Harold solved a division problem in the following way. Check his work. Is the solution valid. Why or why not?

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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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: 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 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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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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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:

this equal to -13.55 hopefully this helps

$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 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 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:

15/16

Step-by-step explanation:

75/80

15/16

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 estimated total audited value of the population using the difference method  is $201,000.

The difference method works as follows :

A difference method is a mathematical expression of the form

f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient.

Given that,

A population of 1,000 accounts .  

The sample items have a mean book of $200 and

A mean audited value of $203  

Therefore, the difference of $203 - $200 = $3  

Now, Apply the difference to the population of accounts and we get,

(1000 account × $3) = $3000

As Given in the question,

The book value in the population is $198,000 and we add the difference previously calculated of $3,000  

So, we have = $198,000 + $3,000

                     = $201,000  

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Answer:

y=1,-4,-9,-14

Step-by-step explanation:

just replace x with the given value and find what it equals to

y=-5(0)+1

y=1

y=-5(1)+1

y=-5+1

y=-4

y=-5(2)+1

y=-10+1

y=-9

y=-5(3)+1

y=-15+1

y=-14

Hopes this helps please mark brainliest

Answer:

Please mark as brainiest

Step-by-step explanation:

when x = 0:

y= -5(0)+1

y=0+1

y=1

when x = 1:

y= -5(1)+1

y= -5+1

y= -4

when x = 2:

y= -5(2)+1

y= -10+1

y= -9

when x = 3:

y= -5(3)+1

y= -15+1

y= -14

The cost for a passenger going to a distance that is 3/2 times more distant than the average is; 15 pesos

We are given that;

Average distance covered per passenger = x² + 5 Km.

Cost per average distance = 10 pesos

Cost per km = 10/(x² + 5) pesos per km

We are told that a passenger now goes a distance that is 3/2 times more distant than the average. Thus, this distance is;

(3/2)(x² + 5) Km

The cost for this given distance will be;

10/(x² + 5) * (3/2)(x² + 5)

= 10 * (3/2)

= 15 pesos

Thus, we conclude that the travelling cost in pesos is 15 pesos

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The coordinates of A is (0,2)

How can a image be reflected?

Behind a mirror's glass, people can see a reflection of themselves. The shiny surface creates that image when light rays strike it and reflect or bounce back, creating a "mirror image." Contrary to popular belief, the reflection is not mirrored from left to right as many people believe.

The coordinates of the point A is (-3,-2)

The rule of reflection over x-axis is

(x,y)→(x,-y)

So the point A after reflecting over the x-axis becomes

A(-3,-2)→ A(-3,2)

To move the point P(x,y), a units right and b units up we use

P(x+a,y+b)

As per the question as it moves 3 units right

∴ A(-3.2)

⇒A(-3+3,2)

The point A now is A(0,2)

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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 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 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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Answer: No they are not equivalent.

Step-by-step explanation: 8(9x-2) = 72x-2

= 8(9x-2) = 72x - 16

= 72x -16 is not equivalent to 72x -2.

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 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 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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Cubic millimeter volume unit is smaller.

You would multiply a measurement in cubic centimeters by 1,000 to translate it to cubic millimeters. This makes sense because you would anticipate needing a lot more cubic millimeters to fill the same space because a cubic centimeter is greater than a cubic millimeter.

Volume:

The total number of cubic units that a cube occupies in three dimensions is its volume. Six faces, twelve edges, and eight vertices make up the three-dimensional shape of a cube. Therefore, the area encircled by a cube's six faces is considered to equal its volume. It differs from 2D shapes in that it adds a third dimension, known as height or thickness, in addition to length and breadth. Since the product of a cube's length, width, and height determines its volume. Cubic units are used to measure it. The volume of a cube increases as the value of its dimensions increases.

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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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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 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

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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