what is the area of a circle if the diameter is 16 millimetres

Answer: the rate of the current is 3 mph.

Step-by-step explanation:

Let x represent the rate of the current.

In still water, Jake paddles at a rate of 5 mph. Paddling with the current in a river, Jake traveled 16 miles. It means that the speed with which she travelled downstream (with the current) is (5 + x) mph

Time = distance/speed

Time spent in paddling downstream is

16/(5 + x)

While paddling upstream, it took an hour longer. The speed with which he paddled upstream is (5 - x) mph.

Jake could only travel 6 miles against the current. It means that the time spent in travelling upstream us

6/(5 - x)

Since it took 1 hour longer, then

6/(5 - x) = 16/(5 + x) + 1

Cross multiplying by (5 - x)(5 + x), it becomes

6(5 + x) = 16(5 - x) + 1(5 + x)(5 - x)

30 + 6x = 80 - 16x + 25 - 5x + 5x - x²

30 + 6x = - x² - 16x + 5x - 5x + 25 + 80

30 + 6x = - x² - 16x + 105

x² + 16x + 6x + 30 - 105 = 0

x² + 22x - 75 = 0

x² + 25x - 3x - 75 = 0

x(x + 25) - 3(x + 25) = 0

x - 3 = 0 or x + 25 = 0

x = 3 or x = - 25

Since x cannot be negative, then x = 3 mph

Answer:   x=3

Step-by-step explanation:

Took test

Answer:

C = 8π

Step-by-step explanation:

C = 2πr

C = 2π(8/2)

C = 2π × 4

C = 8π

Answer:

18.84 units

Step-by-step explanation:

diameter is 6 units so radius will be 3 units.

circumference = 2πr = 2×22/7×3

= 18.84 units

Answer: ACE

The radius of the cone is 9 units

The height of the cone is 12 units

The volume of the cone is represented by the expression 1/3 pie (9)2(12)

Step-by-step explanation:

Answer:

Therefore the maximum height that the reach is 49 feet after 1.75 seconds.

Step-by-step explanation:

Given that,

A ball is thrown vertically upward. After t seconds its height is given by the function

[tex]h=56t-16 t^2[/tex]

where h is height in feet.

Maximum value:

Given function f(x)= at²+bt+c.

Here a= -16 ,  b=56 and c=0

The ball attains its maximum height when [tex]t=-\frac{56}{2.(-16)}=1.75[/tex] s.

Putting the value of t in the given function

[tex]h=(56\times 1.75)-16(1.75)^2[/tex]

  =49 feet

Therefore the maximum height that the reach is 49 feet after 1.75 seconds.

The maximum height the ball will reach is given by the vertex of the parabola represented by the equation 56t - 16t^2. This is reached at t = 1.75 seconds, giving a maximum height of 49 feet.

The equation 56t - 16t^2 represents the trajectory of the ball thrown upwards over time. To identify the maximum height reached by the ball, we should look for the vertex of the parabola this equation graphically represents. This equation is a quadratic function given in the standard form at^2 + bt + c, where a = -16, b = 56, and c = 0. The time at which the maximum height is reached is found by the formula -b / (2.a). This yields t = -56 / (2 * -16) = 1.75 seconds. When substituted back into the equation, the maximum height (h) would be h = 56 * 1.75 - 16 * (1.75)^2 = 49 feet.

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We want to find the length of the light beam from the ship to Nicole.

We will see that the solution is 4,585.76 ft.

We can think of this situation as in a right triangle. The adjacent cathetus is the distance between the lighthouse and the ship. The opposite cathetus is the difference in height between Nicole's position and Nick´s position, it is equal to:

250ft - 10ft = 240ft

And the elevation angle is equal to 3°. So we know the angle and the opposite cathetus to this angle, and we want to find the hypotenuse, which is the length of the light beam.

Then we can use the relation:

Sin(θ) = (opposite cathetus)/(hypotenuse)

Solving it for the hypotenuse we get:

hypotenuse = (opposite cathetus)/sin(θ)

Replacing by the values that we know, we get:

hypotenuse = 240ft/sin(3°) = 4,585.76 ft

The length of the line of sight is 4,585.76 ft

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To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We are given the angle of elevation of the light, the height of the cliff, and need to calculate the length of the line of sight.

To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We have a right triangle formed by the line of sight, the height of the cliff, and the distance from the ship to Nicole. We are given the angle of elevation of the light as 3° and the height of the cliff as 250 feet. Let's denote the length of the line of sight as x and the distance from the ship to Nicole as d. Using the tangent function, we can write:

tan(3°) = 250 / d

Simplifying this equation, we have:

d = 250 / tan(3°)

Now we can substitute the value of tangent of 3° and solve for d. Using a calculator, we find that:

d ~ 8424.78 feet

So, the length of the line of sight from the ship to Nicole is approximately 8424.78 feet.

