A cube has side length a. The side lengths are decreased to 50% of their original size. Write an expression in simplest form for the volume of the new cube in terms of a. An expression is .

(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].

(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].

So, the combined areas of the four semicircles is [tex]241\pi[/tex].

The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].

the probability that in bot rolls we have a sum of, at most, 8, is:

P = 47/ 1,296 = 0.036

The pair is tossed twice. A pair of dice has 36 possible outcomes, so if we toss twice the pair, the total number of outcomes is:

36*36 = 1,296

Now if we define the outcomes as:

{dice 1 (roll1), dice2(roll1), dice 1 (roll2), dice2(roll2) }

The outcomes that give at most a sum of 8 are:

{1, 1, 1, 1}

{2, 1, 1, 1} ( 3 permutations)

{2, 2, 1, 1} ( 6 permutations).

{2, 2, 2, 1} ( 3 permutations)

{3, 1, 1, 1} ( 3 permutations)

{3, 2, 1, 1} ( 12 permutations)

{3, 3, 1, 1} (6 permutations)

{4, 1, 1, 1} (3 permutations)

{4, 2, 1, 1} (6 permutations)

{5, 1, 1 , 1} (3 permutations)

{2, 2, 2, 2}

These are all the outcomes that give a sum of, at most, 8.

If we add all the outcomes we get 47 outcomes.

Then the probability that in bot rolls we have a sum of, at most, 8, is:

P = 47/ 1,296 = 0.036

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Among all the given equations 6(x+3)+x=7x+9+9 is having many solutions.

Given Equations :

6(x+3)+x=7x+2+1

6(x+3)+3=7x+5

6(x+3)+x=6x+3+15

6(x+3)+x=7x+9+9

We have to find the equation having many solutions.

The equation whose both sides are equal to each other is supposed to have many solutions. For determining all equations needs to be solved.

Equation 1

6(x+3)+x=7x+2+1

6x+18=7x+3

No the above equation is not having many solutions.

Equation 2

6(x+3)+3=7x+5

6x+18+3=7x+5

6x+21=7x+5

No the above equation is not having many solutions.

Equation 3

6(x+3)+x=6x+3+15

6x+18+x=6x+18

7x+18=6x+18

No the above equation is not having many solutions.

Equation 4

6(x+3)+x=7x+9+9

6x+18+x=7x+18

7x+18=7x+18

Yes the above equation is having many solutions.

Hence the equation which is having many solutions is 6(x+3)+x=7x+9+9.

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The options given in the question are wrong and the correct options are as under:

1) 6(x+3)+x=7x+2+1

2)6(x+3)+x=7x+5

3)6(x+3)+x=6x+3+15

4) 6(x+3)+x=7x+9+9

Answer:

The last one [tex](x=11.3, y=8)[/tex].

Step-by-step explanation:

1) There are three trigonometric ratios for right-angled triangles.

[tex]sin()=\frac{opposite}{hypotenuse}\\cos()=\frac{adjacent}{hypotenuse}\\tan()=\frac{opposite}{adjacent}[/tex]

In a right triangle, the hypotenuse, h, is the side opposite the right angle. Relative to the acute angle θ, check the attachment, the legs are called the opposite side, o, and the adjacent side a.

2) In this case, we are given a length and an angle to find x and y.

Let's find x first. To find x we need to use [tex]sin()=\frac{opposite}{hypotenuse}[/tex].

[tex]sin(45)=\frac{8}{x}\\sin(45)x=8\\x=\frac{8}{sin(45)} \\x=11.31[/tex]

Find y.

Notice that, we can use the Pythagorean Theorem [tex](c^2=a^2+b^2)[/tex] to find y.

[tex]c^2=a^2+b^2[/tex]

[tex]11.31^2=8^2+b^2\\11.31^2 - 8^2 = b^2\\63.9161 = b^2\\\sqrt{63.9161} = b\\b = 7.99[/tex]

3) Round them off to the nearest tenth.

[tex]x=11.31\\x=11.3[/tex]

[tex]y=7.99\\y=8[/tex]

Therefore, the correct choice is the last one [tex](x=11.3, y=8)[/tex].

