100/2[500/5{6+(21-17)}] simplify
Please answer with process​

Answer:

500 Votes

Step-by-step explanation:

25/100 = 0.25

500/2000 = 0.25

Therefore 500 students would vote for Jen.

A leaking faucet in the S&E building lab, dripping at a rate of one drop per second, will result in a water loss of approximately 4,725 liters in one year.

To calculate the amount of water lost in one year, we need to determine the number of drops per year and then convert it to liters. Since the faucet drips at a rate of one drop per second, there are 60 drops in a minute (60 seconds), which totals to 3,600 drops in an hour (60 minutes).

In a day, there would be 86,400 drops (24 hours * 3,600 drops). Considering a year of 365 days, the total number of drops would be approximately 31,536,000 drops (86,400 drops * 365 days). To convert the number of drops to liters, we need to multiply the total number of drops by the volume of each drop.

Given that each drop contains 0.150 milliliters, we convert it to liters by dividing by 1,000, resulting in 0.00015 liters per drop. Multiplying the total number of drops by the volume per drop, we find that the total water loss is approximately 4,725 liters (31,536,000 drops * 0.00015 liters/drop).

Therefore, in one year, the leaking faucet in the S&E building lab would result in a water loss of approximately 4,725 liters.

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Let:

R = (-3,2)

S = (0, - 5)

T = (4,5)

R' = (4,1)

So:

R(x,y)----->T------->R'(x,y)

Let:

x1 = -3

x2 = 4

y1 = 2

y2 = 1

So:

(-3,4)------->(x+7,y-1)--------->(-3 + 7, 2 - 1) = (4,1)

Therefore:

Answer:

$700

Step-by-step explanation:

She's willing to pay up to $3000.

She pays only $2300.

consumer surplus = $3000 - $2300 = $700

Answer:

$700

Step-by-step explanation:

Anna's consumer surplus is the difference between her willingness to pay and the price she actually paid, which is $3000 - $2300 = $700.

Therefore, the answer is $700.

The correct answer is A.To determine which line is orthogonal to the plane, we need to find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The normal vector of the plane 2x + 4y - 2z = 10 is [2, 4, -2].

Calculating the dot product of this normal vector with the direction vectors of the given lines, we find:

A. [2, 4, -2] ⋅ [-1, 0, 1] = 0 (orthogonal)
B. [2, 4, -2] ⋅ [1, 1, 1] = 4 (not orthogonal)
C. [2, 4, -2] ⋅ [2, 1, 0] = 4 (not orthogonal)
D. [2, 4, -2] ⋅ [-1, 1, 1] = 0 (orthogonal)

Based on the dot products, options A and D have direction vectors that are orthogonal to the plane. Therefore, the lines described by options A and D are orto to the plane. The correct answer is A.

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Step-by-step explanation:

we can model the expression for the inequality as

given the flat rate is $3

let the additional mile be x

hence

3+0.05x<10

step two:

let us proceed to solve for x

3+0.05x<10

0.05x<10-3

0.05x<7

divide both sides by 0.05

x<7/0.05

x<140    

let us plug in 15 into the expression and see if the cost is under $10

3+0.05(15)<10

3+0.75<10

3.75<10

from the analysis, carl will have to take the taxi since cost is less than $10 i.e $3.75

Answer:

The inequality representing the situation is 0.5x + 3 < 10.

Use inverse operations and properties of inequality to solve.

Find that x < 14.

Carl lives 15 miles from home, so he will take a bus.

Step-by-step explanation:

Given the number 64,473

From the right:

• Unit digit = 3

• Tens digit = 7

• Hundred digit = 4

• Thousand digit =4

• Ten thousand digit =6

To round 64,473 to the nearest thousand, we first identify the thousand digit.

Thousand digit = 4

Next, identify the number after the thousand digit.

The number after the thousand digit = 4

When rounding numbers:

• If the number after the required number place is (0,1,2,3,4), we simply write the number.

• If the number after the required number place is (5,6,7,8,9), we round up.

Since the number after the thousand digit is 4. we therefore have that:

64,473 rounded to the nearest thousand = 64,000

The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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\(35 * 6 = 210\\210 / 6 = 35mean\)

Therefore, out of one of the many ways to solve this, I found 35.

