Got a question in connexus 8th grade advanced Math XL

The probability of getting either 1 or 2 on first and second toss is 1/9

How to calculate the probability?

Probability is numerical description for how likely something is to happen. To know probability something event we just divide no the outcome by total possible of the outcome.

The probability of either 1 or 2 side on first toss is

= no the outcome / total possible the outcome

= 2/6

= 1/3

For second toss is same as first toss

= 2/6

= 1/3

Since the second toss is independent, it is called an independent event. So, we just need to multiply the probability on the first toss by the probability on the second toss,

= 1/3 * 1/3

= 1/9

Thus, the probability of getting either 1 or 2 on first and second toss is 1/9

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The y-coordinate of the point that divides the directed line segment from J to K into a ratio of is 5.

The coordinates of point that divides the line segment into m:n ratio can be obtained as follows,

Coordinates of point = [tex](\frac{mx_{2}+ nx_{1} }{m+n} \frac{my_{2}+ ny_{1}}{m+n} )[/tex]

The coordinate of point J is (-3,1)

The coordinate of point K is (-8,11)

Consider the point that divides the line segment into 2:3 ratio as P(x,y).

The coordinates of point that divides the line segment into 2:3 ratio can be calculated as follows,

[tex]Coordinates of P = (\frac{3(-3)+2(-8)}{2+3}, \frac{3(1)+2(11)}{2+3} )[/tex]

[tex]= (\frac{-9-16}{5}, \frac{3+22}{5} )\\\\= (\frac{-25}{5} \frac{25}{5} )[/tex]

= (-5,5)

Hence the answer is The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is 5.

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The constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.

Given:

you receive a $60 gift card to a move theater. a ticket to an afternoon show costs $6 and a ticket to an evening show costs $10. the rules of the gift card state that you can only buy a maximum of 8 total tickets with the card.

x =  the number of afternoon tickets and y = the number of evening tickets.

6x ≤ 60

10y ≤ 60.

so

6x + 10 y = 60.

Therefore the constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.

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The width of the actual parking lot, given the length of the scale drawing and the actual length, is 235 m

The scale is given in the question to be 1 cm : 50 m. This means that for every 1 cm on the scale drawing, the actual dimensions are 50m.

Given that the width of the parking lot on a scale drawing is 4. 7 cm, the width of the actual parking lot will be:

= Width of parking lot on scale drawing x Number of meters per centimeter in drawing

= 4. 7 x 50

= 235 m

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The length of the first piece is 6 inches.

The length of the second piece is 24 inches.

The length of the third piece is 30 inches.

The length of the first piece = x

The length of the second piece = 4 ×x = 4c

The length of the third piece = 5 × x = 5x

Total length of the board = 60

Sum of the length of the three pieces = total length of the board

x + 4x + 5x = 60

10x = 60

x = 60 / 10

x = 6

The length of the second piece = 4 ×6 = 24

The length of the third piece = 5 × 6 = 30

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Answer:

x = 12, y = 15

Step-by-step explanation:

x + y = 27

1 / 2 x + 1 / 3 y = 11

y = 27 - x

1 / 2 x + (27 - x) / 3 = 11

1 / 2 x + 9 - 1 / 3 x = 11

1 / 6 x = 2

x = 12

12 + y = 27

y = 15

A 95% confidence interval is a set of data that contains the real mean of the population 95% of the time. This is not the same as a range that includes 95% of the possible values.

What is Confidence Interval?

In statistics, a confidence interval defines the possibility that a population parameter will fall between a set of values for a certain proportion of the time.

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$135 is markup price when cost is $450.

What is the cost price and an example?

selling price of item = $600

       cost = $450

10%×$650=$585

$585-$450=$135

$135 is markup price .

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The slope will be 1, for the right.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

We know that formula two find the slope of the line joining two points which is

m = (4-3)/(4-3)

m = 1

Hence the slope of the line is shown in the graph is 1.

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The number that represents the shoe rental charge is $3 and the price per game is $2.5.

Given:

The function y=2.5x+3 represents the cost y of bowling x games.

y = 2.5x+3

In the equation the 2.5 represents additional fee.

For 1 game = 2.5*1 = 2.5

For 2 games = 2.5 * 2

= 5

3 is the flat fee for renting the shoes.

Therefore the number that represents the shoe rental charge is $3 and the price per game is $2.5.

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The fraction that 1 4/5 is of 1 2/3 is 1 2/25.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Let the fraction be illustrated as x

Therefore, 1 2/3 of x = 1 4/5

5x/3 = 9/5

Cross multiply

5x × 5 = 3 × 9

25x = 27

Divide

x = 27 / 25

x = 1 2/25.

