A square pyramid is sliced in such a way that the plane passes through all five faces of the pyramid, what is the resulting cross section?

The area of the sector is 72f

The given parameters are:

Angle = f

Diameter = 24

Start by calculating the radius

r = Diameter/2

r = 24/2

r = 12

The area of the sector is

A = (θ/2) × r^2

So, we have

A = (f/2) * 12^2

Evaluate

A = 72f

Hence, the area of the sector is 72f

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Answer: 24,500 ways

Step-by-step explanation:

The number of ways to select 4 appetizers out of 8 is given by the combination C(8,4) = 70. Similarly, the number of ways to select 3 main courses out of 5 is given by C(5,3) = 10, and the number of ways to select 3 desserts out of 7 is given by C(7,3) = 35.

To find the total number of ways to select the full meal consisting of 4 appetizers, 3 main courses, and 3 desserts, we can use the multiplication principle of counting, which states that the total number of ways to perform a sequence of independent tasks is equal to the product of the number of ways to perform each individual task.

Therefore, the total number of ways to select the full meal is given:

70 x 10 x 35 = 24,500

Hence, there are 24,500 ways to select 4 appetizers, 3 main courses, and 3 desserts from the given options.

Answer:

Step-by-step explanation:

The number of ways to select 4 appetizers out of 8 is given by the combination C(8,4) = 70.
Similarly, the number of ways to select 3 main courses out of 5 is given by C(5,3) = 10, and the number of ways to select 3 desserts out of 7 is given by C(7,3) = 35.

To find the total number of ways to select the full meal consisting of 4 appetizers, 3 main courses, and 3 desserts, we can use the multiplication principle of counting, which states that the total number of ways to perform a sequence of independent tasks is equal to the product of the number of ways to perform each individual task.

Therefore, the total number of ways to select the full meal is given:70 x 10 x 35 = 24,500.

Hence, there are 24,500 ways to select 4 appetizers, 3 main courses, and 3 desserts from the given options.

Answer:

The slope is -2.

Step-by-step explanation:

m=y2-y1/x2-x1            (also, y1-y2/x1-x2 is also true.)

=23-15/6-10                  m=15-23/10-6

= 8/-4                            =-8/4

=4/-2                             =-4/2

= 2/-1                             =-2/1

m=-2                             m=-2

Answer:

The partial derivatives are,

w.r.t x

\(\partial z/ \partial x = 1/x\)

And , w.r.t y

\(\partial z/ \partial y= -1/y\)

Step-by-step explanation:

z = In (x/y).

Calculating both partial derivatives (with respect to x and y)

Wrt x,

wrt x, we get,

\(z = In (x/y).\\\partial/ \partial x[z]=\partial/ \partial x[ln(x/y)]\\\partial z/ \partial x = 1/(x/y)(\partial/ \partial x[x/y])\\\partial z/ \partial x = y/(x)(1/y)\\\partial z/ \partial x = 1/x\)

Now,

wrt y,

we get,

\(z = In (x/y).\\\partial / \partial y[z]=\partial / \partial y[ln(x/y)]\\\partial z/ \partial y =(1/(x/y)) \partial/ \partial y [x/y]\\\partial z/ \partial y = y/x(-1)(x)(1/y^2)\\\partial z/ \partial y= -1/y\)

So, we have found both first partial derivatives.

Answer:

y= - 4/1x + 5

Step-by-step explanation:

Answer:

y=-4x+5

Step-by-step explanation:

4 equals the slope (rise over run) and 5 equals the y-intercept

Answer:

On what

Step-by-step explanation:

Given

The table,

The sample size is 27.

To find:

The mean weight of these 27 babies.

Explanation:

It is given that,

That implies,

The mean weight of 27 babies is,

Hence, the mean weight of 27 babies is 6.1 pounds.

Answer:

2684 \(units^{2}\)

Step-by-step explanation:

We find the area of the 4 triangles

area = 1/2 base x height  All the bases area the same measurement

a = 1/2(22)(61)

a = 671

There are 4 sides

671 x 4 = 2684

Answer:

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40

Then the greatest common factor is 2.

The greatest common factor of 18 , 24 and 40 is HCF = 2

The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF

Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers

Product of HCF x LCM = product of two numbers

Given data ,

Let the HCF be represented as H

Let the first number be represented as p

Now , the value of p = 18

Let the second number be represented as q

Now , the value of q = 24

Let the third number be represented as r

Now , the value of r = 40

And , the factors of 18 = 1, 2, 3, 6, 9 and 18

The factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24

The factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40

So , the HCF of 18 , 24 and 40 is the number 2

Hence , the HCF is 2

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Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer: $217.26

Step-by-step explanation:

13.79 x 6 = 82.74

300 - 82.74 = 217.26

Ms. Gregory has $217.26 left.

Answer:

46

Step-by-step explanation:

46

It will take approximately 1.73 seconds for the object to fall 48 feet.

To solve this problem, we can use the concept of direct variation, which states that the distance (s) an object falls varies directly with the square of the time (t) of the fall.

Mathematically, this can be expressed as \(s = kt^2,\) where k is the constant of variation.

Given that the object falls 16 feet in one second, we can substitute these values into the equation to find the value of k.

So, we have \(16 = k\times 1^2,\) which simplifies to 16 = k.

Now, we can use the value of k to find the time it takes for the object to fall 48 feet. Let's denote this time as t2.

Using the equation again, we have \(48 = k \times t2^2.\)

To solve for t2, we can rearrange the equation as \(t2^2 = 48/k\)  and then take the square root of both sides to get t2 = √(48/k).  

Since we found earlier that k = 16, we can substitute this value into the equation to calculate t2.

Therefore, t2 = √(48/16) = √3 = approximately 1.73 seconds.

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Assume that A and B are independent events. it means that the occurrence of event A does not affect the probability of event B and vice versa.

b. Assume that A and B are independent events. My response is Yes, P(A and B) can be defined as P(B) • P(A|B).

In the event that A and B are independent events, at that point the probability of A happening is one that is influenced by the event of B and vice versa. Hence, P(B) is comparable to P(B|A), showing that the probability of occasion B happening remains unaltered in any case of event A's event. Within the same vein, the likelihood of event A happening remains consistent whether event B has stay put or not, indicated as P(A) = P(A|B).

Therefore in response to question 2, The reason why independent events are not affected  by one another is that the likelihood of one event happening has no effect on the probability of the other event occurring.

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Answer:

$320

Step-by-step explanation:

First, convert the percentage to a decimal.

4% = 0.04

Now, you have to multiply the price by the decimal to find his commission.

8000 * 0.04 = 320

He made a commission of $320.

Answer:

Step-by-step explanation:

y=∫ln(x^2) (2x) dx

=ln (x^2) (x^2)-∫(2x/x^2) (x^2) dx+c

=x² ln (x²)-∫2x dx+c

=x²ln(x²)-x²+c

=x²[ln(x²)-1]+c

integration is between an interval so don't understand at x=3

For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

As given in the question,

Height of the right circular cone = 2.5 units

And radius of right circular cone = 7.5 units

Let r be the radius of the cylinder and h be the height of the cylinder.

Volume of a cylinder 'V' = π r² h

Cylinder is inscribed in right circular cone

From origin edge cylinder is inscribed at x distance in right circular cone.

r = 7.5 - x

h = (2.5 /7.5) x

  = x/3

V  = π ( 7.5 - x )² ( x / 3)

⇒ V = π ( x² -15x + 56.25 ) (x/3)

⇒ V = (π /3)( x³ - 15x² + 56.25x)

For maximum volume ,

dV/dx = 0

dV/dx = (π/3)( 3x² -30x + 56.25)

