The end of a car tunnel has the shape
of a semi-circle on top of a rectangle.
The tunnel is exactly 4 km long.
a) Calculate the volume of air in the
tunnel with no cars in it.
b) The air in a car tunnel must be
exchanged frequently. If the exhaust
system pumps the air out at a rate of
10 m3
per second, how long does it
take to replace the stale air with fresh
air in the entire tunnel? Give your
answer in hours and minutes.

y =\((x/2)^2 + 1 or y = (x/2)^2 + 1\)

The curve represents a parabola opening upwards. It is symmetric about the y-axis.

Let's eliminate the parameter t and sketch the curves for each exercise:

1. x = t^2 + 2t, y = t + 1

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 + 2t = x

t = -1 ± √(x + 1)

Substituting the expression for t into the equation y = t + 1, we get:

y = (-1 ± √(x + 1)) + 1

y = -√(x + 1) or y = √(x + 1)

The curve represents two branches of a parabola opening upwards. It is symmetric about the y-axis.

2. x = cos(t), y = sin(t), (0, 2π]

Eliminating the parameter t, we obtain:

\(x^2 + y^2 = cos^2(t) + sin^2(t) \\= 1\)

The curve represents a circle centered at the origin with a radius of 1. It covers a full revolution (360 degrees or 2π) in the counterclockwise direction.

3. x = 2t + 4, y = t - 1

By eliminating the parameter t, we have:

t = (x - 4) / 2

Substituting this expression into the equation for y, we get:

y = ((x - 4) / 2) - 1

y = (x - 6) / 2

The curve represents a line with a slope of 1/2 and a y-intercept of -3. It is inclined upwards from left to right.

4. x = 3 - t, y = 2t - 3, 1.5 ≤ t ≤ 3

Eliminating the parameter t, we have:

t = 3 - x

Substituting this expression into the equation for y, we get:

y = 2(3 - x) - 3

y = 6 - 2x - 3

y = -2x + 3

The curve represents a line with a slope of -2 and a y-intercept of 3. It is inclined downwards from left to right.

\(5. x = 2t^2, y = t^4 + 1\)

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 = x/2

t = ±√(x/2)

Substituting the expressions for t into the equation y = t^4 + 1, we get:

y = (√(\(x/2))^4\) + 1 or y = (-√\((x/2))^4\) + 1

\(y = (x/2)^2 + 1 or y = (x/2)^2 + 1\)

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Answer:(1,7.5)

Step-by-step explanation:

Use Midpoint Formula

The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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Answer:

Step-by-step explanation:

Answer:

The Inequality representing money she can still spend on her friend birthday gift is .

Jordan can still spend at most $30 on her friends birthday gift.

Step-by-step explanation:

Given:

Total money need to spend at most = $45

Money spent on Yoga ball = $15

We need to find how much money she can still spend on her friend birthday gift.

Solution:

Let the money she can still spend on her friend birthday gift be 'x'.

So we can say that;

Money spent on Yoga ball plus money she can still spend on her friend birthday gift should be less than or equal to Total money need to spend.

framing in equation form we get;

The Inequality representing money she can still spend on her friend birthday gift is .

On solving the the above Inequality we get;

we will subtract both side by 15 using subtraction property of Inequality.

Hence Jordan can still spend at most $30 on her friends birthday gift.

Answer:

\(w=9\)

Step-by-step explanation:

\((4w-7)+(7w-2) = 90\\11w-9=90\\11w=99\\w=9\)

Answer:

No.

Step-by-step explanation:

It is given that Darius is putting tiles on the roof of his house.

Darius had completed = \($\frac{4}{5}$\) th of the work

He takes time = \($3 \frac{1}{3}$\) hours to complete \($\frac{4}{5}$\) th of the work

The remaining work = \($1 -\frac{4}{5}$\)

                                 \($=\frac{5-4}{5}$\)

                                 \($=\frac{1}{5}$\)

∴  Darius completes \($\frac{4}{5}$\) th of the work in = \($\frac{10}{3}$\) hours

                           So, \($\frac{1}{5}$\) th of the work in = \($\frac{10}{3} \times \frac{5}{4} \times \frac{1}{5}$\) hours

                                                                 \($=\frac{10}{12}$\) hours

Therefore total time taken to complete the work \($=\frac{10}{3}+\frac{10}{12}$\) hours

                                                                                  \($=\frac{40+10}{12}$\) hours

                                                                                  \($=\frac{50}{12}$\) hours

                                                                                  \($=4\frac{2}{12}$\) hours

                                                                                  \($=4\frac{1}{6}$\) hours

Thus, Darius continues to work at the same rate will not be able to complete the work in 4 hours.  

