Public school per-student expenditures increased approximately linearly from $4.6 thousand in 1990 to $10.8 thousand in 2013. Predict the per-student expenditure in 2024.
In 2024 public school per-student expenditures will be about $thousand.
(Round the final answer to two decimal places as needed. Round all intermediate values to two decimal places as needed.

Tom's estimated travel time is approximately 13.6 hours.

Based on the given scenario, Tom is traveling a distance of approximately 340 nautical miles from Houston to New Orleans by boat. He will be using a medium-sized recreational boat with an average speed of 25 miles per hour.

To estimate the time it will take for his journey, we can use the formula:

Time = Distance / Speed

Substituting the values, we have:

Time = 340 miles / 25 miles per hour

Calculating the division, we find that Tom's estimated travel time is approximately 13.6 hours.

However, it is important to note that this estimate assumes a continuous journey without considering other factors that may affect the travel time. Various elements can impact the actual duration, such as weather conditions, water currents, navigational challenges, refueling stops, and any necessary rest breaks.

Additionally, it is essential for Tom to adhere to all boating regulations and safety guidelines to ensure a smooth and secure voyage.

To obtain a more accurate estimate, Tom should consult local boating authorities, marinas, or experienced sailors familiar with the route.

They can provide valuable insights into the specific conditions and offer guidance on potential challenges that may affect the travel time. Planning for additional buffer time is also recommended to account for unforeseen circumstances and to prioritize safety during the journey.

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The complete question may be like:

Tom plans to travel by boat from Houston, Texas, to New Orleans, Louisiana. He wants to estimate the time it will take for his journey. The distance between the two cities by water is approximately 340 nautical miles. Tom will be traveling on a medium-sized recreational boat that has an average speed of 25 miles per hour. Considering normal weather conditions and assuming a continuous journey, how long will it take Tom to reach New Orleans?

Please provide an answer based on this scenario, taking into account the distance, average speed, and any other relevant factors.

Answer:

y=3x-2

Step-by-step explanation:

You can verify it's not D because the y-intercept is at -2.

You can verify it's not A because that would mean the x-intercept is 2 despite it appearing to be closer to one.

You can verify it's not B because that would mean the x-intercept is 1.5

The value of angle ABE is 52°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.

The sum of interior angle in a triangle is 180°

Angle EBD = 180-(90+27)

= 180-117

= 63°

angle ABE + EBD = ABD

ABE = ABD - EBD

ABE = 115-63

= 52°

Therefore the value of angle ABE is 52°

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Option C is the correct representation of the solution of the inequality equation.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. Any of the symbols for inequality, including greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given the equation, \(\frac{x^{2} + 9x - 22 }{x + 4}\) ≥ 0

factors of x² + 9x - 22 are,

x² + 11x - 2x - 22

x(x + 11) - 2(x + 11) = (x + 11)(x - 2)

\(\frac{(x + 11)(x - 2)}{x +4}\) ≥ 0

x - 2 ≥ 0

x ≥ 2

so the line should be greater than and equal to 2.

so x + 11 ≥ 0

x ≥ -11

1/(x + 4) ≥ 0 or x + 4 < 0

x < -4

and line varies from,

-4 > x ≥ 11

graph of inequality is between -11 and -4 in which -4 is not included and -11 is included.

only the graph of option C satisfied the conditions.

Hence Option C is correct.

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Answer:

-19

Step-by-step explanation:

becuase its -19

\((x_1,y_1) = (-10,-7),~~(x_2, y_2) =(-5,-9)\\\\\text{Slope,}~ m =\dfrac{y_2 -y_1}{x_2 - x_1} =\dfrac{-9+7}{-5+10} = -\dfrac{2}{5} \\\\\\\text{Equation of line:}\\y -y_1 = m(x-x_1)\\\\\implies y +7 = -\dfrac{2}5 \left(x+10 \right)\\\\\implies 5y+35 = -2x -20\\\\\implies 5y+2x +35 +20 =0\\\\\implies 2x +5y +55=0\)

Answer:

11 weeks

Step-by-step explanation:

34+10x=144 equation

10x=110

x=11

check answer

11*$10=$110 money after 11 weeks at $10/week

    +.       34 money saved

     =.     144 money needed.

Answer:

We can't see the paint, and what's the question?

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

the turtle will travel 26 meters in 13 minutes.

In physics and mathematics, distance (d) is the measure of the length between two points in a straight line or along a curved path. It is a scalar quantity that is usually measured in units of meters (m) or other distance units such as kilometers (km), miles (mi), feet (ft), etc.

a. The rule for the distance d traveled by the turtle as a function of minutes traveled t can be expressed as:

d = 2.0t

Where d is the distance in meters and t is the time in minutes.

b. To find out how far the turtle will travel in 13 minutes, we can simply substitute t = 13 in the formula we obtained in part a:

d = 2.0t = 2.0 x 13 = 26 meters

Therefore, the turtle will travel 26 meters in 13 minutes.

c .The graph is shown below:

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Answer: b is the answer maybe i don't know

Step-by-step explanation:

The mixture must be heated an amount of 23 °F to reach a temperature of 132 °F.

