33) A farmer needs to construct a bridge over a stream to connect fields for his sheep to graze. He will do most
of the planning on his own. Name some measurements that will need to be made by a professional engineer.

Answers

Answer 1

Answer:

There are several measurements that a professional engineer would need to make in order to design and construct a bridge over a stream for a farmer's sheep to graze. These measurements may include:

Width and depth of the stream: The engineer will need to determine the width and depth of the stream in order to determine the size and type of bridge that is needed.

Soil composition and stability: The engineer will need to assess the soil composition and stability of the area surrounding the stream in order to determine the foundation and support structure needed for the bridge.

Water flow: The engineer will need to measure the water flow in the stream in order to determine the load-bearing capacity of the bridge and to ensure that it is able to withstand the forces of the water.

Distance between the two banks: The engineer will need to measure the distance between the two banks of the stream in order to determine the length of the bridge and ensure that it is long enough to span the stream.

Height of the banks: The engineer will need to measure the height of the banks of the stream in order to determine the height of the bridge and ensure that it is tall enough to allow the sheep to pass under it.


Related Questions

In coordinate plane the point A(-4,8) B(10,1) and C(-2,-7) are reflected over the y-axi to the point A , B ,C repectively what are the coordinate of A, B, and C

Answers

The distance formula can be used to determine this distance. The formula d = (x 2  x 1 ) 2 + (y 2  y 1 ) 2 can be used to describe the distance that separates the two points (x 1, y 1) and (x 2, y 2).

Which coordinate sequence is correct?

The y-coordinate comes after the x-coordinate in every case. The coordinate grid below demonstrates that the ordered pairs (3,4) and (4,3) are two distinct points!

How are XY coordinates written?

Coordinates are written as (x, y), with the x-axis point being written first and the y-axis point following. The expression "along the corridor, up the stairs" may be used to remind some children of this, instructing them to follow the x axis first and then the y.

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A local store is keeping track of service times. The table below shows the number of customers served and the time it took.

Answers

Answer: It appears to take the same amount of time to serve each customer

It takes 40 minutes to serve  10 customers.

Step-by-step explanation:

It appears to take the same amount of time to serve each customer

To find the number of minutes it takes

Divide the number of times by the number of customers

16/4 = 4

it takes 4 minutes to serve 1 customer

Find the number of time it takes to serve 10 customer

10*4=40

It takes 40 minutes to serve  10 customers.

Simplify the expression.

the linear expression quantity negative 1 over 5 times r minus 6 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 5 times r plus 8 end quantity

negative 53 over 35 times r minus 2
negative 11 over 35 times r minus 2
negative 11 over 35 times r plus negative 14
3 over 35 times r plus negative 14

Answers

After solving the equation, the value obtained will be equal to negative 11 over 35 times r plus negative 14. Hence, option C is correct.

What is an expression?

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given statement in the question,

The equation will be,

(-1/5r - 6 - 5/7r) - (-3/5r) - 8

Rearrange the equation with like terms,

-1/5r - 5/7r + 3/5r - 8 - 6

(-7r - 25r + 21r)/35 -14

=-(11/35)r - 14.

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Mabel buys a television
priced at $84.75. If the
sales tax is 8%, how
much will Mabel pay for
the television?
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Answers

Answer:

Mabel will pay $91.53 for the television.

Step-by-step explanation:

To calculate the total cost of the television including sales tax, we first need to calculate the amount of sales tax by multiplying the price of the television by the sales tax rate. This gives us $84.75 * 0.08 = $6.78 in sales tax.

To find the total cost of the television, we add the price of the television to the sales tax amount. This gives us $84.75 + $6.78 = $91.53.

Therefore, Mabel will pay $91.53 for the television.

Please help quick show work and explain

Answers

The maximum height of the ball is of: 5 feet.The ball is at the maximum height at a time of: 0.25 seconds.The ball hits the ground at a time of: 0.809 seconds.

How to obtain the measures?

The height of the ball after x seconds is given by the quadratic function presented as follows:

y = -16t² + 8t + 4.

