2x+y+2z=2
2x-7y-8z=-2
-2x+4y+3z=8

Answer:

\(h_{max}=5.5\)

Step-by-step explanation:

Given

\(h = -0.1(d + 1)(d - 12)\)

Solving (a): The graph

To do this, we plot h on the vertical axis and d on the horizontal

See attachment for graph

Solving (b): The maximum of h

From the attached graph, h has the maximum value when:

\(d = 4.225\)

So, the maximum of h is:

\(h_{max}=5.5\)

Answer:

C. 5 inches

Step-by-step explanation:

I’m area you have to multiply L • W

But since we don’t know the width we can divide the length by the area.

40/8 = 5

So the answer would be 5.

Another way to solve this problem is with using guess and check.

I hope it helps! Have a great day!

Anygays~

Answer:

C. 5 inches

Step-by-step explanation:

Use the numbers we have in the word problem, so you´d divide 40 by 8 since you´re trying to find the width. 40 is the area and 8 is the length so divide it tofind the width.

40/8 = 5

ANSWER: 5 inches

I hope it helps! Have a great day!

Answer:

vvvvvvvvvv

Step-by-step explanation:

~ Is a sign for similarity. This essentially means you can do rigid transformations to a shape to get the exact shape of another. You would need proportional sides and congruent angles for this to work. The shapes are not proportional so it is not similar.

The correct comparison of the population and sampling distribution is A. Means are the same but the standard deviation of sampling distribution is smaller

X X^2

95 9025

96 9216

98 9604

Sum = 289 27845

n 3

The sample mean 96.33333333 SUM/n

Population mean 96.33333333 SUM/n

Sample standard dev \(1.527525232 \sqrt{((1/(n-1))(SUM(X^2)-(1/n)SUM(X)^2)}\)

Population standard dev \(1.247219129 \sqrt{((1/n)(SUM(X^2)-(1/n)SUM(X)^2)}\)

Population Mean(μ) = 96.33

Population standard deviation (σ) = 1.25

Option A) 95,96,98 and X bar = 96.33

Sampling distribution :

mean (μx = μ) = 96.33

standard deviation(σx = σ/SQRT(n)) = 1.25/SQRT(3) = 0.72

Option A) Means are the same but the standard deviation of the sampling distribution is smaller

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i) 4 more gallons of petrol will be needed to complete the journey.

ii) The cost of the petrol for the 420 km journey is GH¢55.00.

i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.

Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):

Distance covered with 10 gallons = 10 * 30 = 300 km

To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:

Remaining distance = Total distance - Distance covered with available petrol

Remaining distance = 420 km - 300 km = 120 km

Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:

Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons

Therefore, the driver will need 4 more gallons of petrol to complete the journey.

ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.

Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:

Cost of petrol = Total gallons used * Cost per gallon

Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00

Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.

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well, the tax amount is simple, it was $71 and it went up to $86.45, that's a 15.45 difference, so that IS the tax amount.

now, if we take 71(origin amount) to be the 100%, what's 15.45 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 71 & 100\\ 15.45& x \end{array} \implies \cfrac{71}{15.45}~~=~~\cfrac{100}{x} \\\\\\ 71x=1545\implies x=\cfrac{1545}{71}\implies x\approx 21.76\)

Using the Law of Sines, we get an angle of 2.41 degrees and no triangles are produced.

Option (C) is the correct one.

Given, Two sides and an angle are given below.

we have to determine whether the given information results in one​ triangle, two​ triangles, or no triangle at all.

If b = 5, c = 6 and B = 20 degrees in the triangle.

On using the concept of Laws of Sines, we get

sinA/a = sinB/b = sinC/c

sin 20°/5 = sin C/6

0.34/5 = sin C/6

0.007 = sin C/6

sin C = 0.042

C = 2.41

So, the angle C be 2.41 degrees.

which implies that no triangle can be formed or produced with the given data of the triangle.

Hence, No triangles are produced.