The number of hours that Larissa's family will drive is given as follows:

66 hours.

The number of hours that Larissa's family will drive is obtained applying the proportions in the context of the problem.

The map calculates drive time with no stops to be 2 3/4 days, hence the number of hours is obtained as follows, considering that each day is composed by 24 hours:

Then the number of hours that Larissa's family will drive is obtained as follows:

48 + 18 = 66 hours.

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Answer:

4

Step-by-step explanation:

Answer:

\(\dfrac{7}{9}\)

Step-by-step explanation:

\(\dfrac{x+1}{y+1}=\dfrac{4}{5}\\\Rightarrow 5x-4y=-1\)

\(\dfrac{x-5}{y-5}=\dfrac{1}{2}\\\Rightarrow 2x-y=5\)

Putting it in matrix form

\(\begin{bmatrix}a_{1}&b_{1}\\a_{2}&b_{2}\end{bmatrix}{\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}{c_{1}}\\{c_{2}}\end{bmatrix}\\\Rightarrow\begin{bmatrix}5 & -4\\2 & -1\end{bmatrix}\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}-1\\ 5\end{bmatrix}\)

From Cramer's rule we have

\(x=\dfrac{\begin{vmatrix}c_1 &b_1 \\ c_2 & b_2\end{vmatrix}}{\begin{vmatrix}a_1 &b_1 \\ a_2& b_2\end{vmatrix}}\\\Rightarrow x=\dfrac{\begin{vmatrix}-1 &-4 \\ 5 & -1\end{vmatrix}}{\begin{vmatrix}5 &-4 \\ 2& -1\end{vmatrix}}\\\Rightarrow x=\dfrac{1+20}{-5+8}\\\Rightarrow x=7\)

\(y=\dfrac{\begin{vmatrix}a_1 &c_1 \\ a_2 & c_1\end{vmatrix}}{\begin{vmatrix}a_1 &b_1 \\ a_2& b_2\end{vmatrix}}\\\Rightarrow y=\dfrac{\begin{vmatrix}5 &-1 \\ 2 & 5\end{vmatrix}}{\begin{vmatrix}5 &-4 \\ 2& -1 \end{vmatrix}}\\\Rightarrow y=\dfrac{25+2}{-5+8}\\\Rightarrow y=9\)

Verifying the results

\(\dfrac{7+1}{9+1}=\dfrac{8}{10}=\dfrac{4}{5}\)

\(\dfrac{7-5}{9-5}=\dfrac{2}{4}=\dfrac{1}{2}\)

Hence, the fraction is \(\dfrac{7}{9}\).

Answer:

this is a positive correlation

Step-by-step explanation:

it is going up so its positive

The first mistake McKenna made when change the expression to standard form is in step 2.

PEMDAS in mathematics it is a order of operations that must be prioritize when involving more than one operation. PEMDAS is abbreviation for Parentheses, Exponents, Multiply, Divide, Add, Subtract.

For multiply and divide the priority is for those who come first. Also for add and subtract the priority is for those who come first. And for the rest is the priority in order Parentheses, Exponents, Multiply and Divide, Add and Subtract.

In step 2, McKenna added 3 and -5 first when McKenna should have multiplied -5 by (3a+6). Thus, the step 2 is the first time McKenna made a mistake during change the expression to standard form.

You question is incomplete, but most probably your full question was

McKenna was asked to write the following expression in standard form.

3−5(3a+6)

When writing the expression in standard from, McKenna made a mistake.

3−5(3a+6)

3+(−5)(3a+6) Step 1

−2(3a+6) Step 2

−6a+(−12) Step 3

−6a−12 Step 4

McKenna made her first mistake in

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Time taken by Miguel car to drive is, 1.6 hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.

We know that;

⇒ Speed = Distance / Time

⇒ Time = Distance / Speed

Here, Speed = 53 miles per hour

Distance = 84.8 miles

Hence, We get;

⇒ Time = 84.8 / 53

⇒ Time = 1.6 hour

Thus, Time taken by Miguel car to drive is, 1.6 hour.

