Hull House

Muckrakers

Protestants

Women's Suffrage

Pairs;

Investigative journalists

Temperance Movement

Neighbourhood assistance

Nineteenth Amendment

Answer: 3n ants

Step-by-step explanation:

         If there are n ants one month, and the ants triple every month, then next month there will be 3n ants.

         We can multiply 3 by n to show it tripling.

      To test this, 3(10,000) = 30,000 and 3(270,000) = 810,000, which corresponds to what you've filled out in the table.

[tex] \boxed{ \sf{ \color{purple}\huge Answer :}}[/tex]

[tex] \: \: [/tex]

[tex] \large \tt \purple↪ \: \: \: \: \: 5x - 16 = x + 10 [/tex]

[tex] \: \: [/tex]

[tex]\large \tt \purple↪ \: \: \: \: \:5x - x = 10 + 16 [/tex]

[tex] \: [/tex]

[tex]\large \tt \purple↪ \: \: \: \: \: 4x = 26[/tex]

[tex] \: [/tex]

[tex]\large \tt \purple↪ \: \: \: \: \: x = \cancel\frac{26}{4} [/tex]

[tex] \: \: [/tex]

[tex] \underline{ \boxed{\large \tt \purple↪ \red{ \: \: \: \: x = \frac{13}{2} }}}{ \large✓}[/tex]

[tex] \: \: [/tex]

hope helps ~

Answer:

7.55

Step-by-step explanation:

A midpoint can be found by doing 7.2 + 7.9 then dividing by the number of points (in this case 2).

Answer:

[tex]400m^3[/tex]

Step-by-step explanation:

Use the formula [tex]V=\frac{1}{3}Ah[/tex]

Where h=the height of the pyramid (12cm)

A=the base area of the pyramid, also known as the area of the square (10cm*10cm=100cm)

So, inserting this into the equation:

[tex]V=\frac{1}{3} (100)(12)[/tex]

[tex]V=\frac{1}{3} (1200)[/tex]

[tex]V=400m^3[/tex]

Answer:

1025.76

Step-by-step explanation:

Formula for a right rectangular pyramid is (l*w*h)/3

The length and width are both 18.7, so we can plug that in. The height is 8.8.

It becomes:

(18.7*18.7*8.8)/3, which equals the answer above.

The value of m based on the given equation -7 + 4m + 10 = 15 - 2m is 2

-7 + 4m + 10 = 15 - 2m

4m + 2m = 15 + 7 - 10

6m = 12

m = 12/6

m = 2

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Answer:

x/2 = 19-11

x/2 = 8

x = 8×2

x= 16

Answer:

x=16

Step-by-step explanation:

x/2 + 11 = 19

*2     *2    *2    Multiply 2 on both sides to make x stand by itself

x+22 = 38

  -22   -22

x=16

Check

Plug in 16 instead of x.

16/2 + 11 = 19

8+11=19

19=19

Hope it helps:)

Answer:

Step-by-step explanation:

The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse

The width that Mason should set his compass when constructing segment FG is: A. The distance from B to E.

FG should be congruent to segment BE. Based on this Mason should set his compass to the width of segment BE when Mason is constructing segment FG.

Hence, the width that Mason should set his compass when constructing segment FG is the distance from B to E which is option is A.

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Answer:

b to e

Step-by-step explanation:

plato

Based on definition of unit circle and angle properties on Cartesian plane, we find the following results: A: π/5, B: 3π/7, C: 4π/3.

Units circles are commonly used to understand angles and trigonometric functions in a simple way. Vectors in a unit circle are ordered pairs of polar form: (x, y) = (cos θ, sin θ).

To solve this problem, we must take these tips into account:

Then, we have the following results: A: π/5, B: 3π/7, C: 4π/3.

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x² ( 4x - 3)

Apply the multiplicative law of distribution.

Multiply the monomial

Multiply the monomial

Therefore, the correct option is "C".

The next step Juan will take is to multiply the second fraction by (x-2)/(x-2).

Given that Juan needs to rewrite this difference as one expression (3x/(x²-7x+10))-(2x/(3x-15)) and factor the denominator as (3x/(x-2)(x-5))-(2x/3(x-5)).

An algebraic expression in mathematics is an expression composed of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

The given expression is (3x/(x²-7x+10))-(2x/(3x-15))

Firstly, we will factored the denominator as

(3x/(x-2)(x-5))-(2x/3(x-5)).

Now, we will multiply and divide the second fraction by (x-2), we get

(3x/(x-2)(x-5))-((2x(x-2))/3(x-5)(x-2)).

Hence, the next step when subtracting these expressions (3x/(x-2)(x-5))-(2x/3(x-5)) is multiply the second fraction by (x-2)/(x-2).

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Answer:

A

Step-by-step explanation:

There is a 0.02275 to 0.0968 chance that a random family's bill will be between $350 and $400.

Provided that,

Mean of the population = 500

The standard deviation(S.D) of the population = 75

Assume,the variable in normal distribution = X

Z= (x- mean)/ S.D

Provided , x = $350 - $400

Z= 350-500/75 = -2(when x=$350)

Z= 400-500/75 = -1.3 (taken x= $400)

The probability that a household will spend between $350 and $400 monthly

P(350>X<400) = P( -2>Z<-1.3)

                        = 0.02275 to 0.0968 (from probability table)

Therefore, the final answer is 0.02275 to 0.0968.

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The total surface area of the trapezoidal prism is 180m². Option C

The formula for the total surface area of a trapezoidal prism is;

Total surface area = h (b + d) + l (a + b + c + d)

Where

b and d are parallel sides = 3, 9

h is the distance = 8

l is the length of the trapezoidal prism. = 12

Substitute into the formula

Total surface area = [tex]8(3 + 6) + 12(3 + 6)[/tex]

Total surface area = 72 + 108

Total surface area = 180 m²

Thus, the total surface area of the trapezoidal prism is 180m². Option C

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The total number of 5 digit palindrome that we have is 900.

This is the term that is used to refer to a number or a word phrase that is the same way when it is written from the front and from the back.

Examples of palindrome numbers are

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Answer: A

Step-by-step explanation:

[tex]m\angle ABC=59^{\circ}[/tex] by the inscribed angle theorem.