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Answer:

It would take 27.5 minutes the element to decay to 154 grams.

Step-by-step explanation:

The decay equation:

[tex]\frac {dN}{dt}\propto -N[/tex]

[tex]\Rightarrow \R\frac {dN}{dt}=-\lambda N[/tex]

[tex]\Rightarrow \frac {dN}N=-\lambda dt[/tex]

Integrating both sides

[tex]\Rightarrow \int \frac {dN}N=\int-\lambda dt[/tex]

[tex]\Rightarrow ln|N|=-\lambda t+c[/tex]

When t=0, N=[tex]N_0[/tex] = initial amount

[tex]ln|N_0|=-\lambda .0+c[/tex]

[tex]\Rightarrow c=ln|N_0|[/tex]

[tex]ln|N|=-\lambda t+ln|N_0|[/tex]

[tex]\Rightarrow ln|N|-ln|N_0|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{N}{N_0}|=-\lambda t[/tex]

Decay equation:              

                    [tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]

Given that, the half life of of element X is 11 minutes.

For half life, [tex]N=\frac12 N_0[/tex],  t= 11 min.

[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{\frac12N_0}{N_0}|=-\lambda . 11[/tex]

[tex]\Rightarrow ln|\frac12}|=-\lambda . 11[/tex]

[tex]\Rightarrow -\lambda . 11=ln|\frac12}|[/tex]

[tex]\Rightarrow \lambda =\frac{ln|\frac12|}{-11}[/tex]

[tex]\Rightarrow \lambda =\frac{ln|2|}{11}[/tex]                [ [tex]ln|\frac12|=ln|1|-ln|2|=-ln|2|[/tex] , since ln|1|=0]

N=154 grams, [tex]N_0[/tex] = 870 grams, t=?

[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{154}{870}|=-\frac{ln|2|}{11}.t[/tex]

[tex]\Rightarrow t= \frac{ln|\frac{154}{870}|\times 11}{-ln|2|}[/tex]

      =27.5 minutes

It would take 27.5 minutes the element to decay to 154 grams.

Answer:

60.6 minutes

Step-by-step explanation:

--------------------------------

Answer:

Teacher has 0 . Student has 1 apple

Step-by-step explanation:

Answer:

[tex]15\,\,kg/cm^2[/tex]

Step-by-step explanation:

Given:

The volume of a gas "V" varies inversely with the pressure "P" put on it.

Volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex]

To find:

pressure when volume is 480 [tex]cm^3[/tex]

Solution:

As  of a gas "V" varies inversely with the pressure "P" put on it,

[tex]V=\frac{k}{P}[/tex]

Here, k is a constant

As volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex], put [tex]V=360\,,\,P=20[/tex]

[tex]360=\frac{k}{20}\\k=360\times 20\\=7200[/tex]

So,

[tex]V=\frac{7200}{P}[/tex]

Put [tex]V=480[/tex]

[tex]480=\frac{7200}{P}\\P=\frac{7200}{480}\\=15\,\,kg/cm^2[/tex]

Answer:

(1) The coefficient of x in this expression is -10.

(2) The value of the expression for x = 15 is -9.

Step-by-step explanation:

(1)

A coefficient is a numerical value that is placed before a variable or is multiplied by the variable in an algebraic equation.

For example, in the algebraic equation 4x² + 5y the coefficient of variable y is 5.

The expression given is:

1 - 10 x + 4 y

The coefficient of x in this expression is -10.

(2)

The expression provided is:

[tex]f(x)=\frac{1}{5}x - 12[/tex]

Compute the value of the expression for x = 15 as follows:

[tex]f(x)=\frac{1}{5}x - 12\\=(\frac{1}{5}\times 15) - 12\\=3-12\\=-9[/tex]

Thus, the value of the expression for x = 15 is -9.