The fraction is 1 2/25.

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The mean of the previous four tasks was 77%.

What is Mean?

The mean is just the average of the given set of values. It represents a data set's values being distributed evenly.

Solution:

Mean = Sum of Observation / Total Number of Observation

Let, the sum of previous four values be x

According to the question,

78 = x + 82 / 5

here, 5 is the total number of observations

so,

x can be calculated by cross multiplication

390 - 82 = x

x = 308

Since, we have the sum of the four values and the numer of observations is 4, then mean would be

Mean = 308/4

Mean = 77%

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The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given tabel,

Suppose the number of guest ∝ food prepared.

Take the first data,

12 ∝ 15

12 = k(15)

k = 12/15 = 0.8

Hence "The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8".

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The given question is incomplete, the complete question follows,

The number needed to multiply the amount of each ingredient by to adjust the recipe is 5. It's determined by dividing the number of people that needs to be served by the number of people the provided ingredients will serve.

1 ¼ teaspoons salt

3 ¾ cups sugar

5 eggs

10 tablespoons milk

10 ½ cups chocolate chips

1. Number needed to multiply the amount of each ingredient by to adjust the recipe = Number of people that needs to be served ÷ The ingredients provided serves

= 60/12

= 5

2. Steps involved in finding out how much flour you will need to make 60 servings of chocolate chip cookies.

Quantity of flour provided = 1 ¼ cups

Flour needed for 60 servings = Quantity of flour provided × number needed to multiply each ingredients with

= 1 ¼ × 5

= 5/4 × 5

= 25/4

= 6 ¼

3. Steps involved in finding out how much baking soda you will need to make 60 servings of chocolate chip cookies

baking soda needed for 60 servings = Quantity of baking soda provided × number needed to multiply each ingredients with

= ½ × 5

= 5/2

= 2 ½

4. Teaspoons salt = ¼ × 5 = 5/4 = 1 ¼

Cups sugar = ¾ × 5 = 15/4 = 3 ¾

Eggs = 1 × 5 = 5

tablespoons milk = 2 × 5 = 10

Cups chocolate chips = 1 ¾ × 6 = 7/4 × 6 = 42/4 = 10 ½

5. The number of eggs needed for 60 servings than 12 servings = eggs needed for 60 servings - ieggs needed for 60 servings

= 5 - 1

= 4

6. Number needed to multiply the amount of each ingredient by to adjust the recipe to 78 servings = Number of people that needs to be served ÷ The ingredients provided serves

= 78/12

= 6 ½

7. One time I made a mistake of keeping bad company, it really affected my studies because I lost concentration in school. My parents were disappointed in me but they helped me get back on the right track.

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Answer:

x = 2

Step-by-step explanation:

The image shows a large rectangle with a similar, smaller triangle inside of it. The small leg on the small rectangle is 4, and the small leg on the large rectangle is 12. This tells me that the scale factor is 3.

If the scale factor is 3, then

[tex]6*3=6+6x[/tex]

Simplify

[tex]18=6+6x\\12=6x\\x=2\\[/tex]

The parametric equations of the curve are x = -10 + 1t and y = -20 - 4t

A parametric equation is defined as a type of equation that employs an independent variable called a parameter (often denoted by t)

Given: The line with slope -4, passing through (-10, -20)

We can use the given properties of the curve to describe it parametrically as follows

The slope of -4 implies that if y decreases by 4, x increases by 1  i.e slope = Δy/Δx = -4/1. Thus, we have

x = -10 + 1t

y = -20 - 4t

Therefore, the parametric equations are x = -10 + 1t and y = -20 - 4t. So (x(t) , y(t)) = (-10 + 1t,  -20 - 4t)

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Answer:

1/10 or 0.1 m^3

Step-by-step explanation:

V = 1/4 * 2/3 * 3/5 = 6/60 = 1/10 m^3 = 0.1 m^3

The vertical axis of symmetry is x =  -1

the domain is {-2 2}

the range is {-6, 0}

The domain refers to all possible value in the input of a graph. The input is the x coordinate and the possible values here is within the interval

The range refers to all possible value in the out put of a graph. The out put is the y coordinate and the possible values here is within the interval

Axis of symmetry refers to where the graph is bisected, the problem asked of vertical axis of symmetry. Therefore the line will be between the y coordinates

The vertical axis of symmetry and this x = -1

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Answer: The question is a bit unclear but the value of -9 is -9, the absolute value of -9 is 9. Does that answer your question?