Answer:

30

Step-by-step explanation:

4x + 10 = 4*5 + 10 = 20 + 10 = 30

Answer:

(5p - 7q) + (3q - 4p + 12) + (6q - 13pq - 15)

Open brackets

5p - 7q + 3q - 4p + 12 + 6q - 13pq - 15

Combine like terms,

5p - 4p - 7q + 3q + 6q - 13pq + 12 - 15

p + 2q - 13pq - 3

Thus, The answer is (p + 2q - 13pq - 3)

Answer:

p + 2q - 13pq - 3

Step-by-step explanation:

Now we have to,

→ Add the following expressions.

The expressions are,

→ 5p - 7q, 3q - 4p + 12, 6q - 13pq - 15

Let's solve the problem,

→ (5p - 7q) + (3q - 4p + 12) + (6q - 13pq - 15)

→ 5p - 7q + 3q - 4p + 12 + 6q - 13pq - 15

→ (5p - 4p) + (-7q + 3q + 6q) + (-13pq) + (12 - 15)

→ (p) + (2q) + (-13pq) + (-3)

→ p + 2q - 13pq - 3

Hence, answer is p + 2q - 13pq - 3.

The measure of variability should be used for both sets of data to determine the location with the most consistent temperature is IQR (Interquartile Range).

The reason for this is that IQR is less sensitive to extreme values or outliers, which can affect the range significantly. In the case of the histograms provided, it appears that Sunny Town is skewed and Desert Landing is roughly symmetric, which further supports the use of IQR as a measure of variability.

Therefore, we can calculate the IQR for both sets of data and compare them to determine which location has the most consistent temperature.

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The cliff divers dive headfirst from the top of cliff. 1/2 or 0.5 second is the time period will the diver's height exceed that of the cliff.

An object that moves along the vertical axis due to gravitational acceleration is called a free-falling object. The free fall position is given by the following equation of motion:

yₜ = y₀ + v₀t + 1/2(at²)

Where y₀--> the initial height of the object

v₀--> the initial velocity

t --> time

a --> the acceleration due to gravity and is equal to a = g = - 32.2 ft²/sec

We have given that,

Initial velocity of divers , v₀ = 8 feet/sec

Initial Height of top of cliff , s₀ = 87 feet

position function, s(t) = - 16t²+ v₀t +s₀

Plugging all known values in above position function,

s(t) = -16 t² + 8t + 87

The the diver's height exceed that of the cliff means, s(t) > 87

=> -16 t² + 8t + 87 > 87

Subtract 87 from both sides, we get

-16t^2 + 8t > 0 , now we solve this inequality by changing it in a equality,

-16 t² + 8t = 0

=> -8 t( 2t - 1) = 0 => -8t = 0 , 2t -1 = 0

=> either t = 0 or t = 1/2

So the first half second, the person is above the height of the cliff.

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Complete question:

Use the position function s(t)-16t2+ vot +so position, t time) to answer the following: Divers in Acapulco, Mexico, dive headfirst at 8 feet per second from the top of a cliff 87 feet above the Pacific Ocean. During which time period will a diver's height exceed that of the cliff? (vo initial velocity, so initial.

The final marked up price is $586.5

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here: Discount %=15 Marked price=$600 and after the sale marked up percentage is 15%

Thus, Discounted price = 600×(1-15%)

                                        = 600× 0.85

                                         =$510

And therefore the marked up price after sale is= $510×(1+15%)

                                                                              = $586.5

Hence, The final marked up price is $586.5

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First a few reminders:

• For a ≠ 0 and b ≥ 0, \(\sqrt[a]{b}=b^{\frac1a}\)

• 4 = 2² and 8 = 2³

• For real numbers a, b, c, we have \((a^b)^c=a^{bc}\)

• For any real numbers a and n (so long as both are not zero), we have \(\frac1{a^n}=a^{-n}\)

• For any numbers a, b, c, \(a^b\times a^c=a^{b+c}\)

So we have

\(\sqrt2=2^{\frac12}\)

\(\dfrac1{\sqrt2}=2^{-\frac12}\)