Answer:

b.38

Step-by-step explanation:

Answer:

[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]

And we can use the complement rule and the normal standard distribution or excel and we got:

[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the IQ of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(100,15)[/tex]  

Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]

We select a sample of n = 50 and we want to find the probability that:

[tex]P(\bar X >104)[/tex]

Since the distribution for X is normal then we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}} [/tex]

And using this formula we got:

[tex] P( \bar X >104) = P(Z > \frac{104-100}{\frac{15}{\sqrt{50}}}) = P(Z>1.886)[/tex]

And we can use the complement rule and the normal standard distribution or excel and we got:

[tex] P(z>1.886) = 1-P(Z<1.886) = 1-0.970 = 0.03[/tex]

Answer:

1.84ft

Step-by-step explanation:

From the figure attached,

AB = Height of the window = 15ft

Let the distance between the base of the housr and the fence 'C' = xft

If the angle of depression = 7°

Then angle of elevation of the top of the fence from the house = 7°

Now from right triangle ABC,

tan7° = x/15

x = tan7°×15

x = 0.1227×15

x = 1.84ft

Therefore, distance of the house from the fence is 1.84ft

Answer:I think it is 226

Step-by-step explanation:

85/2= 42.5 then 268 - 42.5= 225.5 then round it and you get 226

Answer:

140 individuals were surveyed

42 people are planning on going to the mountains

Step-by-step explanation:

The question is missing the information regarding the percentage of people who said that they were going to each of the possible destinations. After a quick google search I've found that, in the original question, 32% of individuals were going to the beach, 15% to the desert, 23% to major cities, and 30% to the mountains.

If 21 people said they were going to the desert, and that corresponds to 15% of the total number of people surveyed, the number of people surveyed is:

[tex]21=n*0.15\\n=140\ individuals[/tex]

140 individuals were surveyed

Since 30% responded "the mountains", the number of people planning on going to the mountains is:

[tex]m = 140*0.30\\m=42\ people[/tex]

42 people are planning on going to the mountains

Answer:

A,B and C

Step-by-step explanation:

Answer

a,b,c are the correct answer

Step-by-step explanation:

hope it helps you my luvs

Answer:

C

Step-by-step explanation:

0 is less than or equal to x is less than infinity.  PERIODT.

The domain of the function y = √x will be [0, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

y = √x

The graph of the function is similar to the rightward parabola, the function is not defined for the negative value of x, because the function becomes imaginary.

For the domain of the function, the value of x should be greater than equal to zero.

Because the value under the square root should be greater than or equal to zero.

Then the domain of the function y = √x will be

x ≥ 0

Thus, the domain of the function y = √x will be [0, ∞).

The graph of the function is given below.

More about the domain and range link is given below.

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Answer:

The answer is p = 4 + 2h .

Step-by-step explanation:

It is given that Victor has already taken 4 pages and he will take 2 pages per hour of class. So you have to make an equation of p in terms of h :

Let p be pages,

Let h be hours,

p = 4 + (2×h)

p = 4 + 2h

Answer:

g = 8

Step-by-step explanation:

We're going to isolate g to find out what it equals, so we have to divide both sides by 6.

6g=48

__   __

6     6

g = 8

The solution to the equation 6g = 48 is g = 8.

In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical equation:

6g = 48

By dividing both sides of the equation by 6, we have:

g = 48/6

g = 8

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Answer: A) 5/2

B) 10pi for A and 4pi for B

C) 5/2

Step-by-step explanation:

Please find the attached file for the solution

The rate of the passenger train is 100 miles per hour.

Given:

1. The passenger train traveled 100 miles in the same amount of time it took the freight train to travel 90 miles.

2. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train.

We can set up equations based on the distances traveled and the rates:

1. For the passenger train:

[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\[ 100 = r_p \times \text{Time} \]2. For the freight train:\[ 90 = r_f \times \text{Time} \]Since we know that the rate of the freight train (\( r_f \)) is 10 miles per hour slower than the rate of the passenger train (\( r_p \)), we can express \( r_f \) in terms of \( r_p \):\[ r_f = r_p - 10 \][/tex]

Now, we need to find the time it took for both trains to travel their respective distances. Since the time is the same for both trains, we can equate the expressions for time:

[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]For both trains, time is the same, so:\[ \frac{100}{r_p} = \frac{90}{r_f} \]Substitute \( r_f = r_p - 10 \):\[ \frac{100}{r_p} = \frac{90}{r_p - 10} \]Now, let's solve for \( r_p \):\[ 100(r_p - 10) = 90r_p \]\[ 100r_p - 1000 = 90r_p \]\[ 10r_p = 1000 \]\[ r_p = \frac{1000}{10} \]\[ r_p = 100 \][/tex]

So, the rate of the passenger train is 100 miles per hour.

Answer:

[tex]177 \frac{7}{9} cm^2[/tex]

Step-by-step explanation:

Length of the Plastic Sheet= 96cm

Width of the plastic Sheet =70cm

If a square of side x is cut from each corner of the plastic sheet to form the box.

Length of the box=96-2x

Width of the box=70-2x

Height of the box =x

Volume of the box = LWH

Volume=(96-2x)(70-2x)x

The maximum volume of the box is obtained at the point where the derivative is zero.

[tex]V=(96-2x)(70-2x)x\\V^{'}=4(x-42)(3x-40)[/tex]

Setting the derivative to 0.

[tex]4(x-42)(3x-40)=0\\x-42=0\: 3x-40=0\\x=42\:or\: x=\frac{40}{3}[/tex]

Since we are looking for the minimum value of x,

[tex]x=\frac{40}{3}\\\text{Area of the Square} = x^2\\=\frac{40}{3} X \frac{40}{3}\\=177 \frac{7}{9} cm^2[/tex]

Answer:

Answer:

1/2

Step-by-step explanation:

Answer:

x<18

Step-by-step explanation:

-4x>72 / divide both side ÷-4

x<-18

xe(-œ,-18)

Answer:

Option (a).

Step-by-step explanation:

It is given that 3n is an odd number.

We need to find an even number from the given options.

Even numbers: Which are divisible by 2.

Odd numbers: Which are not divisible by 2.

We need know that the numbers are alternatively even and odd.

If we add or subtract 1 from an odd number, we always get an even number.

If we add or subtract 2 from an odd number, we always get an odd number.

3n is an odd number. So,

3n-1 is an odd number.

3n+2 is an even number.

3n+2 is an even number.

3n+2n is an even number because 2n is an even number and sum of two even numbers in always an even number.

Therefore, the correct option is (a).

Answer:

Blue Terrace: 6.1

Paradiso Grill: 6.3

Step-by-step explanation This is the right answer

Answer:

6.1 and 6.3

Step-by-step explanation:

Answer:

-44

Step-by-step explanation:

Answer:

[tex]P(x) = -10x^2+290x-530[/tex]    

Step-by-step explanation:

We are given the following in the question:

[tex]\dfrac{dP}{dx} = -20x + 290[/tex]

Initial condition:

[tex]P(5) = $670[/tex]

Solving the given differential equation, we get,

[tex]\dfrac{dP}{dx} = -20x + 290\\\\dP=(-20x + 290)dx\\\text{Integrating both sides}\\\\\displaystyle\int dP = \int (-20x + 290)dx\\\\P(x) = -20\dfrac{x^2}{2} + 290x + C\\\\\text{where C is constant of integration}\\P(x) = -10x^2+290x + C\\P(5) = 670\\670 = -10(5)^2+290(5) + C\\670 = 1200 + C\\\Rightarrow C = -530\\P(x) = -10x^2+290x-530[/tex]

is the required profit function.

To determine the profit function, integrate the given marginal profit function. After integration, apply the initial condition to find the integration constant. The final profit function is [tex]P(x) = -10x^2 + 290x - 60.[/tex]

The subject matter of this question is calculus, specifically how to determine the profit function based from the given marginal profit and initial condition. To determine the profit function, you need to integrate the marginal profit function. The marginal profit is given as dP/dx = -20x + 290. When you integrate this, you will get [tex]P(x) = -10x^2 + 290x + C[/tex], where C is an integration constant that we determine using the initial condition P(5) = 670.

To do this, substitute 5 into x in the equation and set P(x) equal to[tex]670: 670 = -10*5^2 + 290*5 + C.[/tex] Solving for C, you will find that C equals -60. So the profit function is [tex]P(x) = -10x^2 + 290x - 60.[/tex]

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Answer:

f(4) = -11

If g(x) = 2 then x = 0

Step-by-step explanation:

here it asks to determine graphically, so we need to use the provided graph:

f(4) = -11 ( just notice the y-coordinate of the point of x-coordination 4)

If g(x) = 2 then x = 0 (just notice the x-coordinate of the point of y-coordination 2)

Answer:

At the end of one hour, John would be ahead of Anny by 4.33 miles

Step-by-step explanation:

In this question, we are to state who jogs Farther between these. 2 persons per hour.

Any jogs 1/3 of a mile in 1/5 of an hour, what this means that he jogs one-third of a mile in 1/5 * 60 in 12 minutes

John however jogs 1/5 miles in 1/30 of hour. This means he jugs one-fifth of a mile in 1/30 * 60 in 2 minutes

Let’s go back to Any

if Any jogs 1/3 in 12 minutes, then the whole lap will be completed in 36 minutes

Thus if he can jog 1 mile in 36 minutes, then in 60 minutes he would have jogged 1.67 miles

If he Jogs 1/5 in 2 minutes, this mean that the whole lap of 1 mile would be completed in 10 minutes

Thus if he can jug 1 mile in 10 minutes, then in 60 minutes, he will be able to jug a whopping 6 miles

This shows that John is actually faster than Any.

By how much distance? that would be 6 - 1.67 = 4.33 miles