A rectangular prism has a length of 4cm, a height of 9cm, and a width of 16cm. What is its volume, in cubic cm?

The half-life of radon-222 is approximately 3.84 days. We can find it in the following manner.

The half-life of a radioactive substance is the amount of time it takes for half of the initial amount of the substance to decay.

We can use the fact that the sample of radon-222 has decayed to 58% of its original amount after 3 days to determine its half-life.

Let N0 be the original amount of radon-222 and N(t) be the amount remaining after time t. We know that:

N(3) = 0.58N₀

We can use the formula for radioactive decay:

\(N(t) = N₀ * (1/2)^(t/h)\)

here h is the half-life.

Substituting in N(3) and simplifying:

\(0.58N₀ = N₀ * (1/2)^(3/h)\)

0.58 = (1/2)^(3/h)

Taking the natural logarithm of both sides:

\(ln(0.58) = ln[(1/2)^(3/h)]\)

ln(0.58) = (3/h) * ln(1/2)

h = -3 / ln(1/2) * ln(0.58)

Using a calculator, we get:

h ≈ 3.84 days

Therefore, the half-life of radon-222 is approximately 3.84 days.

Learn more about radon-222 here brainly.com/question/12498384

#SPJ4

The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

\(b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2\)

Roots of quadrant equation have Samsame sign if product of roots >0.

\(\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0\)

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

To know more about roots go through:-

https://brainly.com/question/428672

#SPJ4

The statement that is true about the proportional relationship of the graph is;

C: Bags of Sand should be on the x-axis, and Bags of Cement should be on the y-axis.

We are told that the equation c equals one fourth times s. This is expressed as;

c = ¹/₄s

Where;

c is the number bags of cements

s is the number of bags of sands required to make concrete.

We can see that the number of bags of cements is directly proportional to the number of bags of sands required to make concrete.

In this question, the number of bags of sand is the independent variable while the number of bags of cement is the dependent variable.

From the graph attached, we see that the number of bags of sand is on the y-axis, while the number of bags of cement is on the x-axis.

Hence, the correct statement is option (C) Bags of Sand should be on the x-axis, and Bags of Cement should be on the y-axis.

Read more about proportional relationship of Linear Graphs at; https://brainly.com/question/12242745

#SPJ1

Answer:

Obviously B

Step-by-step explanation:

The following system of equations has no solutions, the correct option is A.

For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

We have given that;

system of equations are

x+y=-4.....1

-x-y=4......2

Now,

Rearranging the equation 2

-4=x+y

Its equal to equation 1

Therefore, the system of equations will have no solution.

Learn more about solving system of equations here:

https://brainly.com/question/2825832

#SPJ1

It will represent the change in temperature between midnight and 6, the correct option is C.

H(t) is the rate at which the temperature changes. So, if we integrate H(t), we will get the change of temperature.

In this case, we have:

\(\int\limits^6_0 {H(t)} \, dt\)

This will give the change in temperature between 6:00 AM (represented by the 6) and midnight (represented with the 0).

So the correct option is C.

If you want to learn more about integration, you can read:

https://brainly.com/question/18760518

The function is not increasing on any interval.

First, we need to find the first derivative of the function:

y = -3x² - 5x + 2

y' = -6x - 5

Next, we need to find the critical points of the function by setting the first derivative equal to zero:

-6x - 5 = 0

-6x = 5

x = -5/6

Now, we need to use the second derivative test to determine where the function is increasing, decreasing, concave up, and concave down:

y'' = -6

Since the second derivative is a constant negative value, the function is concave down on the entire domain of x.

Now, we can use the first derivative and the critical point to determine where the function is increasing and decreasing:

When x < -5/6, the first derivative is positive, so the function is increasing.

When x > -5/6, the first derivative is negative, so the function is decreasing.

Therefore, the function is not increasing on any interval.

In interval notation, the function is increasing on the interval (-∞, -5/6) and decreasing on the interval (-5/6, ∞).

So, the correct choice is B. The function is not increasing on any interval.

See more about function at; https://brainly.com/question/23819325

#SPJ11

Answer:

  Multiplying by 1 does not change the ratio

Step-by-step explanation:

Multiplying a/b by c/c gives the equivalent ratio (ac)/(bc) because c/c is 1, the multiplicative identity element. Multiplying by 1 does not change the ratio.

Answer:help me pls then ill help u

Step-by-step explanation:

A train traveled at a constant speed for six hours and traveled a distance of 408 miles. What is the best estimate of the number of miles the train could travel in 2.5 hours? *

To find the probability that the equipment is functioning properly, we need to consider the cases where 6, 7, 8, or all 9 components are operational.

Let's calculate the probability for each case and add them together.
For 6 components to be operational, we have to choose any 6 out of the 9 components. The probability of each chosen component working is p, and the probability of each unchosen component failing is (1 - p). So, the probability for 6 operational components is (9 choose 6) * \(p^6 * (1 - p)^3.\)
Similarly, for 7 operational components, the probability is (9 choose 7) \(* p^7 * (1 - p)^2.\)
For 8 operational components, the probability is (9 choose 8) * \(p^8 * (1 - p).\)
Lastly, for all 9 components to be operational, the probability is\(p^9.\)
Adding up these probabilities will give us the overall probability that the equipment is functioning properly.

To know more about functioning visit:

brainly.com/question/13139976

#SPJ11

Since minutes are 1/60 of a degree, we can simplify this to cos (79 + 15/60) = cos (78.25). We can use a calculator to find the exact value, which is 0.268954236.

cos 79 15' = cos (79 + 15/60)

= cos (78 + 45/60)

= cos (78 + 0.75)

= cos (78.75)

= cos (78 + 45/60 + 0.25)

= cos (78.25)

= 0.268954236

The cosine of 79 degrees and 15 minutes is 0.268954236. To calculate this, we convert the minutes to 1/60 of a degree and add it to the angle of 79 degrees. Then, we plug 78.25 into the cosine equation and get the result.

Learn more about value here

https://brainly.com/question/18523098

#SPJ4

The derived quadratic function is y = \((x+5)^2\) + 3.

A quadratic function is a mathematical function of the form f(x) = ax² + bx + c, where a, b, and c are constants, and x is the variable. It is a second-degree polynomial function that creates a parabolic curve when graphed. The term ax²  is the quadratic term, bx is the linear term, and c is the constant term.

The quadratic function with a vertex at (h,k) and a point (x,y) on the parabola can be written in the form of y = a(x-h)² + k. Using the given values, we have:

(h,k) = (-5, 3)

(x,y) = (2, 9)

Substituting these values in the equation, we get:

9 = a\((2 - (-5))^2\) + 3

Simplifying this equation, we get:

6a = 6

a = 1

Therefore, the quadratic function is:

y = \((x+5)^2\) + 3

Learn more about parabola:

https://brainly.com/question/25651698
#SPJ4

Answer:

20:21

Step-by-step explanation:

Let's first start by converting each ratio so that the number of girls is the same

2:3

4:7

The least common multiple of 3 and 4 is 12 so...

8:12

  12:21

We add 8 and 12 to get the number of junior members...

8+12=20

Then we put it in a ratio with the amount of adult members...

20:21

Answer:

the answer is D: undefined becous it's lies at Y-axis

Answer: $4

Step-by-step explanation:

The elevation of the Lucas Oil Stadium is 40735ft

We should know that elevation is defined as the Height of a geographic location above a fixed reference point

31 NFL stadium ranges from 3ft to 5280ft at Mecedez Benz Superdome, New Orleans, Louisiana

The elevation of the sports Authority field at mile high is 275

= 275+7(5280)ft

Multiplying the brackets, we have

275+40460ft

Adding up to get

40735ft

In conclusion, the elevation of Lucas Oil Stadium is 40730ft

Learn more about elevation on https://brainly.com/question/29477960

#SPJ1

Answer: 126

Step-by-step explanation:

7 x 18 = 126

It is asking you to multiply the distance by the time, or 7 x 18

Answer:

the height of the candle before it is lit

Step-by-step explanation:

When the candle is first lit, time is 0.

At tome 0, x = 0 and the height is -0.25(0) + 5 = 5.

The height is 0 at time zero, so the constant term, 5, represents the height of the candle before it is lit.

If you want to round a number within an arithmetic expression, you should use the ROUND function.

The ROUND function allows you to specify the number of decimal places to which you want to round a given number. It is commonly used in programming languages and spreadsheet software.

The syntax for the ROUND function typically involves specifying the number or expression you want to round and the number of decimal places to round to. For example, if you want to round a number, let's say 3.14159, to two decimal places, you would use the ROUND function like this: ROUND(3.14159, 2), which would result in 3.14.

Using the ROUND function ensures that the rounded number is calculated within the arithmetic expression, providing the desired level of precision in the calculation.

Know more about ROUND function here:

https://brainly.com/question/29295263

#SPJ11

Answer:

$3.65

Step-by-step explanation:

False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.

To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).

Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.

Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:

f'(x) = 5cos(x) - sin(x).

This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).

In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).

To learn more about derivative, click here: brainly.com/question/23819325

#SPJ11

Answer: multiply

Step-by-step explanation:

The work done by vector field F on the particle moving along curve C is 11.

To compute the work done by vector field F on a particle moving along curve C, we can use the line integral. The line integral of a vector field F along a curve C is given by:

∫ F · dr

where F is the vector field and dr is the differential displacement along the curve.

Given:

Curve C: r(t) = (1 + 3sin(t))i + (1 + 4sin²(t))j + (1 + 4sin³(t))k, 0 ≤ t ≤ π/2

Vector Field F: F(x, y, z) = xi + yj + zk

To compute the line integral, we need to parameterize the curve C. We can use the given parameterization r(t) to obtain the differential displacement vector field dr.

dr = (dx/dt)dt i + (dy/dt)dt j + (dz/dt)dt k

Let's calculate the line integral step-by-step:

Calculate the differential displacement vector dr:

dx/dt = 3cos(t)

dy/dt = 8sin(t)cos(t)

dz/dt = 12sin²(t)cos(t)

dr = (3cos(t))dt i + (8sin(t)cos(t))dt j + (12sin²(t)cos(t))dt k

Compute F · dr:

F · dr = (xi + yj + zk) · ((3cos(t))dt i + (8sin(t)cos(t))dt j + (12sin²(t)cos(t))dt k)

= 3cos(t)dt + 8sin(t)cos(t)dt + 12sin²(t)cos(t)dt

= (3cos(t) + 8sin(t)cos(t) + 12sin²(t)cos(t))dt

Integrate F · dr along the curve C with respect to t from 0 to π/2:

∫ F · dr = ∫[0 to π/2] (3cos(t) + 8sin(t)cos(t) + 12sin²(t)cos(t))dt

To evaluate this integral, we can split it into three separate integrals:

I₁ = ∫[0 to π/2] 3cos(t) dt

I₂ = ∫[0 to π/2] 8sin(t)cos(t) dt

I₃ = ∫[0 to π/2] 12sin²(t)cos(t) dt

Let's calculate each integral:

I₁ = ∫[0 to π/2] 3cos(t) dt

= [3sin(t)] from 0 to π/2

= 3sin(π/2) - 3sin(0)

= 3 - 0 = 3

I₂ = ∫[0 to π/2] 8sin(t)cos(t) dt

= [4sin²(t)] from 0 to π/2

= 4sin²(π/2) - 4sin²(0)

= 4 - 0

= 4

I₃ = ∫[0 to π/2] 12sin²(t)cos(t) dt

= [4sin³(t)] from 0 to π/2

= 4sin³(π/2) - 4sin³(0)

= 4 - 0

= 4

Now, we can find the total line integral:

∫ F · dr = I₁ + I₂ + I₃

= 3 + 4 + 4

= 11

Therefore, the work done by vector field F on the particle moving along curve C is 11.

To know more about vector field check the below link:

https://brainly.com/question/31400700

#SPJ4

Incomplete question:

If C is the curve given by r (t) = (1 + 3 sin t) i + (1+4 sin² t) j + (1+4 sin³ t) k, 0 ≤t ≤ π/2 and F is the radial vector field F(x, y, z) = xi+yj+zk, compute the work done by F on a particle moving along C.