Step-by-step explanation:

The actual measurements of bedroom are 4.8 feet and 13.8 feet. Therefore, option A is the correct answer.

Given that, on a given blueprint, 1 in. :6 ft.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

The dimensions of the bedroom on the blueprint are 0.8 inches × 2.3 inches

Here, 0.8 × 6

= 4.8 feet

2.3 × 6

= 13.8 feet

The actual measurements of bedroom are 4.8 feet and 13.8 feet. Therefore, option A is the correct answer.

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The value of the linear expression quantity negative 1 over 4 times r minus 8 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 4 times r plus 9 end quantity is B. negative 3 over 14 times r plus negative 17

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Based on the information given, the expression will be:

= (-1/4r - 8 - 5/7r) - (-3/4r + 9)

Collect like terms

-1/4r - 5/7r + 3/4r - 8 - 9.

= - 3/14r - 17

In conclusion, the correct option is B.

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Answer:

Step-by-step explanation:

b

The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8.

What are the ratio and proportion?

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given table,

Suppose the number of guest ∝ food prepared.

Take the first data,

12 ∝ 15

12 = k(15)

k = 12/15 = 0.8

Hence "The constant of proportionality is the ratio of the number of guests to the food prepared is 0.8".

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Answer:

[tex]x=6, y=-2[/tex]

Step-by-step explanation:

[tex]-2=3x-20 \\ \\ 3x=18 \\ \\ x=6 \\ \\ \therefore x=6, y=-2[/tex]

Answer:

The answer is x = 6. If you want to solve the equation by inputting the x and y value, then take the x value and input it into the equation as well as the y value.

Step-by-step explanation:

To solve this equation, plug in the value equal to y and solve for x. The first thing you have to do is make the equation -2 = 4x - 20, since we already have the value for y which is given in the question. Then add 20 to both sides of the equation. We now have 18 = 3x, divide both sides by 3 and you have your answer.

Hence, X = 6.

Answer:

-7

Step-by-step explanation:

Given inequality:

[tex]4x - 12 \leq 16 + 8x[/tex]

Subtract 4x from both sides:

[tex]\implies 4x - 12-4x \leq 16 + 8x -4x[/tex]

[tex]\implies -12\leq 16+4x[/tex]

Subtract 16 from both sides:

[tex]\implies -12-16\leq 16+4x-16[/tex]

[tex]\implies -28\leq 4x[/tex]

[tex]\implies 4x \geq -28[/tex]

Divide both sides by 4:

[tex]\implies 4x \div 4 \geq -28 \div 4[/tex]

[tex]\implies x \geq -7[/tex]

This means that x is equal to or greater than -7.

Therefore, the value of x that is in the solution set of the inequality is -7 as -10, -9 and -8 are all less than -7.

Answer:

x ≥ -7

Step-by-step explanation:

Given inequation,

→ 4x - 12 ≤ 16 + 8x

Then the value of x will be,

→ 4x - 12 ≤ 16 + 8x

→ 4x - 8x ≤ 16 + 12

→ -4x ≤ 28

→ x ≥ 28/-4

→ [ x ≥ -7 ]

Hence, the value of x is -7.

The area of the triangle is 43.81 square units

The side a = 8 units

The side b = 11 units

The perimeter of the triangle = 32 units

First we have to find the third side of the triangle

a + b + c = 32

Substitute the values in the equation

8 + 11  + c = 32

19 + c = 32

c = 32 - 19

c = 13 units

Then the area of the triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

The value of s = (a + b + c) / 2

= (8 + 11 + 13) / 2

= 32/2

= 16

Substitute the values in the equation

The area of the triangle = [tex]\sqrt{16(16-8)(16-11)(16-13)}[/tex]

Subtract the terms

= [tex]\sqrt{(16)(8)(5)(3)}[/tex]

= [tex]\sqrt{1920}[/tex]

= 43.81 square units

Hence, the area of the triangle is 43.81 square units

The complete question is:

Find the area of a triangle , two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.

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I will have to reject the offer of the rival company since it's lesser than $40560.

From the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:

= 40 × 19.50 × 52

= $40560

The rival company offers you an annual salary is $36000.

I'll reject the rival company's offer since it's lower.

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Answer:

The bill after tipping 21 percent would be $104.30.

Step-by-step explanation:

$86.20 x 0.21 = $18.102

$86.20 + $18.102 = $104.302

$104.302 ≈ 104.30

Hope my answer helped! Have a great afternoon.