the volume of a cube with length x is V(x)=x^3. The volume of the sphere with radius 1/2x is shown in the graph. Over the interval [1,2], which volume is increasing faster?

Answer:

  a. The proof is in your picture

  b. Yes

  c. All four triangles are congruent by the HL theorem

Step-by-step explanation:

Given AB≅CB in ∆ABC with BD⊥AC, you want to show ∆ABD≅∆CBD, and you want to know if these are congruent to ∆CEG and ∆FEG.

Your picture correctly shows a proof that ∆ABD≅∆CBD by the HL postulate.

Sides CE and FE are marked congruent to each other and sides AB and CB. The altitudes BD and EG of these isosceles triangles are marked as congruent. Hence all four triangles, ∆ABD, ∆CBD, ∆CEG, and ∆FEG are congruent by the HL theorem.

The same HL theorem reasoning applies to all of the triangles.

__

Additional comment

The distance from the light to the stage is said to be the same for both lights. That would be measured perpendicular to the stage, and is the shortest such distance. We are assuming that BD and EG are those perpendicular distances, as we see no markings on the diagram indicating right angles.

Answer:

1 and 2 are functions, 3 is not a function.

Step-by-step explanation:

One x-value can lead to one y-value. If the x-value leads to more than one y-value like #3, then the relation is not a function.

If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

The probability that x is either less than 3 or greater than 8 is 0.375   .

In the question ,

it is given that ,

a continuous random variable X , is uniformly distributed between 2 and 10 ,

So , alpha(α) = 2 and beta(β) = 10 .

the probability that x is either less than 3 or greater than 8 can be calculated by :

P(X < 3  or X > 8) = 1 - (8 - 3)/(β - α)

= 1 - (8 - 3)/(10 - 2)

= 1 - 5/8

On simplifying further ,

we get ,

= 0.375

Therefore , the probability P(X < 3  or X > 8) is = 0.375   .

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Answer:

Step-by-step explanation:

He made a mistake in step one turning the 7 into a -7

[tex]x^{2}[/tex] - 3x + 7 = 0

Solving:

[tex]1x^{2}[/tex] - 3x + 7 = 0  ← If the term doesn't have a coefficient, it is considered that the coefficient is 1.

[tex]1x^{2}[/tex] + (-3x) + 7 = 0 ← Identify the coefficients a, b, and c of the quadratic equation.

a = 1, b = -3, c = 7

x = - (-3) ±√[tex](-3)^{2}[/tex] - 4 x 1 x 7

                 2 x 1

x = 3 ± √[tex](3)^{2}[/tex] - 4 x 7

                2

x = 3 ± √9 - 4 x 7

                2

x = 3 ±√9 - 28

             2

x = 3 ± √-19

         2

The square root of a negative number does not exist in the set of real numbers.  

x = ∉ R

[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_3(y)=11.03\hspace{5em}\log_3(z)=7.74\hspace{5em}\log_3(t)=5.44 \\\\[-0.35em] ~\dotfill[/tex]

[tex]12\log_3\left( \cfrac{z^7}{y^5 t^2} \right)\qquad \textit{let's nevermind the 12 for now} \\\\\\ \log_3\left( \cfrac{z^7}{y^5 t^2} \right)\implies \log_3(z^7)-\log_3(y^5 t^2)\implies \log_3(z^7)-[\log_3(y^5)+\log_3(t^2)] \\\\\\ \log_3(z^7)-\log_3(y^5)-\log_3(t^2)\implies 7\log_3(z)-5\log_3(y)-2\log_3(t) \\\\\\ 7(7.74)-5(11.03)-2(5.44)\implies \stackrel{\textit{let's put back the 12}}{12 ~~ [7(7.74)-5(11.03)-2(5.44)]} \\\\\\ ~\hfill \text{\LARGE -142.2}~\hfill[/tex]

Answer: It should not be able to

Step-by-step explanation:

It should always be in the middle, aka its name, "Median"

Answer:

Step-by-step explanation:

since $68 is your total, let's use the example z=y+x

z is our total, and we know that he made a total of $68, therefore z is the number 68.

We also know that James made a total of $48 washing cars, which gives us the answer 48 as y. So in order to find x, we would need to subtract 68 and 48, which is called using the communtative property. Thsi answer would give us the remaining amount of money we do not yet know.

So 68-48= 20. therefore James made $20 at the art contest.

Answer: About 20.82 liters.

Step-by-step explanation:

         To go from gallons to liters, we will multiply by 3.785. Since we are in half gallons, we will multiply 11 by 0.5 for 5.5 full gallons. Now, we will multiply;

        5.5 gallons * 3.785 = 20.8198 ≈ 20.82 liters

Answer:

Step-by-step explanation:

(-3)(k) = -15

-3k = -15

k = -15/-3

k = 5

(2x+3)(x+5) = 0

2x + 3 = 0

2x = -3

x = -3/2

x+ 5 = 0

x = -5

The​ manager's likely​ error is $20 if a store is instructed by corporate headquarters to put a markup of ​11% on all items. An item costing ​$18 is displayed by the store.  

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

A markup of ​11% on all items. An item costing ​$18 is displayed by the store manager at a selling price of ​$2.

The manager’s likely error was forgetting to add the $2 back to the $18.

$2= 11% of $18 = 1.98(=2)

For a markup,

= $2 + $18

= $20

Thus, the​ manager's likely​ error is $20 if a store is instructed by corporate headquarters to put a markup of ​11% on all items. An item costing ​$18 is displayed by the store.

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Khadija has 8 nickels and 2 quarters

From the question, we have the following parameters that can be used in our computation:

Worth of coins = $0.90

Type of coins = Dimes and quarters

Represent the nickels with n and the quarters with q

So, we have the following representation

n + q = 10

0.05n + 0.25q = 0.9

Make n the subject

n = 10 - q

So, we have

0.05(10 - q) + 0.25q = 0.9

Evaluate the products

0.5 - 0.05q + 0.25q = 0.9

This gives

0.2q = 0.4

Divide both sides by 0.2

q = 2

Recall that

n = 10 - q

So, we have

n = 10 - 2

Evaluate

n = 8

Hence, the number of nickels is 8

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If a boy grows 5 inches, he will be one half a tall as his sister , his sister is 68 inches tall. So the height of the boy is 29 inches

In mathematics, the opposite of multiplication is the process called division. Finding the number of times one quantity is included within another is the procedure. The letters "/" or "" are typically used to denote this. For instance, 8 boys divided by 2 may be expressed as 8/2 or 82. The outcome in this situation would be 4, which is the quantity that 2 may be found in 8 times. The quotient, or outcome of the division, and the remainder, or quantity remaining after dividing, may both be found using division. Calculus, algebra, geometry, and other branches of mathematics all make use of the crucial mathematical notion of division.

How to solve?

If the boy grows 5 inches, he will be 68/2 =34 inches tall

The boy's current height is 34 - 5 = 29 inches

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Time required to spread the rumor so that half of the given heard the rumor is equal to 15 hours (approximately).

As given in the question,

Number of people among whom rumor is spread = 400

Number of people is represented by N(t)

Time is represented by 't' hours

Function representing relation between number of people who heard about the rumor and time

N(t) = 400/ ( 1+ 399 × e^(-0.4t) )

Condition : Half of the given number of people heard the rumor

N(t) = 400/2

      = 200

Substitute the value in the function we get,

200 = 400/ ( 1+ 399 × e^(-0.4t) )

⇒ ( 1+ 399 × e^(-0.4t) ) = 400 ÷ 200

⇒  1 +  399 × e^(-0.4t)  = 2

⇒  399 × e^(-0.4t)  = 2 - 1

⇒ e^(-0.4t)  = 1 ÷ 399

⇒ e^(-0.4t) = 0.002506

⇒ -0.4t = [tex]log _{e}[/tex] (0.002506)

⇒ t= 14.97 hours

⇒ t= 15 hours (round off)

Therefore, time required to spread the rumor among half of the given number of people is equal to 15hours(approximately).