Answer:

A 90

Step-by-step explanation:

multiple ways to prove this.

e.g. since the angle between the two lines from the center of the circle to the 2 tangent touching points is 90 degrees (that is the meaning of these 90 degrees here as the angle of the circle segment defined by the 2 tangent touching points and the circle center), the tangents have the same "behavior" as tan and cot = the tangents at the norm circle at 0 and 90 degrees. they hit each other outside of the circle again at 90 degrees.

another way

imagine the two right triangles of the tangents crossing point to the circle center and the tangent/circle touching points.

the Hypotenuse of each triangle is cutting the 90 degree angle of the circle segment exactly in half (due to the symmetry principle). so the angle between radius side and Hypotenuse is 90/2 = 45 degrees.

that means also the angle of such a right triangle at the tangent crossing point is 45 degrees (as the sum of all angles in a triangle must be 180, we have the remainder of 180 - 90 - 45 = 45 degrees).

the angles of both right triangles at that point are the same, and so we can add 45+45 = 90 degrees for the total angle at the tangent crossing point.

Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour then Karen working alone will paint a house in 3 hours.

Since Betty takes 6 hours to paint a house alone, that indicates she can paint 1/6 of the house in 1 hour.

Karen can even paint 1/x in 1 hour

Both of them will paint the house in 3/2 hours.

We then add them together which gives:

1/6 + 1/x = 3/2x

The lowest common multiple is 6x

1x/6x + 6/6x = 9/6x

We then leave out the denominators

1x + 6 = 9

simplifying the above equation, we get

x = 9 - 6

x = 3

Therefore, the value of x = 3.

Karen working alone will paint a house in 3 hours.

The complete question is:

Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 14 h to paint a house alone. Betty takes 6 h to paint a house alone.

Required:

How long does it take Karen to paint a house working alone?

To learn more about the value of x refer to:

https://brainly.com/question/16831914

#SPJ4

The team scored 2 field goals, 2 safeties, and 4 touchdowns.

A statement proving the equality of two mathematical expressions is known as an equation. The goal is frequently to ascertain the values of the variables that make the equation true, and it may have one or more variables.

The football team scored 8 times and a total of 38 points.

Let T be the number of touchdowns, F be the number of field goals, and S be the number of safeties.

We know, T = F + S and F + S = 4

Substituting, T = F + S into the equation for total points,

we get, 7T + 3F + 2S = 38

Solving for F and S, we get F = 2 and S = 2.

Therefore, the team scored 2 field goals, 2 safeties, and 4 touchdowns.

To know more about equation, visit:

https://brainly.com/question/2228446

#SPJ1

Solve for F and S then get F = 2 and S = 2.

The team scored 4 touchdowns, 2 field goals, and 2 safeties.

The football group scored 8 times, totaling 38 points.

Let,

T is the no.of touchdowns,

F is the no.of field goals, and

S is the no.of safeties.

Touchdown: The ball is in possession of a runner who has moved from the field of play into the end zone and is on, above, or behind the plane of the opposing goal line (extended).

Field Goal: a three-point goal in football obtained by kicking the ball over the crossbar during normal play.

Safeties: NFL defences can score a safety, worth two points, by tackling the offensive player with the ball behind his own goal line or forcing him to run or throw the ball out of bounds behind his own goal line.

We know that,

T = F + S and

F + S = 4

For total points, put T = F + S into the equation.

We get,

7T + 3F + 2S = 38

Solve for F and S,

we get,

F = 2 and S = 2.

As a result, the team tallied 2 field goals, 2 safeties, and 4 touchdowns.

To know more about Equation, visit:

https://brainly.com/question/2972832

#SPJ1

Mean and standard deviation is more affected by extreme observations.

Mean is the summation of all the values divided by the total number of values. It is also called as average. Median is the middle value.Standard deviation is the dispersion of a dataset relative to its mean. In case of extreme items arithmetic mean is affected very much. For this reason, it no longer remains representative of the distribution. As standard deviation is the positive square root of the arithmetic mean of the square of deviations of all given values, it is also affected by extreme items. As median is a partition value, it is not affected by extreme items.

To know more about standard deviation refer below link:

https://brainly.com/question/16555520

#SPJ4

Answer:

A, \(\frac{5\sqrt{74}}{74}\)

Step-by-step explanation:

Cosine of an angle is equal to the adjacent side of that angle over the hypotenuse of the triangle. Since the adjacent side is 5, and the hypotenuse is √74, the value is 5 / √74.

However, we can't have radicals (square roots) in the denominator, so we multiply the top and bottom by √74 so that the radical goes on the top.

Answer:

the answer is 24

Step-by-step explanation:

36 times 2x is 24

90+36=126

180-126=54

54/2=27

x = 27

Hope you enjoy it! :)