Temperature is the measure of how "hot" a system is. Physically speaking, temperature is closely related to atomic and molecular motion within a system. In this problem we find a mixture that must be at a certain temperature, higher than its real one.

Therefore, the amount required to increase the temperature of the mixture is defined by following subtraction:

ΔT = R - r

Where:

If we know that r = 109 °F and R = 132 °F, then the temperature difference is:

ΔT = 132 °F - 109 °F

ΔT = 23 °F

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Answer:

110

Step-by-step explanation:

90 + 10

Answer:

Give me a sec

Step-by-step explanation:

Using relations in a right triangle, the secant of angle θ is given by:

D. 5/4.

The relations in a right triangle are given as follows:

Using the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:

h² = 9² + 12²

h = sqrt(9² + 12²)

h = 15.

The secant of an angle is 1 divided by the cosine, hence:

Which means that option D is correct.

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The maximum amount the firm should pay for the machinery is $61,672.67

The maximum amount that the firm should pay for the machinery can be determined by calculating the present value of the cash flows expected from the new piece of machinery

Present value is the sum of the discounted cash flows from the investment

Discounted year 1 cash flow: $8000 ÷ 1.06 = 7547.17

Discounted year 2 cash flow: $8000 ÷ 1.06² = 7119.97

Discounted year 3 cash flow: $8000 ÷ 1.06³ = 6716.95

Discounted year 4 cash flow: $8000 ÷ 1.06^4 = 6,336.75

Discounted year 5 cash flow: $8000 ÷ 1.06^5 = 5,978.07

Discounted year 6 cash flow: $8000 ÷ 1.06^6 = 5,639.68

Discounted year 7 cash flow: $8000 ÷ 1.06 ^7= 5,3204.57

Discounted year 8 cash flow: $8000 ÷ 1.06^8 = 4,322.15

Discounted year 9 cash flow: $8000 ÷ 1.06^9 = 4,735.19

Discounted year 10 cash flow: $8000 ÷ 1.06^10 = 4,467.16

Discounted year 10 cash flow: $5000  ÷ 1.06^10 = 2,791.97

The sum of the discounted cash flows is $61,672.67

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Answer:

-6x²

36

Step-by-step explanation:

1 / (1 + 6x²) = 1 / (1 − r)

Therefore, r = -6x².

The third term, r², is 36x⁴.

Answer:

A. 0.2734 = 27.34% probability that there are an equal number of boys and girls

B. 0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly

Step-by-step explanation:

In each of these questions, the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

A.The Murray family has produced 8 children.

What is the probability that there are an equal number of boys and girls?

8 children means that \(n = 8\)

Each children is equally as likely to be a boy or a girl, which means that \(p = 0.5\)

This probability is P(X = 4). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 4) = C_{8,4}.(0.5)^{4}.(0.5)^{4} = 0.2734\)

0.2734 = 27.34% probability that there are an equal number of boys and girls

B.Margie has the uncanny ability of being able to guess the correct answer to TRUE/FALSE questions with an 80% accuracy rate. Tomorrow’s test has 7 questions on it and she needs to answer 5 questions correctly in order to make the Honor Roll. If she guesses on every question, what is the probability that she’ll answer exactly 5 questions correctly?

80% accurracy rate means that \(p = 0.8\)

7 questions means that \(n = 7\)

The probability is P(X = 5). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 5) = C_{7,5}.(0.8)^{5}.(0.2)^{2} = 0.2753\)

0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly

Answer:

10000

Step-by-step explanation:

100 hugs x 100 hugs

= 10,000 hugs.

Therefore, nine rabbits will need 7.5 sacks of food for one week.

The unitary method is a mathematical technique that involves finding the value of a single unit to determine the value of a given number of units. It is a method of solving mathematical problems that involve proportional relationships between quantities. The unitary method is commonly used in various areas of mathematics, such as algebra, arithmetic, and geometry. It is also used in everyday life to solve problems related to money, time, distance, and other quantities.

Here,

To solve this problem, we can use proportionality. We know that the number of sacks of food needed is directly proportional to the number of rabbits.

Let x be the number of sacks needed for 9 rabbits. Then, we can set up the following proportion:

6/10 = 9/x

Cross-multiplying, we get:

6x = 90

Dividing both sides by 6, we get:

x = 15/2 or 7.5

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Complete question:

If six rabbits need 10 sacks of food per week, how many sacks will nine rabbits need to eat for one week?

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).

When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).

As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

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Answer:

The half-life of this substance is of 569.27 days.

Step-by-step explanation:

Amount of a substance after t days:

The amount of a substance after t days is given by:

\(P(t) = P(0)e^{-kt}\)

In which P(0) is the initial amount and k is the decay rate, as a decimal.

Suppose a sample of a certain substance decayed to 69.4% of its original amount after 300 days.

This means that \(P(300) = 0.694P(0)\). We use this to find k.