Hence, the inverse of the given function is [tex]{(\frac{x}{10})}^5 - 2[/tex]

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function has three parts, a set of inputs, a set of outputs, and a rule that relates the elements of the set of inputs to the elements of the set of outputs in such a way that each input is assigned exactly one output.

given function,

                 q(x) = 10[tex]\sqrt[5]{x-2}[/tex]

say y=q(x)

now we have,

                y = 10[tex]\sqrt[5]{x-2}[/tex]

                [tex]\frac{y}{10}[/tex] = [tex]\sqrt[5]{x-2}[/tex]

raising to 5th power on both sides,

               [tex](\frac{y}{10})^5[/tex] = x - 2

               x =  [tex](\frac{y}{10})^5[/tex] + 2

               [tex]q^{-1}(x) =[/tex] [tex]{(\frac{x}{10})}^5 - 2[/tex]

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Answer:

y=-0.012x(x-200).

Step-by-step explanation:

1) the given parabola has two zeros: 0 and 200. It means, the required equation is: y=ax(x-200), where a - unknown number;

2) according to the given graph the vertex is (100; 120). It is possible to substitute the coordinates of it into the equation y=ax(x-200) and calculate the value of 'a':

120=a*100(100-200); ⇒ a=-0.012.

3) finally, the required equation is:

[tex]y=-0.012x(x-200).[/tex]

If Erica earned a total of $15450 last year from both the jobs then he earns $2840 from college if she earned 1250 more than four times the amount from college from store.

Given Total amount earned=$15450,Amount earned from store is 1250 more than 4 times earned from college.

Amount from store forms an equation.

let the amount earned from college is x.

According to question:

Amount earned from store=4x+1250

Amount earned from college=x

Total amount earned=4x+1250+x

5x+1250=15450

5x=15450-1250

5x=14200

x=14200/5

x=2840

Put the value of x in 4x+1250 to get amount earned from store=4(2840)+1250=$12610.

Hence the amount earned by Erica from college is $2840.

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The correct option based on the paralel line given is that the corresponding angles are congruent.

Given that a student was told to consider the diagram and asked to prove that angle 1 ≅ angle 2.

We are to find the reason for the second step in the following proof. Since lines A and B are parallel and cut by a transversal, so angles 1 and 3 are corresponding angles. That is, ∠1. ≅ ∠3

Also, angles 2 and 3 are vertically opposite angles, so ∠2 ≅ ∠3.

And, therefore we get ∠1 ≅ ∠2.

Thus, the reason in the second step will be angles 1 and 3 are corresponding angles and corresponding angles are congruent.

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Answer:

             x     +             6      ≥        15

Step-by-step explanation:

Add any number greater than equal to 9 to the number 6 and you get a result of at least 12. Any number less than 9 produces a result that is not at least 15.

Just saying the question was not that descriptive so I don't know if this is what you asked for... Sorry!

Answer:

A. (2,3)

It is rather simple the 9 points between a and B 2/3 of that is 6

Answer:

200

Step-by-step explanation:

it was found that the ratio of people who liked Arithmetic and Algebra is 9 : 8. If 25% liked the both, 80 liked none of these and 20% liked arithmetic only, find the total number of people participated in the survey. Ans: 200

Option 1 is correct. The point T is the number of books and their cost where the subscription with the annual fee costs less.

At y1 = 96

y2 = 30

The service  charge is said to be 3 dollar

We have that y1 is less than y2. This is because 30 is less than 92.

From this we have to conclude that it is the first option. This is because 3 dollars would be charged or less than that.

Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed  dollar annual fee and the other which charges  dollars per book he borrows. Here's a graph that shows a system of equations for this scenario where  is the number of books Aaden borrows and y is the total cost of the subscription. ks) What does point T represent in this ? Choose 1 answer:

A number of books and their cost where the subscription with the annual fee costs less

A number of books and their cost where the subscription that charges per book costs less  of

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The expression which equals 24 is (4 + 2) (3) . Option B

Given the following expression

Let's evaluate each of them. we have

(2 + 4)(3) = 6× 3 = 18

(4 x 2)(3) = 8 × 3 = 24

(4 - 2) + 3 (4 + 3) - 2 = 2 + 3(7) -2 = 2 + 21 - 2 = 23 -2 = 21

Thus, the expression which equals 24 is (4 + 2) (3) . Option B

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The thing that's wrong with the equation is that 2 shouldn't be multiplied by 4 but should have been added.

