A plane left Atlanta at 11:30 a.m. and flew to an airport near Boston. The plane was due at Boston at 3:15 p.m. The plane arrived 25 minutes late. The time of the trip was?

Average speed is the ratio of the total distance traveled to the total time taken. The average speed of the river's current is 2 mi/h.

Average speed is the ratio of the total distance traveled to the total time taken.

As we know that the total time taken by the boat to travel upstream and downstream is 6 hours. And the distance traveled by Kayaker is 9 miles, each time while going upstream and downstream.

We know that when the boat is traveling upstream the water current will try to resist the boat, therefore, the speed of the boat while going upstream is (4-x), where x is the speed of the boat. Similarly, the speed of the boat when going downstream will be (4+x), as the water stream will try to provide a push to the boat. Therefore, the total time taken by the Kayaker can be written as,

Total Time

= Time taken while going upstream + Time taken while going downstream

[tex]\rm 6 = \dfrac{Distance\ upstream}{Speed\ upstream} + \dfrac{Distance\ Downstream}{Speed\ Downstream}[/tex]

[tex]\rm 6 = \dfrac{9}{(4+x)} + \dfrac{9}{(4-x)}[/tex]

Taking the LCM,

[tex]6 = \dfrac{9(4+x)+9(4-x)}{(4+x)(4-x)}\\\\6\times (4+x)(4-x) = 9(4+x)+9(4-x)\\\\6(16-x^2) = 36+9x+36-9x\\\\96 - 6x^2 = 72\\\\-6x^2 = 72-96\\\\6x^2 = 24\\\\x^2 = 4\\\\x =2[/tex]

Hence, the average speed of the river's current in miles per hour is 2 mi/h.

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Step 1

Find the slope of the given line

we have

[tex]10x+2y=-2[/tex]

Isolate the variable y

Subtract [tex]10x[/tex] both sides

[tex]2y=-10x-2[/tex]

Divide by [tex]2[/tex] both sides

[tex]y=-5x-1[/tex]

The slope of the given line is

[tex]m=-5[/tex]

Step 2

Find the equation of the line that is parallel to the given line and passes through the point [tex](0, 12)[/tex]

we know that

If two lines are parallel. then their slope are equal

In this problem we have

[tex]m=-5[/tex]

[tex](0, 12)[/tex]

The equation of the line into slope-intercept form is equal to

[tex]y=mx+b[/tex]

substitute the values

[tex]12=-5*0+b[/tex]

[tex]b=12[/tex]

the equation of the line is

[tex]y=-5x+12[/tex]

therefore

the answer is

[tex]y=-5x+12[/tex]

Answer:

x < 10

Step-by-step explanation:

Answer:

6 days

Step-by-step explanation:

Given that one student can paint a wall in 10 minute and another student in 15 minutes.

Since if number of persons increase, painting time decreases, this is a question of inverse proportion

Hence if they work together they can paint in one day

[tex]\frac{1}{10} +\frac{1}{15}[/tex] part of the work

i.e. work completed in 1 day when they work together

=[tex]\frac{1}{10} +\frac{1}{15} \\=\frac{9+6}{90} \\=\frac{1}{6}[/tex]

Hence in 6 days they can together complete the full work

Since ∠CPD = x and segment PN is the angle bisector of this angle, therefore segment PN equally divides ∠CPD into two angles. Which means that:

∠CPN = ∠NPD = x / 2

Further, segment PN is also the perpendicular bisector of AB which further means that the intersection formed by PN and AB creates a right angle (90°). Therefore:

∠NPD + ∠DPB = 90°

x/2 + ∠DPB = 90°

∠DPB = 90 – x/2

Therefore:

sin∠DPB = sin(90 – x/2) which is not in the choices

However we know that the relationship of sin and cos is:

sin(π/2 - θ) = cos θ

Where,

π/2 = 90

θ = x/2

Therefore:

sin(90 – x/2) = cos(x/2)

Answer:

cos(x/2)

The quantity which is equal to sin ∠DPB is:

This refers to the figure which is formed by two rays with a common endpoint.

Hence, we know that

If we segment PN which is the bisector of AB, it would crerate angle 90 and this would give us:

x/2 + ∠DPB = 90°

∠DPB = 90 – x/2

With this in mind, there is the relation between sin and cos, which would be:

We are aware that

Hence,

sin(90 – x/2) = cos(x/2)

=cos(x/2)

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Using the unitary method, we can estimate that $2000 will be spent on the purchase of 250,000 sheets of paper.

According to the question,

Hence we can say that Using the unitary method, we can estimate that $2000 will be spent on the purchase of 250,000 sheets of paper.

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Final answer:

The algebraic expression representing 'two less than twice a number is the same as four times the number' is solved, resulting in the number being -1.

Explanation:

The student's question involves solving a simple algebraic equation. We are given that two less than twice a number is the same as four times the number. To represent this algebraically, let's let the unknown number be n. The phrase 'twice a number' can be written as 2n. 'Two less than' this expression would be 2n - 2. The statement implies this is equal to four times the number, which is 4n. Therefore, the equation we need to solve is 2n - 2 = 4n. To solve this equation, we need to isolate the variable n on one side of the equals sign.

Subtract 2n from both sides: -2 = 2n.

Divide both sides by 2 to find the value of n: n = -1.

In conclusion, the number that satisfies the condition given is -1.

Answer:

at most 5 weeks

Step-by-step explanation:

Answer:

C) 4

Step-by-step explanation:

The given function is

[tex]f(x)=\left \{ {{2x+5,\:-6\:<\:x\le0} \atop {-2x+3,\:0\:<x\le4}} \right.[/tex]

The function is defined on two intervals.

The first interval is

[tex]-6\:<\:x\le0[/tex] and the second interval is [tex]\:0\:<x\le4[/tex].

[tex]-7[/tex] does not belong to any of these intervals.

[tex]-6[/tex] does not also belong to any of these intervals.

[tex]4[/tex] belongs to the interval [tex]\:0\:<x\le4[/tex].

Hence 4 is in the domain of f(x).

[tex]5[/tex] does not also belong to any of the intervals.

Therefore the correct answer is C.

For this case, we use the cylindrical coordinates: 
x² + y² = r² 
dV = r dz dr dθ 

The limits are:
z = 0 to z = 1/(r²)^10 = 1/r^20
r = 1 to ∞ 
θ = 0 to 2π 

Integrating over the limits:
V = ∫ [0 to 2π] ∫ [1 to ∞] ∫ [0 to 1/r^20] r dz dr dθ 
V = ∫ [0 to 2π] ∫ [1 to ∞] rz | [z = 0 to 1/r^20] dr dθ 
V = ∫ [0 to 2π] ∫ [1 to ∞] 1/r^19 dr dθ 
V = ∫ [0 to 2π] −1/(18r^18) |[1 to ∞] dθ 
V = ∫ [0 to 2π] 1/18 dθ 
V = θ/18 |[0 to 2π] 
V = π/9

The volume of the volcano is an illustration of definite integral

The volume of the volcano is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]

The graphs are given as:

[tex]\mathbf{z = 0}[/tex] and [tex]\mathbf{z = \frac{1}{(x^2 + y^2)^{10}}}[/tex]

The cylinder is:

[tex]\mathbf{x + y =1}[/tex]

For cylindrical coordinates, we have:

[tex]\mathbf{r^2 =x^2 + y^2}[/tex]

So, we have:

[tex]\mathbf{z = \frac{1}{(r^2)^{10}}}[/tex]

[tex]\mathbf{z = \frac{1}{r^{20}}}[/tex]

Where:

[tex]\mathbf{r = 1 \to \infty}[/tex]

[tex]\mathbf{\theta = 0 \to 2\pi}[/tex]

So, the integral is:

[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{20}}} \, r\ dr } \, d\theta }[/tex]

Cancel out r

[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{19}}} \, dr } \, d\theta }[/tex]

Rewrite as:

[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {r^{-19}} \, dr } \, d\theta }[/tex]

Integrate

[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}r^{-18}}} |\limits^{\infty}_1 \, d\theta }[/tex]

Expand

[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(\infty^{-18} -1^{-18}) }} , d\theta }[/tex]

[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(0 -1) }} , d\theta }[/tex]

[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}( -1) }} , d\theta }[/tex]

[tex]\mathbf{V = \int\limits^{2\pi}_0 {{\frac{1}{18} }} , d\theta }[/tex]

Integrate

[tex]\mathbf{V = \frac{1}{18}(\theta)|\limits^{2\pi}_0}[/tex]

Expand

[tex]\mathbf{V = \frac{1}{18}(2\pi - 0)}[/tex]

[tex]\mathbf{V = \frac{1}{18}(2\pi )}[/tex]

Cancel out 2

[tex]\mathbf{V = \frac{1}{9}\pi}[/tex]

Hence, the volume is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]

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To find the upper and lower limits of a 95% confidence interval for the given data, calculate the standard error, use the multiplier of 2, and apply the formula Sample mean ± Multiplier * Standard error.

To calculate the upper and lower limit for a 95% confidence interval, we use the formula: Confidence interval = Sample mean ± Multiplier * Standard error. For this case, the sample mean is $94 and the standard deviation is $10. The standard error is calculated as $10 / √36 = $10 / 6 ≈ $1.67.

With a 95% confidence level, the multiplier is approximately 2. Therefore, the upper limit would be $94 + 2($1.67) = $94 + $3.34 ≈ $97.34, and the lower limit would be $94 - $3.34≈ $90.66.

Answer:

C = f(x)=10x

Step-by-step explanation:

plato answer

Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.  1.97 is the time taken by the ball to hit the ground.

Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given that a ball is thrown from a height of 70 feet with an initial downward velocity of 4/fts. The ball's height h (in feet) after t seconds is given by the following.

h=70-4t-16t²

Now we can take h=0

h=-16t²+70-4t

-16t²+70-4t

Divide by 2

-8t²-2t+35

Now apply quadratic formula

a=-8, b=-2, c=35

t=-b±√b²-4ac/2a

t=2±√-2²-4(-8)(35)/2(-8)

t=2±√4+1120/-16

we get t= 1.97 and t= -2.22

You get the numbers to be : 1.97 and -2.22

We do not consider negative values. So the correct answer is 1.97

Hence 1.97 is the time taken by the ball to hit the ground.

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Answer:

8x^2 - 3x + 7

Step-by-step explanation:

I took the test.