This is a concave down parabola, hence the vertex of the function is the maximum point.

The coefficients of the quadratic function are given as follows:

a = -16, b = 8, c = 4.

Then the x-coordinate of the vertex is given as follows:

x = -b/2a = -8/-32 = 0.25.

The maximum height of the ball is given as follows:

y = -16(0.25)² + 8(0.25) + 4 = -1 + 2 + 4 = 5 feet.

The ball hits the ground when:

y = 0.

Hence:

-16t² + 8t + 4 = 0.

Solving the quadratic equation, the positive solution is given as follows:

t = 0.809 seconds.

The graph of the quadratic function is given by the image shown at the end of the answer.

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which type of rigid transformation is the equivalent of two reflections across intersecting lines?
a. glide reflection
b. rotation
c. reflection
d. none of these

Answers

Answer:

a

Step-by-step explanation:

The equivalent of two reflections across intersecting lines is a glide reflection.

A glide reflection is a combination of a translation and a reflection. It involves moving an object along a line, and then reflecting the object across the same line. Since a reflection is an isometry (a transformation that preserves the distance between points), a glide reflection is also an isometry.

In contrast, a rotation is a transformation that involves turning an object around a fixed point, and a reflection is a transformation that involves flipping an object across a mirror line. Neither of these transformations is equivalent to two reflections across intersecting lines.

Therefore, the correct answer is (a) glide reflection.

A proportional relationship exists between x and y. When X=8 the value of Y is 14
(a) Write an equation for y in terms of x.
(b)your equation to determine the value of y when x=36
in simplest form, what is the ratio of the change in y to the change in x for this relationship? fill in the following:
y increases units for every units of increase in x.

Answers

Answer:

a)y=x+6

b)y=42

c)

Step-by-step explanation:

if x=8 ,y=14that means that y=x +a thus y=14,x=8 14=8+a hence a=14-8. a=6 thus y=x+6

using the equation in a above y =x+6 ,x=36 thus y=36+6 hence y=42

Ahok purchaed 15. 5kg rice and 3. 250kg ugar from the upermarket. Find the total weight of hi purchae

Answers

Using simple mathematical operations we know that Ashok purchased rice and sugar which together weights 18.75kg.

What are mathematical operations?

A mathematical function known as just an operation converts zero or more input values into a precisely defined output value.

A quantity of operands affects the operation's arity.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, we know that:

Ashok purchased 15.5kg of rice and 3.25 kg of sugar.

Now, the total weight of rice and sugar Ashok purchased is:

15.5 + 3.25

18.75kg

Therefore, using simple mathematical operations we know that Ashok purchased rice and sugar which together weights 18.75kg.

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The velocity v of an object dropped from a tall building is given by the formula v = √64d where d is the distance the object has dropped. Solve the formula for d.

Answers

The solution for d in the equation v = √64d is d = v²/64

How to determine the solution for d in the equation?

From the question, we have the following parameters that can be used in our computation:

v = √64d

Take the square root of both sides

So, we have the following representation

v² = 64d

Divide both sides of the equation by 64

So, we have the following representation

v²/64 = d

Rewrite as

d = v²/64

Hence, the value of d is d = v²/64

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Aaron's mom had a long day at work. "I feel like I drank 3 gallons of coffee today!" she joked. If she really drank that much coffee, how many times would she have filled her 12-fluid-ounce mug?

Answers

The number of times that she has filled her 12-fluid-ounce will be 33.307.

What is conversion?

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

We know that in 1 gallon, there are 133.228 fluid ounces.

The amount of coffee in 3 gallons will be given as,

3 gallons = 3 x 133.228

3 gallons = 399.684 fluid ounces

The number of times that she has filled her 12-fluid-ounce will be given as,

⇒ 399.684 / 12

⇒ 33.307

The number of times that she has filled her 12-fluid-ounce will be 33.307.

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4. Given the equation
y =- 3x + 2.5:
a) When x is 1, what value of y makes the equation true?