From the information given, it can be seen that the equation is:

(3x²)(-2x⁴) = 3(-2)x² × x⁴ = 6x^8

Based on the information above, this calculation is incorrect. The correct calculation will be:

(3x²)(-2x⁴) = 3(-2)x² × x⁴

= -6x^6

Therefore, the multiplication should be an addition of the power.

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The system of inequalities that represent the graph is

y ≤ -x +4

y < 3x-1

The correct option is the third option

From the question, we are to determine the system of inequalities that represents the graph

The equation of the solid line is  y = -x +4

Since the lower part of the graph was shaded

Then,

The inequality that represents the solid line is

y ≤ -x +4

The equation of the dotted line is  y = 3x -1

Since the lower part of the graph was shaded,

Then,

The inequality that represents the solid line is

y < 3x-1

Hence, the system of inequalities that represent the graph is

y ≤ -x +4

y < 3x-1

The correct option is the third option

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The most frequent number of over-the-limit items for this dataset is 3.5 - 4.5 and the frequency of the most frequent number of over-the-limit items is 14

The most frequent number of over-the-limit items for this data set is the dataset that has the highest frequency.

This is represented by the class that has the highest bar on the histogram

To do this, we simply check the class that has the highest bar on the histogram.

From the attached histogram the class that has the highest bar on the histogram is 3.5 - 4.5

Hence, the most frequent number of over-the-limit items for this dataset is 3.5 - 4.5

In (a), we have:

The most frequent number of over-the-limit items for this dataset is 3.5 - 4.5

Next, we check the frequency of the most frequent number of over-the-limit items for this dataset

According to the histogram, the most frequent number of over-the-limit items for this dataset has a frequency of 14

Hence, the frequency of the most frequent number of over-the-limit items is 14

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Answer:

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space.

By evaluating in x = π/3, we conclude that the correct option is C.

By looking at the graph, we can see that the function becomes zero when:

x = π/3

Now, this is really trivial.

Just evaluate the four options in x = π/3, and see which ones become equal to zero, and discard the others.

By doing that, you will see that the only option that becomes zero when evaluated in x = π/3 is option C.

[tex]y = 3*sin(2(x - \frac{\pi}{3} ))[/tex]

Then we conclude that it is the only option that can be the correct one.

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Answer:

.

Step-by-step explanation:

A parallelogram has two pairs of parallel lines so if AD // BC and that AD//BC, Then it is indeed a parallelogram

Answer:

Hope it helps!!

Answer:

[tex]a < 0[/tex]   False

[tex]|a| > 0[/tex] True

[tex]|a|=0[/tex]  False

________________________________________________

a is on the right side of 0,

which means a is positive.

The absolute value is the distance to zero (always positive)

Which means the absolute value of a is also positive.

[tex]a < 0[/tex]   is wrong because a is positive

[tex]|a| > 0[/tex]  is correct because a is larger than 0

[tex]|a|=0[/tex]  is wrong because [tex]a[/tex] ≠ [tex]0[/tex]

________________________________________________

Hope this helps :)

Using proportions, the value of x is given as follows: x = 16

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

We are given this following proportion:

[tex]\frac{n}{4} = \frac{k}{x}[/tex]

In this problem, we have that n = 15 and k = 60, hence:

[tex]\frac{15}{4} = \frac{60}{x}[/tex]

Applying cross multiplication:

15x = 60 x 4

Simplifying by 15:

x = 4 x 4

x = 16.

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Answer:

B i think

Step-by-step explanation:

Total cards left

Total hearts left

Probability

Option B

Answer:

[tex]\sf F. \quad \dfrac{1}{4}[/tex]

Step-by-step explanation:

A deck of 52 playing cards contains 13 hearts.

If Sara has 12 cards from this deck in her hand and 3 of them are hearts, then:

Total cards remaining in the deck

= total deck - cards Sara has

= 52 - 12

= 40

Total hearts left in the remaining deck

= total heart cards - heart cards Sara has

= 13 - 3

= 10

So there are 40 cards in the deck and 10 of them are hearts.

Probability Formula[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Therefore, the probability that a card drawn at random from the remainder of the deck will be a heart is:

[tex]\begin{aligned}\implies \sf P(heart) & =\dfrac{\textsf{number of hearts in remaining deck}}{\textsf{total cards in remaining deck}}\\\\ & =\dfrac{10}{40}\\ \\& =\dfrac{1}{4}\end{aligned}[/tex]

The product (a^2x^3 -5x+3a).(-2a^3x) is -2a^5x^4 + 10a^3x^2 - 6a^4x

The expression is given as:

(a^2x^3 -5x+3a).(-2a^3x)

Open the bracket

-2a^3x * a^2x^3 -2a^3x * - 5x -2a^3x * 3a

Evaluate the products

-2a^5x^4 + 10a^3x^2 - 6a^4x

Hence, the product (a^2x^3 -5x+3a).(-2a^3x) is -2a^5x^4 + 10a^3x^2 - 6a^4x

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There are two interpretations we could go for:

Check out the diagram below.

Point A on the red line y = x has two locations it could end up. If we follow method 1, then point A shifts upward to point B. Do this to every point on the red line and the entire red line shifts up 4 units.

Or if you decide to shift 4 units to the left (method 2), then point A moves to point C's location. Doing this to every point on the red line shifts the entire line 4 units to the left.

The equation for the given coordinates (3,0) and (4,4) is 4x-y+3=0.

The given coordinates are (3,0) and (4,4).

The formula to find the slope of an equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].

Now, slope[tex]=\frac{4-0}{4-3} =4[/tex].

The equation of the line is [tex](y-y_{1} )=m(x-x_{1} )[/tex]

⇒(y-3)=4(x-0)

⇒y-3=4x

⇒4x-y+3=0

Therefore, the equation for the given coordinates (3,0) and (4,4) is 4x-y+3=0.

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Answer:

B ∩ (A ∪ C)'

Step-by-step explanation:

It's the B part excluding A and C union. Hence,

(A ∪ C)' ∩ B

Final answer:

The difference of the elevations is 30347 feet.

Step-by-step explanation:

Step 1

The highest elevation is 29028 feet.

Step 2

The lowest elevation is -1319 because it is below the sea level.

Step 3

The difference of the elevations is:

29028 - (-1319)

Step 4

Evaluate the value of expression:

29028 - (-1319) = 30347

Answer:

A. Coffee 4C below the freezing point

Step-by-step explanation:

Negative temperature when talking about water means below the freezing point (below 0). Look up number line. Negative 4 is below 0 whereas positive 4 is above 0. Thus, option A is the best answer

Answer:

A

Step-by-step explanation:

This is because negative number start below zero and since water freezes at zero degrees celsius, Mia's iced coffee is below the freezing point.

The company will continue to manufacture this model for 19 months.

The question is ill-formatted. The understandable format is given below.

An SUV model's monthly sales are anticipated to rise at a rate of

[tex]S'(t)=-24^{1/3}[/tex] SUVs each month, where "t" denotes the number of months and "S(t)" denotes the monthly sales of SUVs. When monthly sales of 300 SUVs are reached, the business intends to discontinue producing this model.

Find S if monthly sales of SUVs are 1,200 at time t=0 (t). How long will the business keep making this model?

Given [tex]S'(t)=-24^{1/3}[/tex] ... ... (1)

Condition (1) at t=0; s(t) =1200

We find S(t)=300 then t=?

a) We find S(t)

from [tex]S'(t)=-24^{1/3}[/tex]

[tex]\implies \frac{dS(t)}{dt}=-24t^{1/3} ~~[\because X'(t)=\frac{dX}{dt} \\\implies dS(t) = -24t^{1/3}dt\\[/tex]

On Integrating both sides

[tex]S(t)=-18t^{4/3}+c ~...~...~(2)[/tex]

Now, at t=0 then S(t)=1200

So, from (2)

1200=0+c

⇒c=1200

[tex]\therefore[/tex]from eq (2)

[tex]S(t)=-18t^{4/3}+1200 ~...~...~(3)[/tex]

b) Considering that the firm intends to cease production of this model once monthly sales exceed 300 SUVs.

So, take S(t)=300

from eq (2) [tex]300=-18t^{4/3}+1200[/tex]

[tex]t^{4/3}=\frac{1200-300}{18}\\=\frac{900}{18}=50\\\implies t=50^{3/4}\\\implies t=18.8030[/tex]

Hence the company will continue 18.8020 months.

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