\(\dfrac1{\sqrt8}=\dfrac1{(2^3)^{\frac12}}=2^{-\frac32}\)

Then the given expression can be rewritten as

\(2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2\times2^{\frac12}-3\times2^{-\frac12}+2^2\times2^{-\frac32}\)

\(2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{1+\frac12}-3\times2^{-\frac12}+2^{2-\frac32}\)

\(2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{\frac32}-3\times2^{-\frac12}+2^{\frac12}\)

Pull out a factor of \(2^{-\frac12}\):

\(2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{-\frac12}\left(2^{\frac32+\frac12}-3+2^{\frac12+\frac12}\right)\)

Simplify this:

\(2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=2^{-\frac12}\left(2^2-3+2^1\right)=2^{-\frac12}(4-3+2)=3\times2^{-\frac12}=\dfrac3{\sqrt2}\)

Rationalize this last result to get the square root out of the denominator:

\(2\sqrt2-\dfrac3{\sqrt2}+\dfrac4{\sqrt8}=\dfrac3{\sqrt2}\times\dfrac{\sqrt2}{\sqrt2}=\dfrac{3\sqrt2}{(\sqrt2)^2}=\boxed{\dfrac{3\sqrt2}2}\)

Answer:

48

Step-by-step explanation:

80 over 100*150

80 divided by 100=0.8 *150=1208student

0.8 *60 = 48

Yes, it is possible to find a power series whose interval of convergence is [0, ∞).

The interval of convergence for a power series is determined by the behavior of the series as the variable approaches different values. The interval can be open, closed, half-open, or infinite.

In the case of [0, ∞), it represents a right-half open interval, indicating that the power series converges for all values of the variable greater than or equal to 0.

To find such a power series, we need to consider the conditions for convergence. The most common tests for convergence of power series are the ratio test and the root test. If the series satisfies the conditions of either test, it will converge within a specific interval.

For a power series to have an interval of convergence of [0, ∞), the coefficients in the series must satisfy certain conditions, such as convergence of the series for x = 0 and divergence for x > 0. This can be achieved by selecting appropriate coefficients and constructing a power series that converges for x = 0 and diverges for x > 0.

In summary, it is indeed possible to find a power series whose interval of convergence is [0, ∞) by carefully selecting the coefficients to meet the convergence conditions for this interval.

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Complete question is:

Is it possible to find a power series whose interval of convergence is [0, ∞)? Explain.

The values of all sub-parts have been obtained.

(a). The radian measure of angle A is 6 radians.

(b). The radian measure of angle B is 3 radians.

(c). The radian measure of angle C is 2 radians.

What is relation between radian and degree?

A circle's whole angle is 360 degrees and two radians. This serves as the foundation for converting angles' measurements between different units. This means that a circle contains an angle whose radian measure is 2 and whose central degree measure is 360. This can be written as:

2π radian = 360° or

π radian = 180°

(a). Evaluate the radian measure of angle A:

Near to 360° and radians measure whole number, so we get,

A = 6 radian {1 radian = 57.296°}.

(b). Evaluate the radian measure of angle B:

Near to 180°, and radian measure whole number, so we get,

B = 3 radian

(c). Evaluate the radian measure of angle C:

Near to 90 and radian measure whole number, so we get,

C = 2 radian.

Hence, the values of all sub-parts have been obtained.

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Answer:

Step-by-step explanation:

If the distance between Singapore and Sydney is 6300 km correct to the nearest 100 km, it means that the actual distance could have been at least 6250 km. If the businessman travelled from Singapore to Sydney and then back to Singapore for six times in a year, it means that he covered each distance 12 times(6 × 2) Then, his total distance would be between

6250 × 12 = 75000 km

And

6300 × 12 = 75600 km

The limit is between 75000 km and 75600 km

The limits is the total distance he travelled is 75,000 km and 75,600km.

The total number of times the businessman travelled from Singapore to Sidney is 12 times. This was determined by multiplying 6 by 2.  If the distance is to the nearest 100km, the actual distance would range from 6250 to 6300km. This is because both distances to the nearest 100km is 6300.

Upper bound = 6250 x 12 = 75,000 km

Lower bound = 6300 x 12 = 75,600 km.

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hi

3/14 = 6/28

2/7 = 6/28

So :   6/28+6/28 +11/28 =  12/28 +11/28 =  23/28  

As 23 is prime, we can not simplify.  

So  23/28 has been taken. and 5/28 remains.

The steps of the analytical problem-solving model include: identifying the problem, exploring alternatives, building an implementation plan, implementing a solution, and evaluating the situation.

Analytical problem solving, as we've defined it above, refers to the approaches and methods you use rather than the particular issue you're trying to resolve.

Analytical issue solving is a crucial prerequisite for problem resolution; the problem itself does not determine whether you need it.

Analytical problem solving involves recognising a problem, investigating it, and then creating ideas (such as causes and solutions) around it.

Solving analytical problems calls for inquiry, examination, and analysis that encourages additional study of the subject (including causality, symptoms, and solution).

According to the steps involved in analytical problem solving model:

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Answer:

Area: 776.7 ft²

Perimeter: 55.1 ft

Step-by-step explanation:

The figure is composed of two semi-circles and a rectangle, solve for the area of each figure:

Two semi-circles (which is one circle because they have the same diameter):

\(A_1=\pi r^2\\A_1=\pi 7.5^2\\A_1=176.714586764...\)

The rectangle:

\(A_2=bh\\A_2=4*15\\A_2=60\)

Add them up to get:

\(A=176.714586764...+600\\A=776.714586764...\)

Rounding gives 776.7

Now, the perimeter.

Solve for the circumference of the circle and add only the bases of the rectangle:

\(C=d\pi \\C=15\pi\\C=47.1238898038...\)

And add the two bases:

\(P=47.1238898038...+2b\\P=47.1238898038...+2(4)\\P=47.1238898038...+8\\P=55.1238898038...\)

Rounding gives 55.1

And don't forget to put the units.

The rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the radius is exactly 3 feet.

To solve this problem, we need to use the formula for the area of a circle:

\(A = πr^2\),

where A is the area and r is the radius.

We also need to use the chain rule of differentiation because we are dealing with a changing radius over time.

First, we can find the rate of change of the area with respect to time (dA/dt) by differentiating the formula for the area:

dA/dt = 2πr(dr/dt)

where dr/dt is the rate of change of the radius with respect to time, which is given as 2 feet per second in the problem.

Therefore, we can substitute these values into the formula to get:

dA/dt = 2π(3)(2)

dA/dt = 12π

So, the rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the

radius is exactly 3 feet.

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Answer:

The result can be shown in multiple forms.

Exact Form: 4√3 = √48

Step-by-step explanation:

Answer

(180,120)

Cannot be determined

Step-by-step explanation:

Fax

The critical point with the maximum revenue is at (180,120)

The objective function is given as:

Revenue = 75x+85y

The critical points are (0,0) (180,120) (300,0)

Substitute these points in the objective function.

Revenue = 75(0)+ 85(0) = 0

Revenue = 75(180)+ 85(120) = 23700

Revenue = 75(300)+ 85(0) = 22500

The maximum revenue is 23700.

Hence, the maximum revenue is at point (180,120)

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Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

21 = 2.50 + 5x

21 - 2.50 = 5x

18.50 = 5x

x = 18.50 / 5

x = 3.7 bags of avocados

To get 3 bags of avocados or 9 avocados

= $5 × 3

= $15

Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

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Answer:

an = a1 + d(n - 1)

a88 = 4 + (-5)(88 - 1)

a88 = 4 + (-5)(87)

a88 = 4 - 435

a88 = -431

So, the 88th term of the arithmetic sequence is -431.

Answer:

520

Step-by-step explanation:

Let the Ratio a:b:c be 7x:13x:20x Respectively.

So, Sum of Ratios is 520...

A+B+C = 520

7x+13x+20x=520

40x=520

x= 520/40

x= 13

Now, Put the value of x

A= 7x= 7×13= 91

B= 13x = 13×13= 169

C= 20x = 20×13= 260

Now Add the numbers if we get 520 it means all the three numbers are correct....

91+169+260= 520