Answers

Answer:

To find the value of y when x is 1, we can substitute 1 for x in the equation and solve for y:

y = -3(1) + 2.5

y = -3 + 2.5

y = -0.5

Therefore, when x is 1, y is -0.5.

is the answer is correct? correct me if im wrong

A boat travels 80 miles downstream in 4 hours. It makes the return trip, against the current, in twice the time. What is the speed of the current? (Remember: rate x time = distance)
[Please show and explain how you solved this word problem.]

Answers

By solving simultaneous linear equation, it can be calculated that

Speed of the current is 5 miles/hour

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here a simultaneous linear equation needs to be solved

Let the speed of boat in still water be x miles/hour and speed of stream be y miles/hour

Speed of the boat downstream = (x  + y) miles/hour

Speed of the boat upstream = (x - y) miles/hour

A boat travels 80 miles downstream in 4 hours

x + y = [tex]\frac{80}{4}[/tex]

x + y = 20 .... (1)

A boat travels 80 miles upstream in 8 hours

x - y = [tex]\frac{80}{8}[/tex]

x - y = 10 .... (2)

Subtracting (2) from (1)

2y = 10

y = [tex]\frac{10}{2}[/tex]

y = 5 miles/hour

Speed of the current is 5 miles/hour

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catherine rolls a standard $6$-sided die five times, and the product of her rolls is $300.$ how many different sequences of rolls could there have been? (the order of the rolls matters.)

Answers

Answer:

150 sequences

Step-by-step explanation:

Let's find the sets of 5 integers less than or equal to 6 that could multiply to 300 (where order doesn't matter for right now):

1, 2, 5, 5, 6

1, 3, 4, 5, 5

2, 2, 3, 5, 5

Now let's find the number of unique ways we could reorder these sets

There are [tex]\frac{5!}{2!} = 60[/tex] ways to order {1, 2, 5, 5, 6}

There are [tex]\frac{5!}{2!} = 60[/tex] ways to order {1, 3, 4, 5, 5}

There are [tex]\frac{5!}{2!2!} = 30[/tex] ways to order {2, 2, 3, 5, 5}

There could have, therefore, been 60 + 60 + 30 = 150 different sequences of rolls

HI, i am in 7th grade i really need help this question is confusing
At the start, the water level of the river was 12 centimeters below its normal water level.
After a day of rain, the water level of the river increased by 18 centimeters.
The next 8 days were dry, and the water level of the river dropped by 2.6 centimeters each day.
Enter a numerical expression representing the water level after the 9 -day period.

What is the value of the expression you entered in part A?
What does the value in part B mean in the situation?

Answers

The changes in the river water level with reference to the normal water level in the 9-day period is analyzed as follows;

Part A: The numerical expression representing the water level after the 9-day period is; -12 + 18 - 8 × 2.6

Part B; -12 + 18 - 8 × 2.6 = -14.8

Part C; The meaning of -14.8 is that the water level after the 9-day period is 14.8 centimeters below the normal water level.

What is a mathematical expression?

A mathematical expression is a collection of numbers and, or variables and operators combined according to the rules of mathematical operations.

Part A

The water level of the river at the start = 12 centimeters below its normal level

The amount by which the water level increases after a day of rain = 18 centimeters

The amount by which the water level reduces in the next 8 days = 2.6 centimeters per day

The numerical expression that represents the water level in the 9-day period is therefore;

-12 + 18 - 8 × 2.6

Part B

The value of the expression -12 + 18 - 8 × 2.6 is; -12 + 18 - 8 × 2.6 = -14.8

Part C

The meaning of the value -14.8 is that the water level after the 9-day period is 14.8 centimeters below the the normal water level of the river

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A circle has a diameter of 20 ft. What is the area?
Show or explain your reasoning.

Lots of love for the ones who helps!! <3

Answers

The area of a circle is given by the formula:

area = pi * r^2

where pi is a constant approximately equal to 3.14 and r is the radius of the circle.

To find the area of the circle, we first need to find the radius. The radius is half the diameter, so the radius of the circle is 20/2 = 10 feet.

Plugging this value into the formula, we get:

area = 3.14 * 10^2 = 3.14 * 100 = 314 square feet

So the area of the circle is 314 square feet.