(π/3) ≠ 0

⇒ 3x² -30x + 56.25 = 0

⇒ 3 ( x² -10x + 18.75) = 0

3 ≠ 0

⇒ x² -10x + 18.75 = 0

x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)

⇒ x = [ 10 ± √ 100 -75]/2

⇒ x=  ( 10 ± 5 ) / 2

⇒ x = 7.5 or 2.5

As r = 7.5 -x

Hence x ≠ 7.5

r = 7.5 -2.5

 = 5 units

h = x/3

  = 2.5/3

  = 0.8333 units

Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

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Answer:

6.45

Step-by-step explanation:

I am not staring at zero.  I am starting at 6.4, so I take 6.4 and add that to half way between 6.5 and 6.4.

6.4 + 1/2(6.5-6.4)  Combine in the parentheses

6.4 + 1/2(.5)  Take half of .5

6.4 + .05  add

6.45

The solution to the Bernoulli equation y' - ⅟ₓ y = 4 / (xy)² involves transforming it into a linear equation through a suitable substitution. By substituting u = y^(1-1/x), we obtain a linear equation in terms of u. Solving this linear equation and reverting the substitution yields the solution for y.

To solve the Bernoulli equation y' - ⅟ₓ y = 4 / (xy)², we can use a substitution to transform it into a linear equation. Let's substitute u = y^(1-1/x). Taking the derivative of u with respect to x using the chain rule, we have du/dx = (1-1/x)y^(-1/x) * y'. Rearranging this equation, we get y' = x(1-1/x)u^(x/(x-1)) * du/dx.

Substituting these expressions for y' and y into the original Bernoulli equation, we have x(1-1/x)u^(x/(x-1)) * du/dx - ⅟ₓ u = 4 / (xy)². Simplifying further, we have (1-1/x)u^(x/(x-1)) * du/dx - ⅟ₓ u = 4 / x³y².

Now, let's multiply the entire equation by x³ to eliminate the denominators. This gives us (1-1/x)(x³u^(x/(x-1))) * du/dx - u = 4 / y².

We can now see that the equation is linear in terms of u. By solving this linear equation, we obtain the value of u. Finally, reverting the substitution u = y^(1-1/x), we can find the solution for y.

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Answer: HL

Step-by-step explanation:

The hypotenuse is actually a shared side of the two triangles. (The line segment that crosses the middle of the rectangle) The hypotenuse is the side of a triangle opposite the 90 degree angle. We can use this for hypotenuse congruency. The diagram also shows the shorter legs of the two triangles are congruent. (The legs refer to the sides that make the 90 degree angle)

So we have hypotenuse congruency and leg congruency.

=HL

Answer:

180

Step-by-step explanation:

The computation shows that there can be 14 7s that will be needed.

From the information, the gym lockers are to be numbered from 1 through 99 using metal numbers to be nailed onto each locker.

The number of 7s that can be found will be:

= 99/7

= 14

Therefore, there can be 14 7s.

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Answer:

a. 37

Step-by-step explanation:

The solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) \(e^{\frac{22t}{3} }\) - (4/3) \(e^{\frac{-16t}{3} }\)

y(t) = (-13/3) \(e^{\frac{22t}{3} }\) + (2/3) \(e^{\frac{-16t}{3} }\)

To solve the system of differential equations, we can use matrix exponential. The system can be written in matrix form as follows:

X' = AX, where X = [x y], A = [22 60; -6 -16]

The matrix exponential of A can be calculated as follows:

\(e^{(At)}\) = I + At + \(\frac{(At)^{2}}{2!}\) + \(\frac{(At)^{3}}{3!}\) + ...

where I is the identity matrix and t is the variable of integration.

We can substitute A and t = 1 into the formula to get:

\(e^{A}\)= I + A + \(\frac{(A)^{2}}{2!}\) + \(\frac{(A)^{3}}{3!}\)+ ...

= [1 0; 0 1] + [22 60; -6 -16] + [44 192; -36 -104]/2! + [ -256 -768; 96 272]/3! + ...

= [1 + 22 + \(\frac{44}{2!}\) - \(\frac{256}{3!}\)*60 + \(\frac{192}{2!}\) - \(\frac{768}{3!}\);

-6 + \(\frac{(-6)}{2!}\) + \(\frac{96}{3!}\) - 16 + \(\frac{(-104)}{2!}\)+ \(\frac{272}{3!}\)]

= [\(\frac{29}{3}\) \(\frac{102}{3}\);

\(\frac{-13}{3}\)  \(\frac{-4}{3}\) ]

Now we can use the initial conditions to find the constants of integration. We have:

X(0) = [x(0) y(0)] = [5 3]

So,

[\(e^{A}\)] [\(c_{1}\)] = [5]

[\(c_{2}\)] [3]

Multiplying both sides by the inverse of \(e^{A}\), we get:

[\(c_{1}\)] = [29/3 102/3]^(-1) [5]

[\(c_{2}\)] [-13/3 -4/3] [3]

Solving this system of linear equations, we get:

\(c_{1}\) = -4/3

\(c_{2}\) = 2/3

Therefore, the solution to the system of differential equations that satisfies the initial conditions x(0)=5 and y(0)=3 is:

x(t) = (29/3) \(e^{\frac{22t}{3} }\) - (4/3) \(e^{\frac{-16t}{3} }\)

y(t) = (-13/3) \(e^{\frac{22t}{3} }\) + (2/3) \(e^{\frac{-16t}{3} }\)

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Answer:

B: 1 triangle

Step-by-step explanation:

I don't know if you've made it to proofs yet, but this format is Side Angle Side (or SAS). In proofs, this means that the triangle is unique. Unique triangles have only ONE solution.

Only one triangle can be constructed with two side lengths of 10 centimeters and 8 centimeters and an angle of 40° between the sides.

A criteria to determine the number of possible triangles is using the law of cosine, in which the length of the missing side (\(c\)) is determined as a function of the two known adjacent sides (\(a, b\)) and a common angle (\(\theta\)):

\(c = \sqrt{a^{2}+b^{2}-2\cdot a\cdot b\cdot \cos \theta}\)   (1)

If we know that \(a = 10\,cm\), \(b = 8\,cm\) and \(\theta = 40^{\circ}\), then the length of the missing side is:

\(c = \sqrt{(10\,cm)^{2}+(8\,cm)^{2}-2\cdot (10\,cm)\cdot (8\,cm)\cdot \cos 40^{\circ}}\)

\(c \approx 6.437\,cm\)

Since there is an unique solution, we conclude that only one triangle can be constructed. \(\blacksquare\)

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Answer:

y = x - 3

Step-by-step explanation:

Answer:

Y= x-3

Step-by-step explanation:

The distance from our y values is -1.

The distance from our x values is -1.

Rise/ Run = Y/X

-1/-1 = 1 or 1/1

You would rise 1 and run 1!

You can use this strategy if you're using graph paper to eventually get the y intercept which is -3.

Hope this helps! :)

Answer:

Independent- Miles traveled, Dependent- cost

Step-by-step explanation:

3dg3nuity

Answer:

I did it :D

Step-by-step explanation:

To find the z-score for a sales associate who earns $37,500, we can use the formula:

z = (x - μ) / σ

Where:

x is the value we want to convert to a z-score (in this case, $37,500),

μ is the mean of the distribution (in this case, $32,500), and

σ is the standard deviation of the distribution (in this case, $2,500).

Substituting the given values into the formula, we have:

z = (37,500 - 32,500) / 2,500

z = 5,000 / 2,500

z = 2

Therefore, the z-score for a sales associate who earns $37,500 is 2.

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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.

The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.

We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:

Z = (Value - Mean) / Standard Deviation

So, the z-score for an associate earning $37,500 would be:

Z = ($37,500 - $32,500) / $2,500

This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.

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