the base of a solid is a circular disk with radius 3. find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.

The Equation of parabola  ( y + 8 )² = 12( x - 2 )

In math, what is a parabola?

A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line.

                 All of the parabola-related ideas are discussed here because it is a crucial component of the conic section topic.

Given,

Directrix is known as x=a Directrix=a=3 Equation of parabola

(Y-y1)²= 4a(X-x1)

Vertex (X1,Y1) = (2,-8)

Directrix=a=3

Equation of parabola

       ( y - y₁ )² = 4a( x - x₁)

        ( y - ( -8))² = 4 * 3(x - 2 )

          ( y + 8 )² = 12( x - 2 )

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suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is  nλe^(-nλx)

Given fx (x) = λe^λx

Fx (x) = 1 – e^-λx      x…0

To find distribution of Min (X1,….Xn)

By applying the equation

fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)

For minimum j = 1

[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx

= ne^[(n-1) λx] λe^(λx)

= nλe^(-λx[1+n-1])

= nλe^(-nλx)

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If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.

How to solve word problems?

Recognize the issue, including all the terminology used to describe it. Recognize what we need to look for, Recognize the issue's context.

Convert the issue into an equation. Give the unknown a variable (or variables) to symbolize, Indicate exactly what the variable stands for.

Put the strategy into action and find a solution.

Given:

Elephants at the Norfolk zoo are fed = 1/2 of the barrel

Buffalo are fed 7/10 as much corn as the elephants = 7/10 * Elephants fed

= 7/10 * 1/2

= 7/20

Therefore, If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.

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Answer:

To solve the given trigonometric equation, we can start by isolating the cos(theta) term on one side of the equation. We can do this by dividing both sides of the equation by csc(theta):cos(theta) * csc(theta) - 2cos(theta) = 0

cos(theta) * csc(theta) / csc(theta) - 2cos(theta) / csc(theta) = 0 / csc(theta)

cos(theta) - 2cos(theta) / csc(theta) = 0Next, we can combine like terms on the left side of the equation:cos(theta) - 2cos(theta) / csc(theta) = 0

-2cos(theta) / csc(theta) + cos(theta) = 0

(1 - 2 / csc(theta)) cos(theta) = 0Since cos(theta) cannot be equal to 0 (because the angle theta is between 0 and 2pi), the only solution to this equation is:1 - 2 / csc(theta) = 0

1 = 2 / csc(theta)

csc(theta) = 2This means that the value of csc(theta) is equal to 2. To find the value of theta, we can use the inverse cosecant function (arcsec) to solve for theta:theta = arcsec(2)The value of arcsec(2) is approximately 1.047198, which is the solution to the given equation for theta.Note that this is just one solution to the equation, as there may be other solutions for theta depending on the values of the trigonometric functions. It is important to check that the solution falls within the given range of 0 < theta < 2pi.

Answer: -26=2(3p-5) is false

Step-by-step explanation:

The solution is 4

Substitute in 4 in place of the variables to prove whether its false or true

1/4(4)+17=18

18=18 true

5=4(4)-11

5=16-11

5=5 true

-26=2(3(4)-5)

-26=2(7)

-26[tex]\neq[/tex]14

3(4+4)=24

3(8)=24

24=24 true

-26=2(3p-5) is false

Answer:

The third option is false, because when you plug in 4 for p, you get 14, and 14 is not equal to -26.

Hope this helps! :D

Step-by-step explanation:

Balinese metallophones have thicker metal keys than Javanese ones so   they produce a brighter sound. therefore correct answer is B.

A metallophone is any musical instrument in which the sound- producing body is a piece of metal( other than a substance string), conforming of tuned essence bars, tubes, rods, coliseums, or plates. ultimate repeatedly the metal body is struck to produce sound, generally with a mallet, but may likewise be triggered by discordance, keyboard action, or other means.

Metallophones have been used in music in Asia for thousands of spells. There are several different types used in Balinese and Javanese gamelan ensembles, containing the gender, gangsa and saron. These devices have a single row of bars, tuned to the distinctive pelog or slendro scales, or a subset of them.

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The total amount paid for the used car plus expenses will be $6,914.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Zaida purchased a used car for $6,500.

State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.

Now,

Since, Zaida purchased a used car for $6,500. State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.

Hence, The total amount paid for the used car plus expenses is,

⇒ $6500 + 4% of 6500 + $72 + $45 + $37

⇒ $6500 + $260 + $154

⇒ $6,914

Thus, The total amount paid for the used car plus expenses = $6,914

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I don't see the picture. Can you send it in the message.

Answer:

44.44 %

Step-by-step explanation:

16 000 / 36 000 = .4444   = 44.44%

The range of projectile =21556.122 m

The maximum height of the projectile will be = 5280.03 m

The speed at which the projectile hits will be 650 m/s.

Initial speed [tex]v_0=650 \:m/s[/tex]

Angle of elevation [tex]\theta=30^{\circ}[/tex]

Acceleration due to gravity [tex]=9.8 m/s^2[/tex]

i) Range of the Projectile:

[tex]$$\begin{aligned}& R=\frac{v_0^2 \sin (2 \theta)}{g}=\frac{(650)^2 \sin (30)}{9.8} \\& R=21556.122 m\end{aligned}$$[/tex]

ii) Maximum Height of the projectile.

[tex]$$\begin{aligned}& H=\frac{v_0{ }^2 \sin ^2 \theta}{2 g}=\frac{(650)^2 \sin ^2(30)}{2 \times 9.8} \\& H=5389.03 m\end{aligned}$$[/tex]

iii) The speed at which the projectile hits the ground is the same as the initial speed.

i.e. speed [tex]$=650 \mathrm{~m} / \mathrm{s}$[/tex]

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I expect to land right side up using probability is 2.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability.

Probability theory, which is widely employed in disciplines including statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these ideas an axiomatic mathematical formalization.

I expect to land right side up using probability is 10(0.2)

so that the answer is 2.

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let z be standard normal random variable. let v be chi-squared random variable with d degrees of freedom. let x and v be independent random variables. [tex]$= \frac{1}{\sqrt{2\pi}}\int_{0}^{\in[/tex]

Let [tex]$X$[/tex]and [tex]$V$[/tex] be independent random variables.

[tex]$X \sim N(0,1)$[/tex] , [tex]$V \sim \chi^2(d)$[/tex]

We know that for a standard normal random variable [tex]$X$[/tex] and a [tex]$\chi^2$[/tex] random variable [tex]$V$[/tex] with [tex]$d$[/tex] degrees of freedom, the random variable [tex]$T$[/tex] given by:

[tex]$T = \frac{X}{\sqrt{\frac{V}{d}}}$[/tex]

has a student t-distribution with d degrees of freedom.

This can be seen by the following calculation:

[tex]$f_T(t) = \int_{-\infty}^{\infty} f_X(xt)\frac{1}{\sqrt{2\pi v}}e^{-\frac{v}{2}}\frac{v^{d/2}}{\Gamma(d/2)}\frac{1}{v^{d/2}}e^{-\frac{v}{2d}t^2}dv$[/tex]

[tex]$= \frac{1}{\sqrt{2\pi}}\int_{0}^{\in[/tex]

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Answer:

<=> (8+9y)x=-y+9

<=> 8x+9yx+y=9

<=> y(9x+1)=9-8x

<=> y=(9-8x)/(9x+1)

domain: 9x+1 [tex]\geq[/tex] 0 <=> x [tex]\geq[/tex] -1/9 => R / {-1/9}

range: R/{-8/9} (horizontal asymptot)

The value of x and y for the given linear equations are as follows.

For question8: x=4,y=-1

For question9 :x=-1.2, y=-(111/37)

An equation in which is  the highest power of to the  variables 1 is knowns as the  linear equation. Mathematically: it is an  algebraic equations that can be also  written in the form of  ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.

Question 8

5x+4y=16------- eq1

-2x-4y=-4-------ea 2

5x=16-4y

X=(16-4y)/5

X=4(4-y)/5

Now substitute the value of x in equations 2

-2x-4y=-4

-2(4(4-y)/5)-4y=-4

-2(16-4y)/5-4y=-4

(-32+8y)/5-4y=-4

-32+8y-20y=-20

8y-20y= -20+32

-12y=12

y=-1

Now substitue the value of y in following equation

5x+4y=16

5x+4(-1)=16

5x-4=16

5x=4+16

x=20/5

x=4

Question 9

-5x+y=3-------------eq 1

3x-8y=24-------------eq2

-5x=-3-y

-5x= -(3+y)

x=(3+y)/5

Now substitute the value of x in equation 2

3(3+y)/5-8y=24

(9+3y)/5-8y=24

9+3y-40y=24

3y-40y=120-9

y=-(111/37)

Now substitue the value of y in following equation

-5x+y=3

-5x+(-111/37)=3

-185x-111=111

-185x=222

x= -222/185

x= -1.2

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A line of two points (4, 2) and (-1, k) is perpendicular to the line y=2x+1, then k = 9/2.

Given a line with equation y = mx + c, the slope is denoted by m.

Given 2 points with slopes m₁ and m₂, those two lines are perpendicular if:

m₁ x m₂ = -1

The given line equation is:  y = 2x+1

Hence,

m₁ = 2

Compute the slope from 2 points: (4, 2) and (-1, k)

m₂ = (k - 2) / (-1 - 4)

m₂ = (-1/5) (k - 2)

Use the condition for perpendicular lines:

m₁ x m₂ = -1

2 x (-1/5) (k - 2) = -1

2k - 4 = 5

2k = 9

k = 9/2

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The weight of the baseball equipment in the container is 7(4/5) pounds.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Container weight = 23(2/5) pounds

Baseball equipment.