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Answer:

ok man

Step-by-step explanation:

Answer:

Assuming the parent function of f(x) = x²

Transformations:

Complete question is;

A labourer is paid rs. 8 per hour for an 8 hour day and ½ times that rate for each hour in excess of 8 hours in a single day. if the labourer received rs. 80 for a single day's work, how long did he work on that day?

Answer:

Total working time for the day = 12 hours

Step-by-step explanation:

Money paid to the labourer for initial 8 hrs of work = 8 × 8 = rs. 64.

Now, we are told that he receives rs. 80 in total for that day. And that he receives ½ times the initial rate for each extra hour after the initial 8 hour period.

Thus;

½ × 8 × y = (80 - 64)

Where y is the duration of extra hours.

So;

4y = 16

y = 16/4 hours

y = 4 hours

Now, since extra hours = 4 hours and normal working hours = 8 hours.

Then, total working time for that day = 8 + 4 = 12 hours

Answer:

Step-by-step explanation:

The box  when shipped is 5 pounds

The box alone =                 2 pounds         Subtract

What's left is                       3 pounds

1 sea turtle weighs            1 pound

3 sea turtles weigh            x

1/3 = 1 / x                             Cross multiply

1*x = 3*1

x = 3

He ships 3 sea turtles.

Answer:

The height and  width of the interior tile =  3·x + 4 - 4 = 3·x and 2·x + 4  - 4= 2·x

Please see attached diagram

Step-by-step explanation:

The given parameters are;

The given rectangular floor tile  with width = 3·x + 4 and height = 2·x + 4

Where, x is in centimetres

The interior tile maintains a height to width ration of 2:3

The dimension of the trim border = 2 cm

Therefore;

The relationship between the width and height of the interior and exterior tiles is given as follows

Width of exterior tile = Width of interior tile + 2 × The dimension of the trim border

Which gives;

Width of exterior tile = Width of interior tile + 2 × 2 = Width of interior tile + 4

Height of exterior tile = Height of interior tile + 2 × The dimension of the trim border

Height of exterior tile = Height of interior tile + 2 × 2 = Height of interior tile + 4

Where the interior tile maintains a height to width ration of 2:3, we have;

For a unit length x, The height and the width of the interior tiles are 2·x:3·x

Therefore, for a given height 2·x, the width will be 3·x

Given the width of the exterior tile =  3·x + 4

The height of the exterior tile will then be 2·x + 4 and the width of the exterior tile will be 3·x + 4

The sides ratio of the interior tiles remain 2·x:3·x = 2/3

Answer:

it took Goran 1 hour longer to clean the bathroom than it took him to clean the den.

Step-by-step explanation:

Answer:

To convert 3 1/2 hours to an improper fraction:

3 1/2 = 7/2

So, Goran took a total of:

1/8 + 7/2 = 8/8 + 28/8 = 36/8 = 4 1/2 hours

Thus, it took Goran:

4 1/2 - 3 1/2 = 1 hour longer to clean the bathroom.

Explanation:

To solve the problem, we first need to convert the mixed number 3 1/2 to an improper fraction. We can do this by multiplying the whole number (3) by the denominator of the fraction (2) and adding the numerator (1):

3 x 2 + 1 = 7

So, 3 1/2 is equal to 7/2.

Next, we can add the time it took Goran to clean the den (1/8 hours) to the time it took him to clean the bathroom (7/2 hours):

1/8 + 7/2 = 8/8 + 28/8 = 36/8 = 4 1/2 hours

Therefore, it took Goran a total of 4 1/2 hours to clean both the den and the bathroom.

To find out how much longer it took Goran to clean the bathroom, we can subtract the time it took him to clean the den (1/8 hours) from the time it took him to clean both the den and the bathroom (4 1/2 hours):

4 1/2 - 3 1/2 = 1 hour

Therefore, it took Goran 1 hour longer to clean the bathroom than it took him to clean the den.

The ordered pair (3, - 2) is not a solution to the equation 2x - y = 4

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x,y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

Given, an equation 2x - y = 4 now if  (3, - 2) is an ordered pair then putting the numerical value of x must satisfy the y value.

when x = 3,

2(3) - y = 4.