\(P(t) = P(0)e^{-kt}\)

\(0.694 = P(0)e^{-300k}\)

\(e^{-300k} = 0.694\)

\(\ln{e^{-300k}} = \ln{0.694}\)

\(-300k = \ln{0.694}\)

\(k = -\frac{\ln{0.694}}{300}\)

\(k = 0.0012\)

So

\(P(t) = P(0)e^{-0.0012t}\)

What is the half-life (in days) of this substance?

This is t for which P(t) = 0.5P(0). So

\(0.5P(0) = P(0)e^{-0.0012t}\)

\(e^{-0.0012t} = 0.5\)

\(\ln{e^{-0.0012t}} = \ln{0.5}\)

\(-0.0012t = \ln{0.5}\)

\(t = -\frac{\ln{0.5}}{0.0012}\)

\(t = 569.27\)

The half-life of this substance is of 569.27 days.

Answer:

-10

Step-by-step explanation:

y : x

= 5 : 4

4z = -8

= -8 / 4 = -2 = z

y : x

= 5 * -2 : 4 * -2

= -10 : -8

Answer:

x=-2

Step-by-step explanation:

3(2x-1)+2x=4x-11

6x-3+2x=4x-11

8x-3=4x-11

8x=4x-8

4x=-8

x=-2

The answer to the equation is \(x=-2\)

First, you must use distributive property to simplify the equation.

\(6x-3+2x=4x-11\)

Then, you must combine like terms.

\((6x+2x)-3=4x-11\)

\(8x-3=4x=11\)

Next, you must subtract 4x on each side

\(4x-3=-11\)

Then, add 3 on both sides

\(4x=-8\)

Finally, divide both sides by 4

\(\frac{4x}{4} =\frac{-8}{4}\)

\(x=-2\)

Answer:

A. x≤2

Step-by-step explanation:

If the circle is shaded in, x can equal that number or anything shaded in that direction.

Answer:

the answer is A. x <= 2

Step-by-step explanation:

filled dot means the number it's on is included.

So X can be 2 and anything below it

The metrics of dispersion are mean deviation and range. While quartile deviation is a measure of dispersion, quartiles themselves are not.

25% from the lowest to the highest number in the first quartile. 25.1% to 50% in the second quartile (till median) Three-quarter range: 51% to 75% (above the median) 25% of the highest values are in the fourth quartile.

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3). As the second quartile, the median is used (Q2). The distance between the upper and lower quartiles is known as the interquartile range.

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Using a system of equations, it is found that she has 52 nickels and 18 dimes in the desk.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given by:

There are 70 coins, hence:

x + y = 70.

A nickel is worth $0.05, while a dime is worth $0.1, and there is a total of $4.40 in the desk, hence:

0.05x + 0.1y = 4.4.

From the first equation, we have that:

y = 70 - x.

Replacing in the second:

0.05x + 0.1(70 - x) = 4.4.

0.05x = 2.6

x = 2.6/0.05.

x = 52

Then:

y = 70 - x = 70 - 52 = 18.

She has 52 nickels and 18 dimes in the desk.

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To realign the handlebars to your bike, you would need to:

Bicycles' steering is controlled by a handlebar. As it is typically immediately mechanically connected to a pivoting front wheel via a stem that is then attached to the fork, it is the equivalent of a tiller for vehicles and watercraft.

The steps to fix your big Flyer bike has been given above.

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Answer:

h = 452.5 ft

Step-by-step explanation:

Angle of elevation from P to top of the pole = 65°

Horizontal distance between the pole and point P = 21 ft

By Applying tan rule in the given triangle ABP,

tan(∠APB) = \(\frac{AB}{PB}\)

tan(65°) = \(\frac{h}{21}\)

h = 21[tan(65°)]

h = 452.491

h ≈ 452.5 ft

Therefore, height of the pole is 452.5 ft.

Answer:

The answer is "\((25.32, 30.68)\)"

Step-by-step explanation:

Given:

\(\bar x = 28\\\\ \sigma = 4\\\\n =26\\\\\)

When \(98\%\) confidence level so, the z:

\(\alpha = 1 - 98\% = 1 - 0.98 = 0.2\\\\\frac{\alpha}{2} =\frac{0.02}{2} = 0.01\\\\Z_{\frac{\alpha}{2}} = Z_{0.01} = 1.645\ \ \ ( Using \ z \ table )\\\\\)

\(E = Z_{\frac{\alpha}{2} \times ( \frac{\sigma}{\sqrt{n}})\)  

\(= 1.645 \times (\frac{4}{\sqrt{26}})\\\\=2.68\)

When  98% confidence interval estimate of the population mean  is,

\(\bar x - E < \mu < \bar x + E\\\\28 - 2.68 < \mu < 28 + 2.68\\\\25.32 < \mu < 30.68\\\\(25.32, 30.68)\\\\\)

Given the following formula in getting the velocity of an object:

Where,

h = height the object has fallen

We get,

Therefore, the velocity of the object falling at 25 ft, is 40 ft./sec.