Answer:

100π, or about 312. Could also be 314.16 if it needs to be rounded.

Step-by-step explanation:

First, the area of a circle is πr^2

To find radius, it's diameter/2.

So the radius is 20/2 which is 10.

With this, we plug it in: π(10)^2 = π100 = 100π.

That is an exact answer. For a rounded answer, assume π = 3.14.

3.14*100 = 314 sqr feet.

However, it you want to round the final answer, 100π is around 314.159265359 thus making rounding to the nearest hundredth 314.16.

Arturo is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday, spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange, and rolls a fair die in the shape of a cube that has six sides labeled 1 to 6?

Answers

There are 6 different possible outcomes.

What is probability ?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The party which calls the coin's side wins.

We find it because when we turn a coin very often, humans get half the heads and half the tails.

The chances of swinging the head are 1/2 , and the chances of swinging the tail are 1/2 .

Total outcomes = 2×5×6

                           = 60

So the final answer is 60

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The larget taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. The total weight of thee two ingredient wa 617. 3 kg. How many kilogram of each ingredient were ued?

Answers

The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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Two idewalk in a park are repreented by line on a coordinate grid. Two point on each of the line are hown in the table. Sidewalk 1 x y 0 3 2 7 Sidewalk 2 x y 1 5 3 3 (a) Write the equation for Sidewalk 1 in lope-intercept form. (b) Write the equation for Sidewalk 2 in lope-intercept form. (c) I the ytem of equation conitent independent, coincident, or inconitent? Explain. (d) If the two idewalk interect, what are the coordinate of the point of interection? Ue the ubtitution method and how your work

Answers

a) The equation is: y = 2x + 3. b) The equations are :Point - slope form: y - 5 = -(x - 1).Slope - intercept form: y = -x + 6. c) The systems are consistent independent. d) The point of intersection is (1, 5).

Linear function

A linear function is defined in slope-intercept formula by the rule presented as follows:

y = mx + b.

In which:

m is the constant rate of change of the function, called slope.

b is the value of y when x = 0, called intercept.

For Sidewalk 1, it is found that:

When x increases by 2, y increases by 4, hence the slope is of m = 2.

When x = 0, y = 3, hence the intercept is of b = 3.

Then the rule is:

y = 2x + 3.

For Sidewalk 2, when x changes by 2, y decays by 2, hence the slope is:

m = -2/2 = -1.

The line goes through point (1,5), hence the equation in point-slope form is:

y - 5 = -(x - 1).

Combining the like terms, the slope-intercept form is:

y - 5 = -x + 1

y = -x + 6.

Since the two lines have different slopes, the system is consistent independent.

The x-coordinate of the intersection is:

-x + 6 = 3 + 2x.

3x = 3

x = 1.

The y-coordinate is:

-x + 6 = -1 + 6 = 5.

Hence the intersection point is:

(1, 5).

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​ 2x(x+4)+7=(x+8)+2x(x+1)+122x(x+4)+7=(x+8)+2x(x+1)+12

Answers

Answer:

x = (-10 + sqrt(180)) / 8

= -1.25 + 0.75 * sqrt(5)

x = (-10 - sqrt(180)) / 8

= -1.25 - 0.75 * sqrt(5)

Step-by-step explanation:

To solve the given equation, we need to combine like terms and isolate the variable on one side of the equation. The given equation is:

2x(x+4)+7=(x+8)+2x(x+1)+12

We can start by expanding the parentheses on the left-hand side to obtain:

2x^2 + 8x + 7 = x + 8 + 2x^2 + 2x + 12

We can then combine like terms on both sides of the equation to get:

4x^2 + 10x - 5 = 0

To solve for x, we can use the quadratic formula, which states that the solutions of the equation ax^2 + bx + c = 0 are given by:

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

In the given equation, we have a = 4, b = 10, and c = -5, so the solutions are:

x = (-10 +/- sqrt(10^2 - 4 * 4 * (-5))) / 2 * 4

= (-10 +/- sqrt(100 + 80)) / 8

= (-10 +/- sqrt(180)) / 8

This gives us two solutions:

x = (-10 + sqrt(180)) / 8

= -1.25 + 0.75 * sqrt(5)

x = (-10 - sqrt(180)) / 8

= -1.25 - 0.75 * sqrt(5)

These are the two solutions of the given equation. Note that we could also write the solutions in a simplified form by factoring the quadratic and using the zero product property, but the quadratic formula is generally more reliable and easier to use.

a population has a mean of 120 and a standard deviation of 10. if a sample of size 25 is collected, how much distance on average is expected between the sample mean and the population mean?

Answers

When a sample of size 25 is taken from a population with a mean of 120 and a standard deviation of 10,The expected distance between the sample mean and the population mean is 2.5.

The mean of a population is the average value of all the data points, while the standard deviation is a measure of how spread out the data points are. When a sample of size 25 is taken from a population with a mean of 120 and a standard deviation of 10, the expected distance between the sample mean and the population mean is 2.5. This is because the standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard deviation of the sample mean would be 10/5 = 2, and the expected distance between the sample mean and the population mean would be 2 x 2.5 = 2.5.

Standard deviation of the sample mean = Population standard deviation / √ Sample size

= 10 / √25

= 10 / 5

= 2

Expected distance between the sample mean and the population mean = 2 x 2.5

= 2.5

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State the corresponding part used on a specific segment or angle

Answers

They all look correct to me!

f the toss of a coin comes down heads, you win two dollars. if it comes down tails, you lose fifty cents. how much would you expect to gain after 21 tosses (in $ dollars)? $ .

Answers

In each toss, the expected value is the probability of winning multiplied by the amount won, minus the probability of losing multiplied by the amount lost. The probability of winning is 1/2, or 0.5, and the probability of losing is also 1/2, or 0.5. The amount won is $2, and the amount lost is $0.50. So the expected value of each toss is 0.5 * $2 - 0.5 * $0.50 = $0.75.

Therefore, after 21 tosses, you would expect to gain an amount equal to 21 * $0.75 = $<<21*0.75=15.75>>15.75.

What does basic probability mean in math?

The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.

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Solve the following inequality algebraically: negative 2 less-than startfraction x over 3 endfraction 1 less-than 5 a. negative 9 greater-than x greater-than 12 b. negative 9 less-than x less-than 12 c. negative 2 less-than x less-than 5 d. negative 2 greater-than x greater-than 5

Answers

The solution to the inequality algebraically is -9 < x < 12

How to solve the inequality algebraically

From the question, we have the following parameters that can be used in our computation:

negative 2 less-than startfraction x over 3 endfraction 1 less-than 5

Express the statement using numbers and expressions

So, we have the following representation

-2 < x/3 + 1 < 5

Subtract 1 from all sides of the inequality

This gives

-3 < x/3 < 4

Multiply through the inequality by 3

So, we have

-9 < x < 12

Hence, the solution is -9 < x < 12

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Answer:

b. Negative 9 less-than x less-than 12

Step-by-step explanation:

Umm please help me with this

Answers

Answer:

for the first question it would be 7.5

The second one would we 28

The third one would be A

Step-by-step explanation:

What i mr Portillo cat weigh 6 kilogram her dog weigh 22 kilogram more than her cat

Answers

The total weight of Mrs. Portillo's cat and the dog is 34 kilograms.  

Mathematical operations:

The mathematical operations known as operators focus on particular activities, such as adding, taking away, adding multiple times and dividing equally, etc.

The four fundamental operations in Maths are

1. Addition

2. Subtracting

3. Multiplications

4. Divisions

Here we use Addition to solve the problem

Here we have

Cat's weight = 6 kilograms

Her dog weighs 22 kilograms more than her cat

Weight of dog = Cat's weight + 22 kilograms

= 6 kilograms + 22 kilograms

= 28 kilograms

Total weight of Mrs. Portillo's cat and dog = 6 + 28 = 34 kilograms

Therefore,

The total weight of Mrs. Portillo's cat and the dog is 34 kilograms.  

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Complete Question:

What is the total weight of her cat and dog? Mrs. Portillo's cat weighs 6 kilograms her dog weighs 22 kilograms more than her cat.

analia wants to know which school has higher academic achievements relative to the number of teachers per student. 1) analia thought of two different ways to define this quantity. identify these two definitions among the following options. choose 2 answers: choose 2 answers: (choice a) a graduation rate divided by number of teachers (choice b) b graduation rate divided by teachers per student (choice c) c sat average divided by number of teachers (choice d) d sat average divided by teachers per student 2) determine which school has higher academic achievements relative to the number of teachers per student, according to the two definitions. did you get the same result for both definitions? choose 1 answer: choose 1 answer: (choice a) a yes. according to both definitions, school a has higher academic achievements relative to the number of teachers per student. (choice b) b yes. according to both definitions, school b has higher academic achievements relative to the number of teachers per student. (choice c) c no. the definitions have opposite results.

Answers

The two different quantities Analia thought to measure which school has higher academic performance are :

B. Graduation rate / Budget per student

D. SAT average / Budget per student

How to find the different quantities Analia thought to measure which school has higher academic performance?

In other to define a quantity which measures academic achievement;

We take the ratio of a related metric or parameter which is a measure of the academic performance of the student in each school and the budget per student for each school .

The parameters which could be used to measure academic achievement are;

The graduation rate of each school.

The SAT average of each school.

Hence, the quantity to measure academic achievement relative to budget per student could be expressed as ;

Graduation rate / Budget per student

SAT average / Budget per student

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2.6 sq. cm X 3.1 cm

Answers

Answer 8.06 X 10-8 M*4

Step-by-step explanation: No Explanation Just Answer srry could think of a way to say it.

2. If the distance travelled by a rickshaw in one hour is 10 km, then the distance travelled by the same rickshaw with the same speed in one minute is:

Answers

Answer:

166 meters/minute

Step-by-step explanation:

get speed in m/sec by multiplying 10 with 5/18

=

2.7m/sec

multiply it by 60 to get meters/minute

=

166 meters/minutes

Answer: 10/60, so 1/6 of a km of km per minute

Step-by-step explanation:

Which pair of points represents a line segment with a slope of and a length of 15 units?

Answers

By using slope, it can be calculated that

(-8, -5) and (1, 7) represents a line with slope of [tex]\frac{4}{3}[/tex] and length 15 units

What is slope of a line?

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

For the first option

(-11, 7) and (1, -2)

Slope = [tex]\frac{-2-7}{1 - (-11)}[/tex]

          = [tex]-\frac{9}{18}[/tex]

          = [tex]-\frac{1}{2}[/tex]

First option is wrong

For the second option

(-2, -6) and (4, 2)

Slope = [tex]\frac{2 - (-6)}{4 - (-2)}[/tex]

          = [tex]\frac{8}{6}[/tex]

          = [tex]\frac{4}{3}[/tex]

Length =

[tex]\sqrt{(4 - (-2))^2 + (2-(-6))^2}\\\sqrt{36+64}\\\sqrt{100}\\[/tex]

10 units

Second option is wrong

For the third option

(-3, -2) and (9, 7)

Slope = [tex]\frac{7 - (-2)}{9 - (-3)}[/tex]

          = [tex]\frac{9}{12}[/tex]

          = [tex]\frac{3}{4}[/tex]

Third option is wrong

For the fourth option

(-8, -5) and (1, 7)

Slope = [tex]\frac{7 - (-5)}{1 - (-8)}[/tex]

          = [tex]\frac{8}{6}[/tex]

          = [tex]\frac{4}{3}[/tex]

Length =

[tex]\sqrt{(1 - (-8))^2 + (7-(-5))^2}\\\sqrt{81+144}\\\sqrt{225}\\[/tex]

15 units

Fourth option is correct

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Translate the sentence into an inequality. The sum of 8 and y is greater than or equal to 17.

Answers

Answer:

8+y[tex]\geq[/tex]17

Step-by-step explanation:

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