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Answer:

Step-by-step explanation:

180 = 2x + 10 +3x

170 = 5x

34 = x

m∠B = 3(34) = 102°

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

All ten conditions of a vector space are satisfied for V = Rⁿ over R, and therefore it is indeed a vector space over R.

Let V = Rⁿ.

To verify that it is a vector space over R, we need to verify that the following conditions hold:

Closure under vector addition: For any two vectors u and v in V, u + v is also in V. This is easy to see since u and v are each n-dimensional real-valued vectors, and their sum is also an n-dimensional real-valued vector.

Commutativity of vector addition:

For any two vectors u and v in V, u + v = v + u. This follows from the commutativity of addition in R.

Associativity of vector addition:

For any three vectors u, v, and w in V, (u + v) + w = u + (v + w). This follows from the associativity of addition in R.

Identity element for vector addition: There exists a vector 0 in V such that for any vector u in V, u + 0 = u. The zero vector with all n components equal to zero is such an element.

Inverse elements for vector addition: For any vector u in V, there exists a vector -u in V such that u + (-u) = 0.

The additive inverse of the vector u is the vector with each component negated, that is, (-u)i = -ui for i = 1, ..., n.

Closure under scalar multiplication: For any scalar c in R and any vector u in V, cu is also in V. This follows from the fact that each component of cu is obtained by multiplying the corresponding component of u by the scalar c.

Distributivity of scalar multiplication over vector addition: For any scalar c in R and any vectors u and v in V, c(u + v) = cu + cv. This follows from the distributivity of multiplication in R.

Distributivity of scalar multiplication over scalar addition: For any scalars c and d in R and any vector u in V, (c + d)u = cu + du. This also follows from the distributivity of multiplication in R.

Associativity of scalar multiplication: For any scalars c and d in R and any vector u in V, c(du) = (cd)u

This follows from the associativity of multiplication in R.

Identity element for scalar multiplication: For any vector u in V, 1u = u. The scalar 1 acts as the identity element under scalar multiplication.

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Answer:

ko nhầm thì là Thái Lan ...... đúng là Thái Lan

Answer:

So the correct option is:

d) x = (3 ± √13) / 2

Step-by-step explanation:

To find the solutions of the equation x^2 - 3x - 1 = 0 using the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a), we can identify the values of a, b, and c from the given equation.

a = 1

b = -3

c = -1

Substituting these values into the quadratic formula, we get:

x = (-(-3) ± √((-3)^2 - 4(1)(-1))) / (2(1))

Simplifying further:

x = (3 ± √(9 + 4)) / 2

x = (3 ± √13) / 2

Therefore, the exact solutions of the equation x^2 - 3x - 1 = 0 are:

x = (3 + √13) / 2

x = (3 - √13) / 2

Answer:

c. x = the quantity of 3 plus or minus the square root of 13 all over 2

Step-by-step explanation:

Using quadratic formula with a = 1, b = -3, and c = -1.

x = [-(-3) ± √{(-3)^2 - 4(1)(-1)}] / ]2(1)]

x = (3 ± √13)/2

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

To estimate the standard deviation using the range rule of thumb, we can use the following formula:

Standard Deviation ≈ Range / 4

First, let's find the range of the race speeds:

Range = Maximum Value - Minimum Value

In this case, the maximum value is 189.2 and the minimum value is 175.6.

Range = 189.2 - 175.6 = 13.6

Now, we can use the range to estimate the standard deviation:

Standard Deviation ≈ 13.6 / 4 ≈ 3.4

Rounding to the nearest tenth, the estimated standard deviation is approximately 3.4.

The estimated standard deviation of the race speeds, using the range rule of thumb, is approximately 3.4.

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The given system is singular because we can find a combination of the three equations that adds up to 0=1.

To do this, we multiply the first equation by -1, the second equation by 2, and the third equation by -4, giving us the following:

-1*(2u + 2v + 4w = 1) + 2*(u + v + 2w = 0) - 4*(3w = 1 + vy + 2w = 0) = 0

This simplifies to 0 + 0 + 0 = 1, which is impossible, showing that the system is singular.

To allow the equation to have solutions, we replace the 0 on the right of the equation with a variable x, giving us the equation 0 + 0 + 0 = x. Solving this equation, we can set x = 0, which gives us 0 + 0 + 0 = 0, which is a valid equation with the solution x = 0.