The complete question is:

A rumor spreads among a group of 400 people. The number of people, N(t), who have heard the rumor by the time t in hours since the rumor started to spread can be approximated by a function of the form

N(t) = 400 / (1+399e^(-0.4t))

Approximately how long will it take until half the people have heard the rumor?

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Answer:

(-1, 3), (3, 3), (5, 3), (1, 0)

Step-by-step explanation:

A translation of 4 units to the right means adding 4 to every x-coordinate.

The new coordinates are:

(-1, 3), (3, 3), (5, 3), (1, 0)

Not enough information to answer

Option C is the correct answer.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

A roller-coaster goes over a 12 m tall hill and then approaches a 30 m hill.

The minimum velocity the roller-coaster would need when going over the 12 m hill to make it to the top of the 30 m hill.

To find the minimum velocity we need to know the acceleration of the roller coaster that comes down the 12 m tall hill.

The value of the acceleration is not given.

So,

We can not find the minimum velocity.

Thus,

Not enough information to answer

Option C is the correct answer.

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The values of sin2x, cos2x and tan2x is  [tex]-\frac{3\sqrt{13}}{11}[/tex], 2/11 and  [tex]-\frac{3\sqrt{13}}{2}[/tex] respectively.

What is tan function?

The tan function, one of the primary six trigonometric functions, is typically expressed as tan x. It is the ratio of the angle's opposite and adjacent sides when a right-angled triangle is being considered.

Tangent is a verb that means "to touch" in Latin, from the root tangere. A circle is precisely the point at which a line tan to it intersects. In trigonometry, the tan function, a periodic function, is crucial. Utilizing the unit circle will make understanding the tangent function the simplest possible.

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The required system of equations is x+y = 21 and 7x +14y = 252.

Systems of equations are sets of equations where the solution is the intersecting point(s) between the equations.There are three methods typically used to solve systems of linear equations: graphing, the substitution method, and the elimination method. These methods can be applied to more complex systems of nonlinear equations as well.

Let the number of small boxes be x.

Let the number of large boxes be y.

The volume of each small box is 7 cubic feet.

The volume of each large box is 14 cubic feet.

The total number of boxes is 21.

Total volume of all boxes is 252 cubic feet.

So, x+y = 21.

This is the first equation.

Also, the total volume is equal to the sum of the volumes of all individual boxes.

So,  7x + 14y = 252

Thus, the required system of equations is x+y = 21 and 7x +14y = 252.

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The required system of equations is x + y = 21 and 7x + 14y = 252 using the concept of equations.

A system of equations in algebra is made up of two or more equations that are solved together to obtain the solution for a two or more variable problem.

Volume of each small box is 7 cubic feet and volume of each large box is 14 cubic feet. Take the number of small boxes to be x and number of large boxes to be y.

Given total number of boxes shipped is 21. Therefore using the concept of equation,

x + y = 21  --- (1)

Total volume of small box is given by:

Total volume of small box = (Volume of a small box) * (Number of small box)

Total volume of small box = 7x

Similarly the total volume of large box is,

Total volume of small box = 14y

Given the total volume of carried box is 252 cubic feet. Using the concept of equations,

7x + 14y = 252  ---(2)

The equations (1) and (2) gives the required system of equations.

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The correct order to solve the equation is given below .

In the question ,

it is given that ,

the equation is 3*([tex]2^{2 t - 5}[/tex]) - 4 = 10  ,

Step(1) , adding 4 to each side of the equation ,

3*([tex]2^{2 t - 5}[/tex]) = 14

Step(2) , dividing both sides of the equation by 3 ,

we get ,  ([tex]2^{2 t - 5}[/tex]) = 14/3  .