= 1/3 of 23(2/5) pounds

= 1/3 x 117/5

= 39/5

= 7(4/5) pounds

= 7.8 pounds

Thus,

The weight of the baseball is 7.8 pounds.

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Answer:20.5 miles

Step-by-step explanation:

the formula for distance, rate (speed), and time is

Distance=rate×time

D=40 (this is the speed he was going for the first customer) × [tex]\frac{12}{60}[/tex] (time)

the time is 12/60 because we the speed was in miles per HOUR and the time was in miles per MINUTE. To convert minutes to hours, we divide by 60.

D=40× [tex]\frac{12}{60}[/tex]

D=48/6

D=8 miles

Second trip:

D= 50×[tex]\frac{15}{60}[/tex]

D=50×[tex]\frac{1}{4}[/tex] (15/60 simplified is 1/4)

D= 12.5 miles

ANSWER: 8 miles + 12.5 miles = 20.5 miles

As per the given distribution, the mean of the sampling distribution is Pa - Pb

The term mean in distribution refers adding all numbers in the data set and then dividing by the number of values in the set.

Here we have given that the proportions of flowers that are blue are papa and pbpb , respectively.

And we need to find the mean of the sampling distribution

While we looking into the given question the mean of a sampling distribution is the population mean from which values are sampled.

Here for a population of mean µ, then the mean of the sampling distribution is μx

=> μα = μ

Here from the given parameters, let us consider that then independent random samples of 50 species-a flowers and 100 species-b flowers are selected

Then it can be written as Pa refers sample proportion of blue specie - a and Pb refers sample proportion of blue specie - b

Therefore, the resulting mean is Pa - Pb

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Answer:

h - (3/h)

Step-by-step explanation:

The expression for the sequence of operations described is h - (3/h).

To evaluate this expression, we would first need to divide 3 by h to find the quotient, and then subtract that quotient from h. This would give us the final result of the sequence of operations.

For example, if h = 10, we would first divide 3 by 10 to get 0.3. We would then subtract 0.3 from 10 to get 9.7. This would be the final result of the sequence of operations.

In general, the expression h - (3/h) can be used to represent any sequence of operations that involves subtracting the quotient of 3 from h. The value of h can be any number, and the final result of the sequence of operations will depend on the specific value of h that is used.

The percentage of students who owns either a television or stereo is given by the set formula P ( A ∪ B ) = 23 %

What is Set Theory Formula?

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

The equation is n(A∪B) = n(A) + n(B) - n(A⋂B)

Given data ,

Percentage of college students who owns a television or stereo be represented as = P ( A ∪ B )

Percentage of college students who owns a television is P ( A ) = 15 %

Percentage of college students who owns a stereo is P ( B ) = 10 %

Let the percentage of college students who owns a television and stereo  is P ( A ∩ B ) = 2 %

So , the value of P ( A ∪ B ) is calculated as

P (A∪B) = P ( A ) + P ( B ) - P ( A ⋂ B )

Substituting the values in the equation , we get

P (A∪B) = 15 + 10 - 2

On simplifying the equation , we get

P (A∪B) = 25 - 2

P (A∪B) = 23 %

Therefore , the value of P (A∪B) is 23 %

Hence , the percentage of students is 23 %

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The system of the equation is written as

xx + yy ≥ 16

$4.25xx + $0.75yy ≤ $30

the graph is attached and the solution from the graph is (5.1, 10.9)

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

If xx represents the number of cupcakes purchased

yy represents the number of cookies purchased

cupcakes for $4.25 each and cookies for $0.75 each. Myesha has $30

$4.25xx + $0.75yy = $30

buy at least ( ≥ ) 16 cupcakes and cookies altogether

xx + yy ≥ 16

The simultaneous equation

xx + yy ≥ 16

$4.25xx + $0.75yy = $30

One solution from the graph is (5, 11)

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Answer:

D.) No solution

Step-by-step explanation:

Not exactly sure what the question is, not quite sure what it's asking but based on what I see on the graph, I'd say that it's D.) no solution, because both lines are parallel meaning that there is no solution to the system of equation. If there were to be a solution to the equation you would have to see an intersection which is where both lines meet/touch at a certain point. If both lines have the same point and are on top of one another that means that it has infinitely many solutions...

(If wrong, I'm sorry)

unit D must be the youngest rock unit and the order of formation must be A, B, C, D

The Law of Cross Cutting Relations states that any feature (such as a fault or a like) that cuts across a rock unit must be younger than the rock unit.