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Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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Answer:

\(y=-3x+8\)

Step-by-step explanation:

\(-2x+6y=-4\\6y=2x-4\\y=\frac{1}{3}x+\frac{2}{3}\\\)

if two lines perpendicular,

\(m_{1} .m_{2}=-1\\ \frac{1}{3} .m_{2}=-1\\m_{2}=-3\)

the line perpendicular to this line is

\(y=-3x+k\) ; k ∈ R

the line passes through the point (5,-7)

so,

\(-7=-3.(5)+k\\-7=-15+k\\k=8\)

∴the equation of a line that passes through the point (5,-7) and is perpendicular to the line -2x+6y=-4 is

\(y=-3x+8\)

Answer:

250 $3 tickets and 100 $2 tickets were sold.

Step-by-step explanation:

easy :)

She will need the amount 1 jar of meat (32 cals, 4g protein) and 2 jars of vegetables (32 cals, 2g protein) to get 4g of protein and 112 calories.

A mother is trying to decide which baby foods to serve her infant. She has a jar of meat with 4g of protein and 32 calories, and a jar of vegetables with 2g of protein and 16 calories. To get the desired amount of protein and calories, she will need to serve 1 jar of meat and 2 jars of vegetables. This will give her 4g of protein and 112 calories total. This combination of foods will provide the infant with the necessary nutrition for growth and development. It's important to make sure that infants are getting enough protein and calories during the first year of life, so this combination of food is a great way to ensure that the infant is getting the nutrients that they need.

1 jar of meat = 4g of protein and 32 calories

1 jar of vegetables = 2g of protein and 16 calories

Therefore, in order to get 4g of protein and 112 calories:

1 jar of meat = 4g of protein and 32 calories

2 jars of vegetables = 4g of protein and 32 calories

Total: 4g of protein and 112 calories

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Expression is; 29 - x = 16 an expression to represent this situation.

Where in mathematics is an expression?

An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

                               Term is a mathematical concept that refers to a constant, a single variable, or a mixture of variables and constants along with multiplication or division. Example of an algebraic expression: 3x + 9; 5x + 10

We are told that at lunchtime, it was 29 degrees Celsius and that by sunset, the temperature had dropped to 16 degrees Celsius.

Let the drop be x.

Thus;

29 - x = 16

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The complete question is -

On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

Angles are 6 types.

1.Acute Angle: An acute angle is any angle that is less than 90 degrees and is between 0 degrees and 90 degrees.

2.Obtuse Angle: Opposite of an acute angle is an obtuse angle. In other terms, an obtuse angle is one that is larger than 90 degrees and less than 180 degrees. It is the angle that is between 90 degrees and 180 degrees.

3. Right Angle: A right angle is always 90 degrees in length. Acute angles are those that are less than 90 degrees, whereas obtuse angles are those that are higher than 90 degrees.

4. Straight Angle: A straight angle has a measured angle of 180 degrees. Since the angle between its arms is 180 degrees, you can see that it is simply a straight line.

5.Reflex angle: The arms make an acute angle because this measurement is less than 90 degrees. What about the angle on the opposite side, though? What is the name of the larger angle that complements the acute angle? It is referred to as a reflex angle.

A reflex angle is any angle having a dimension higher than 180 degrees but less than 360 degrees (which corresponds to 0 degrees).

6.Complete Rotation: Entire rotation or full angle refers to an angle with a value of 360 degrees. When one of the arms extends completely, it is created.

Angles are 6 types.

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The ranges overlap, it is possible for both measurements to be correct.

Since they show how precise and accurate the numbers being utilised are, significant figures are crucial in measurements and computations. In order to prevent mistakes and maintain the required degree of precision, it is crucial to maintain consistency in the number of significant figures throughout computations. This indicates the amount of uncertainty in a measurement.

Given that, Deondra measures an object as 2 3/4 inches and  Abdul measures 2 1/2 inches to the nearest half inch.

The actual length for Deondra is  between 2 5/8 inches and 2 7/8 inches.

For Abdul the actual length is between 2 inches and 3 inches.

Since the ranges overlap, it is possible for both measurements to be correct.

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Answer:

QT=8 VQ=17 this is what i came up with because i myself have ur question and i don't know what it is?