Step(3) , taking log on each side ,

log([tex]2^{2 t - 5}[/tex]) = log(14/3)

Step(4) , Using the Exponential Property and writing 14/3 in decimal form ,

we get ,

(2t - 5)*log(2) = log(4.67)

Step(5) , Dividing each side by log(2)  ,

we get ,  2t-5 = log(4.67)/log(2) .

Step(6) , Add 5 to each side of equation

we get , 2t = 2.23 + 5  ;

Step(7) , Simplifying we get  ,

we get , t = 3.625  .

Therefore , the the solution of the given equation is t = 3.625   .

The given question is incomplete , the complete question is

Arrange the steps in the correct order to solve the equation,

3*([tex]2^{2 t - 5}[/tex]) - 4 = 10  .

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Based on the given parameters, the value of the money to invest initially is $99341.383

The given parameters about the compound interest are

Amount, A = $181000

Interest Rate, R = 5%

Time, t = 19 years

Number of times, n = 365 i.e. continuously

To calculate the amount, we have:

A = P + CI

Where

C = P(1 + R)^t

So, we have

A = P(1 + R)^t

This can be rewritten as

A = P(1 + R/n)^nt

Substitute the known values in the above equation

181000 = A * (1 + 5%/365)^(12*365)

So, we have

A = 181000 /[(1 + 5%/365)^(12*365)]

Evaluate the expression

A = 99341.383

Hence, the amount of the investment is $99341.383

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Answer:

5

Step-by-step explanation:

The answer to this Question based on Profits is No they cant make 5000$ profit

What is profit?

Profit is simply the extra money we earn on selling good etc things and there are tonnes of different ways of making money and profit

Solution:

Here Diego high school soccer team started a fundraiser selling treats at their games

Initial money spent = 1000$

They decided to make 0.3$ revenue on both candy and soda hence total 0.6$ revenue in one pack

one pack costs for 2$ where 0.6$ is revenue and actual cost is 1.4$

Total packs to sell = 1000/1.4

= 714 packs

hence total profit = 714 * 0.6 = 428$

hence maximum revenue they can make is 428$ and it is maximum

hence they cant make 5000$ profit

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The required quadratic equation is x² - 12x + 36 Or (x - 6)².

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know (a - b) = a² - 2ab + b².

Given, An expression 36 - 12x + __

now, here b² = 36 ⇒ b = 6,

∴ - 2ab = - 2(a)(6).

So, a = 1.

∴ The required quadratic equation is x² - 12x + 36 Or (x - 6)².

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Answer:

Step-by-step explanation:

12

x=12y

2:3

3:14

nope-60/2=30

495/9=55

Answer: 19120 Toaster

Step-by-step explanation: We just need to take $478000 divided by 25, equal to 19120 Toaster!

Answer:

p=12345

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

You want the graphed triangle rotated 90° CW about the point (2, -1).

After rotation 90° CW, points will be as far to the south and west of the center of rotation as they are east and south in the original image. This is shown by the blue triangle in the attachment.

Answer:

25

Step-by-step explanation:

first add the degrees: 50+30+25=105, then 180-105 is 75, 75=3s, s is 25

(im not sure completely im only in 7th grade)

Answer: y= -2/3x + 0

Step-by-step explanation: y=mx+b

The Y-intercept is at (0,0), so b is 0

Slope is -2/3

So the equation is y=-2/3x + 0

Answer:

[tex]y=\frac{1}{2}x+2[/tex]

Step-by-step explanation:

Using the points [tex](0,2)[/tex] and [tex](2,3)[/tex], the gradient is [tex]\frac{3-2}{2-0}=\frac{1}{2}[/tex].

The [tex]y[/tex]-intercept is [tex](0,2)[/tex], so the equation is [tex]y=\frac{1}{2}x+2[/tex].