In the picture, the dark colored rock (unit D) cuts across all of the other rock units (A, B, and C).

Therefore, unit D must be the youngest rock unit and the order of formation must be A, B, C, D.

Therefore, the order of formation is A, B, C, D.

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Answer:

55 degrees

Step-by-step explanation:

Sum of ALL three angles of a triangle ALWAYS equal 180

rule is 6x+5 will equal the sum of the 2 known angles because of this

6x+5=3x+x+45

6x+5=4x+45

-4x.    -4x

2x+5=45

    -5. -5

2x=40

/2. /2

x=20

6(20)+5

120+5

125

180-125

55

hopes this helps please mark brainliest

Answer:

10

Step-by-step explanation:

2 1/2 divided by 1/4

1. Make improper

5/2 divided by 1/4

2. Keep Change Flip (Multiply by reciprocals)

5/2x4/1

3. Solve!

20/2

4. Simplify

10/1=10

To answer this question, we first need to determine the objective and constraint equations.

The objective is to maximize the area of the rectangular garden, which is given by the equation $A = xy$.

The constraint is that the total cost of the fencing must not exceed $320. In other words, we have the equation $6x + 2(y+x) \le 320$.

To express the quantity to be maximized as a function of $x$, we can simply plug in the equation for the area of the rectangular garden into the objective equation. This gives us the function $f(x) = xy = x^2y$.

To find the optimal values of $x$ and $y$, we can use the method of Lagrange multipliers. Let $\lambda$ be the Lagrange multiplier. The Lagrange function is given by

$$L(x,y,\lambda) = x^2y + \lambda(6x + 2(y+x) - 320)$$

To find the optimal values of $x$ and $y$, we need to find the values of $x$ and $y$ that maximize $L(x,y,\lambda)$. To do this, we take the partial derivatives of $L(x,y,\lambda)$ with respect to $x$ and $y$ and set them equal to 0. This gives us the equations

$$\frac{\partial L}{\partial x} = 2xy + 6\lambda = 0 \quad \text{and} \quad \frac{\partial L}{\partial y} = x^2 + 2\lambda = 0$$

We can solve these equations simultaneously to find the optimal values of $x$ and $y$. First, we can solve for $y$ in the second equation to get

$$y = -\frac{x^2}{2\lambda}$$

Substituting this expression for $y$ into the first equation, we get

$$2x \left(-\frac{x^2}{2\lambda}\right) + 6\lambda = 0 \quad \Rightarrow \quad -x^3 + 12\lambda^2 = 0$$

Since $\lambda$ cannot be 0, we can divide both sides of this equation by $-12\lambda^2$ to get

$$x^3 = 12\lambda^2 \quad \Rightarrow \quad x = \sqrt[3]{12\lambda^2}$$

Substituting this expression for $x$ into the expression for $y$, we get

$$y = -\frac{\sqrt[3]{12\lambda^2}}{2\lambda}$$

Now we need to find the value of $\lambda$ that satisfies the constraint $6x + 2(y+x) \le 320$. Substituting the expressions for $x$ and $y$ into this equation, we get

$$6\sqrt[3]{12\lambda^2} + 2\left(-\frac{\sqrt[3]{12\lambda^2}}{2\lambda} + \sqrt[3]{12\lambda^2}\right) \le 320$$

Simplifying, we get

$$-\frac{\sqrt[3]{12\lambda^2}}{2\lambda} + 10\sqrt[3]{12\lambda^2} \le 320$$

Dividing both sides by $10\sqrt[3]{12\lambda^

The development made to the Judaism is mentioned below;

Action as Leader;

Abraham;

Abraham's care for others is one of his leadership strengths. Abraham expressed his sorrow for Sodom and Gomorrah when the Lord informed him that they would be destroyed. He "stick his neck out for his people," as one who cares for others. He pleaded with God on their behalf.

Moses;

Early on, Moses realized he didn't have to handle everything by himself. He eventually succeeded as a leader by using delegation.

David;

As a man of God, David had learned to wait on the Lord, but he also had to learn how to be patient with those around him.

Solomon;

His name in Hebrew means peace and he used his wisdom to bring about peace in the world through deeds rather than conquest.

Contribution to Judaism

Abraham;

Before Abraham, people believed in multiple gods; Abraham was the first to preach that there is only one God. Ironically, Terach, Abraham's father, had made a fortune by selling idols of several deities.

Moses;

The Jews were delivered from slavery in Egypt by Moses, who also guided them to the Holy Land that God had promised.

David;

Many of the Old Testament Psalms are attributed to him; they were probably penned on his renowned lyre, upon which he was reputed to be a master.

Solomon;

As the Israelite monarch who constructed the first Temple in Jerusalem, Solomon is well-known. He was also the second and final king of a united Israel, which was at the height of its power during his rule (after his father, David).

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