What is the volume of the prism below?
Aw
2
23
units
$3
3. units
5 units 3
A units 3

Since the value of y varies directly with x, the ratio of y to x is always constant. We can set up the proportion:

y/x = 18/12

Then we can solve for y by cross multiplying:

y = (18/12)x

= (3/2)x

= (3/2)(60)

= 90

So when x = 60, y = 90.

To find the mass of a thin funnel in the shape of a cone, we need to integrate the density function over the given volume. In this case, the cone is defined by the equation z = x² + y², with 1 ≤ z ≤ 3, and the density function is (x, y, z) = 7 - z. Therefore, the mass of the thin funnel in the shape of a cone is 6π.

The volume of the cone can be expressed in cylindrical coordinates as V = ∫∫∫ρ(r,θ,z) r dz dr dθ, where ρ(r,θ,z) is the density function and r, θ, z are the cylindrical coordinates. In this case, the density function is given as (x, y, z) = 7 - z.

Converting to cylindrical coordinates, we have z = r², and the limits for integration become 1 ≤ r² ≤ 3, 0 ≤ θ ≤ 2π, and 1 ≤ z ≤ 3.

The mass can be calculated as M = ∫∫∫(7 - z) r dz dr dθ. Integrating with respect to z first, we have M = ∫∫(7z - (1/2)z²) dr dθ, with the limits 1 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π.

Integrating with respect to r and θ, we obtain M = ∫(7(3/2) - (1/2)(3²)) dθ = ∫(21/2 - 9/2) dθ = 6π.

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By elimination, the solution of the system of equations, r + 3s = 7 and 2r - s = 7, is (r , s) = (4 , 1).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in r and s, a variable should be eliminated by adding/subtracting the two equations.

First, multiply the first equation by 2.

r + 3s = 7 ⇒ 2r + 6s = 14     (equation 1)

Subtracting the two equations will eliminate the variable r.

2r + 6s = 14     (equation 1)

2r  -   s = 7     (equation 2)

    7s    = 7

s = 1

Substitute the value of s to any of the two equations and solve for r.

2r - s = 7     (equation 2)

2r - 1 = 7

2r = 7 + 1

2r = 8

r = 4

Hence, the solution of the system of equations is (r , s) = (4 , 1).

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The number of days spent or taken by assistant with work efficiency of 2 units per day to do the work alone is equals to the 7.5 days.

We have provide that there is a carpenter and his assistant can do a piece of work.

Number of days taken by both carpenter and his assistant to do a piece of work = 3 days.

Number of days taken by carpenter and to do the same piece of work alone = 5 days.

We have to determine number of taken by assistant and to do the same piece of work alone.

Let the required number of days that the assistant take to do the work alone be 'x days'. As we know, total available work units = LCM (3,5) = 15 units

Ability or efficiency of a person or man is calculated by dividing the total work units to the number of working days spent to do the work.

Now, Ability or efficiency of both carpenter and his assistant work together = 15/5

= 3 units/day

Similarly, Ability or efficiency of carpenter = 15/3

= 5 units/day

So, Ability or efficiency of assistant= 5 - 3 = 2 -(1)

Using efficiency formula, efficiency of assistant

= 15/x --(2)

from (1) and(2), 15/x = 2

=> 2x = 15

=> x = 7.5

Hence, required number of days are 7.5 days.

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The probability that the answerof the 1st question is correct is 1/15.

So, the probability of the correct answer:

Probability formula: P = Favourable events/Total events

Where total events are 15 and favorable event is 1.

Now calculate as follows:

Therefore, the probability that the answerof the 1st question is correct is 1/15.

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The Laplace transform table contains properties and formulas for common transforms, as well as the inverse Laplace transform and the shift theorem. It also includes properties such as linearity, scaling, and time shifting.

The Laplace transform table is an important tool for solving linear differential equations. It contains information about common transformations and their associated formulas, as well as the inverse Laplace transform and the shift theorem. The table also includes properties such as linearity, scaling, and time shifting. Linearity states that if a function f(t) is a linear combination of two functions f1(t) and f2(t), then its Laplace transform F(s) is the sum of the Laplace transforms of f1(t) and f2(t). Scaling states that if a function f(t) is multiplied by constant k, then its Laplace transform F(s) is divided by k. Time shifting states that if a function f(t) is shifted by x units in time, then its Laplace transform F(s) is multiplied by \(e^(-sx)\). These properties can be used to simplify Laplace transforms and to solve linear differential equations. The Laplace transform table is a useful tool for engineers and physicists who use linear differential equations in their work.

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To derive the least-squares fit for the model y = a1x + a2x^2 with a zero intercept, we need to minimize the sum of squared residuals. Let's denote the observed data points as (xi, yi) for i = 1 to n.

The objective is to find the values of a1 and a2 that minimize the following sum of squared residuals:

SSR = ∑(yi - (a1xi + a2xi^2))^2

To find the minimum, we differentiate SSR with respect to a1 and a2 separately and set the derivatives equal to zero.

Partial derivative with respect to a1:

∂SSR/∂a1 = -2∑(yi - (a1xi + a2xi^2))*xi = 0

Partial derivative with respect to a2:

∂SSR/∂a2 = -2∑(yi - (a1xi + a2xi^2))*xi^2 = 0

Expanding the above equations:

∑(yixi) - a1∑(xi^2) - a2∑(xi^3) = 0 ------ (1)

∑(yixi^2) - a1∑(xi^3) - a2∑(xi^4) = 0 ------ (2)

Now, let's solve these equations to find the values of a1 and a2.