6 - y = 4.

- y = 4 - 6.

- y = - 2.

y = 2.

So,  (3, - 2) is not a solution to an equation 2x - y = 4.

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Answer:

6x+3

Step-by-step explanation:

If you're just combining like terms this is the correct answer

Hope attachment helps (✿^‿^)

Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

Meaning of probability :

Probability is calculation of how likely some event will happen. Whenever we are not sure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are going to happen.

The analysis of events governed by probability is called statistics.

According to the given information :

Red section = \(\frac{2}{5}\)

multiply numerator and denominator by \(2\) we get

Red section = \(\frac{4}{10}\)

 Blue section = \(\frac{1}{2}\)

 multiply numerator and denominator by \(5\) we get

 Blue section = \(\frac{5}{10}\)

 Green section = \(1\)- Red section - Blue section

 Green section =\(1-\frac{4}{10} -\frac{5}{10}\)

  Green section = \(\frac{1}{10}\)

Therefore Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

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Answer: The answer is 171.2 Miles

Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.

Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.

A division problem that have an estimated quotient of 12 is: C. 47.6 ÷ 3.9.

In Mathematics, a quotient can be defined as a mathematical expression that is typically used for the representation of the division of a number by another number.

This ultimately implies that, a quotient in terms of numerical data simply refers to a division of a number (numerator) by another number (denominator).

Quotient = 8 ÷ 0.95 = 8.42

Quotient = 18 ÷ 2.2 = 8.18.

Quotient = 47.6 ÷ 3.9 = 12.21 ≈ 12.0.

Quotient = 10.6 ÷ 1.89 = 5.61.

Quotient = 71.9 ÷ 6.5 = 11.06.

Quotient = 123.4 ÷ 9.2 = 13.41.

Quotient = 157.4 ÷ 16.4 = 9.60.

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Answer:

See below

Step-by-step explanation:

As CD⊥AB, ∠BDC = ∠ADC = 90°

∠BDC ≅ ∠ADC

and

We can substitute ∠ADC with ∠BDC and ∠DAC with ∠DBC

Then we get same equation for ∠BCD and ∠ACD

Therefore ∠BCD = ∠ACD = 1/2∠ACB

It proves that CD bisects ∠ACB

Equivalent fraction for 2/3 using 12 as a denominator :-

2/3 × 4/4 = 8/12

Equivalent fraction for 3/4 using 12 as a denominator :-

3/4 × 3/3 = 9/12

_______

RainbowSalt2222 ☔

Step-by-step explanation:

(7m - 3)² = 49m² - 42m + 9

play it through and do the actual multiplication behind the square :

(7m - 3)² = (7m - 3)(7m - 3) =

= 7m×7m + 7m×(-3) + (-3)×7m + (-3)(-3) =

= 49m² - 2×21m + 9 = 49m² - 42m + 9

Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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Answer:

y^-1= x +8

Step-by-step explanation:

this may be helpful for you

Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

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Answer:

Hello im am Drawing

Step-by-step explanation:

Answer:

3  3/4

(Decimal: 3.75)

Step-by-step explanation:

Hi!

Your answer is:

Hope this helps!

Let's write in scientific notation

\(\\ \sf\longmapsto 40180min\)

\(\\ \sf\longmapsto 40180(60)\)

\(\\ \sf\longmapsto 2410800\)

\(\\ \sf\longmapsto 2410\times 10^2\)

\(\\ \sf\longmapsto 2.4\times 10^5s\)

The square root of 76.8 is 8.76.

Square root of 76.8 is 8.746.

Given,

\(\sqrt{76.8}\)

Now,

Simplifying the square root :

If square root of x is to be calculated then,

\(\sqrt{x}\) = \(x^{1/2}\)

Similarly,

\(\sqrt{76.8}\) = \(76.8^{1/2}\)

= 8.746

Thus the square root of 76.8 is 8.746.

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