From equation (1):

a1∑(xi^2) + a2∑(xi^3) = ∑(yi*xi) ------ (3)

From equation (2):

a1∑(xi^3) + a2∑(xi^4) = ∑(yi*xi^2) ------ (4)

We can express equations (3) and (4) in matrix form as:

| ∑(xi^2) ∑(xi^3) | | a1 | = | ∑(yixi) |

| ∑(xi^3) ∑(xi^4) | | a2 | = | ∑(yixi^2) |

Solving this system of linear equations will give us the values of a1 and a2.

Once a1 and a2 are determined, we have the least-squares fit of the model y = a1x + a2x^2 with a zero intercept.

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Answer:

$3.02

Step-by-step explanation:

You just subtract 97.98-94.96.

Answer:

3.02

Step-by-step explanation:

you subtract 94.96 from 97.98

Pretty sure is A or D.

The mean wait time for callers during the tax filing season was greater than 15 minutes.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test whether there is enough evidence to reject the IRS claim that the mean wait time for callers is at most 15 minutes,

we can use a one-sample t-test with a significance level of α = 0.05.

The null hypothesis is that the true mean wait time μ is equal to 15 minutes,

and the alternative hypothesis is that μ is greater than 15 minutes. Mathematically, this can be expressed as:

H₀: μ ≤ 15

Ha: μ > 15

We can calculate the test statistic t using the formula:

t = (x - μ) / (s / √(n))

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (16.7 - 15) / (2.7 / √(40))

t = 4.07

Using a t-table or calculator with 39 degrees of freedom (n-1), we find that the p-value associated with this test statistic is less than 0.0001.

This means that if the true mean wait time is really 15 minutes, the probability of obtaining a sample mean of 16.7 minutes or greater is less than 0.0001.

Hence, this p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is enough evidence to suggest that the true mean wait time for callers during the tax filing season was greater than 15 minutes.

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If there exists an odd prime number p and a number x that is co-prime to p, such that x^2 ≡ a (mod p), then Fermat's Little Theorem can be used to show that a^(p-1)/2 ≡ 1 (mod p).


1. Assume that there exists an odd prime number p and a number x that is co-prime to p, such that x^2 ≡ a (mod p).

2. According to Fermat's Little Theorem, if p is a prime number and a is an integer not divisible by p, then a^(p-1) ≡ 1 (mod p).

3. Since x is co-prime to p, x is not divisible by p, and thus a^((p-1)/2) ≡ 1 (mod p) for x^2 ≡ a (mod p).

4. Therefore, a^(p-1)/2 ≡ 1 (mod p) is proven using Fermat's Little Theorem.

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Answer: a soda costs $4

Step-by-step explanation:

add totals and divied by each number

Answer: $4

Step-by-step explanation:

Boys are taller than girls on average, with a larger center of data and larger range in height;

the dot plots are not shown.

Answer:

Answer is A

Step-by-step explanation:

Hope it helps

Answer:

SN = √29 cm = 5.39 cm (2 dp)

Step-by-step explanation:

Using the given information, we can create a new right triangle with hypotenuse SN, then use Pythagoras' Theorem to find the length of SN.

Extend the line SU to the left until it is under point N → label this point P.  Connect point P to point N.  This creates a new right triangle (see attachment).

If BU = 4 cm, and M is the midpoint of BU, then UM = 2 cm

⇒ PN = UM = 2 cm

As NM = 2, then PU = 2 cm

⇒ PS = PU + US = 2 + 3 = 5 cm

Therefore, the two legs of the right triangle with SN as its hypotenuse are 2 cm and 5 cm.

Using Pythagoras' Theorem:

⇒ a² + b² = c²

⇒ 2² + 5² = SN²

⇒ 4 + 25 = SN²

⇒ SN² = 29

⇒ SN = √29 cm = 5.39 cm (2 dp)

Answer:

x = 4

Step-by-step explanation:

Given the equation:

\(\displaystyle{4^x - 4^0 - 255=0}\)

We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,

\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)

Add both sides by 256, so we have:

\(\displaystyle{4^x=256}\)

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

\(\displaystyle{4^x=2^8}\)

Convert to the same base:

\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)

When two sides have same base, solve the equation through exponents:

\(\displaystyle{2x=8}\)

Divide both sides by 2, so we have:

\(\displaystyle{x=4}\)

Answer:

However, when you look at the restrictions for the function, you see that the square root portion of the function is only valid when x > 5. If x < or = 5, the other part of the function is valid, and because it has no square root or denominator, all real numbers are valid as the domain for this piecewise function....!!!

Answer:

Step-by-step explanation:

12 ≤ t ≤ 25

t ≤ 13 miles

Answer:

There's 3 answers: the third, fourth, and the sixth one. 1  2  3

                                                                                           4  5  6

Step-by-step explanation:

The expression in the question gets simplified to p-6, and so does the third one, fourth one is just itself, and the sixth one also simplifies to p-6.

Answer:

21 years

Step-by-step explanation:

Lawrence did research on many different swimmers. He graphed each swimmer with a tick on the graph. The more ticks, the higher amount of people. Because most of the ticks are on 21, If I did this right, It should be 21.

Answer:

The height of the plane to the nearest mile is 175 miles

Step-by-step explanation:

Here, we want to calculate the direction of the plane

A diagrammatic representation of this will be interesting

Please check an attachment for this

From the diagram, consider the triangle OAB

we want to calculate the height of this triangle

We simply apply trigonometric identity

Thus, we have that;

Sine 33 = h/322

h = 322 sine 33

h = 175.37

h is approximately 175 miles

Answer:

16x^3+16x^2+30

Step-by-step explanation: