Timothy built a base for a circular tabletop. The base can support a tabletop with a radius of at least 6 inches, but not more than 23 inches. What is the smallest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch. What is the largest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch.

Answer:

Q1 B

Q2 23.7yd

Step-by-step explanation:

Solution of Q2 is in the picture

Answer:

a) [tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]

Therefore letter B is the correct answer.

b) TP = 23.7 yards  

Step-by-step explanation:

a) We can rewrite [tex](b-x)^{2}[/tex] as (b-x)(b-x), so we have a product of two binomials. We can use the FOIL method to multiply it:

[tex](b-x)(b-x)=b^{2}-bx-bx+x^{2}=b^{2}-2bx+x^{2}[/tex]

so the the Law of Cosines equation will be write as:

[tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]

Therefore letter B is the correct answer.

b) Here we can use the Law of sines.

∠A angle between TD and TP = 65°

∠B angle between TD and DP = 77°

∠C angle between TP and DP = 180° - 77° - 65° = 38°

The equation is:

[tex]\frac{TP}{sin(B)}=\frac{TD}{sin(C)}[/tex]

[tex]\frac{TP}{sin(77)}=\frac{15}{sin(38)}[/tex]    

Solving it for TP, we have:

[tex]TP=sin(77)\frac{15}{sin(38)}=23.7 yards[/tex]  

I hope it helps you!  

Answer:

The answer would be c.

Step-by-step explanation:

What I'm understanding from this question is,

In the first attachment, Which has the questions selected on Shows there are two shapes.

Those two shapes have to go in to the identify the tessellation Created using the given regular polygons.

As you can see in answer C. Both shapes are represented in that tessellation.

For example, In the attachment below ] I will be showing you an example of what the question might look like for This certain tessellation.

You obviously know that square is tiltedMake a diamond shaped. That is why the diamond and hexagon is correct!

hope this helps! if it helps in any way plz mark as branliest !

[tex]\frac{1}{2}[/tex] > [tex]\frac{2}{5}[/tex]

The wider/open part of the symbol (aka the mouth) faces the larger number, which in this case is [tex]\frac{1}{2}[/tex].

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

a) 16 in²

b) 20 cm²

Step-by-step explanation:

In any prism, a cross section parallel to parallel faces will have the same shape and area as either of those faces. (That is why we say a prism has a uniform cross section.)

a) The face(s) parallel to the cut plane are squares 4 in on a side, so that is the shape of the cross section. Its area is (4 in)² = 16 in².

__

b) The face(s) parallel to the cut plane are rectangles 4 cm by 5 cm. That is the shape of the cross section. Its area is (4 cm)(5 cm) = 20 cm².

Answer:

532.5 or 532[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

3/4 x 710

= 3 x 710 ÷ 4

=  532.5 or 532[tex]\frac{1}{2}[/tex]

Final answer:

To find 3/4 times 710, multiply 710 by 3 to get 2130, then divide that result by 4 to get 532.5. Therefore, 3/4 times 710 equals 532.5.

Explanation:

The question asks for the result of multiplying 3/4 with 710. To perform this calculation we simply take the number 710 and multiply it by the fraction 3/4. Multiplying a whole number by a fraction involves multiplying the numerator of the fraction by the whole number and then dividing the result by the denominator of the fraction.

Here's a step-by-step breakdown:

Therefore, 3/4 times 710 is 532.5.

Answer:

(w - 2.5)(w + 2.5)

(-4v - 9)(-4v + 9)

Step-by-step explanation:

* Lets explain what is the a difference of two squares

- If we multiply two binomial and the answer just two terms with

 negative sign between them and the two terms are square numbers

 we called this answer a difference of two squares

- Examples

# (a + b)(a - b)

- Lets multiply them

∵ (a × a) + (a × -b) + (b × a) + (b × -b)

∴ a² - ab + ba - b²

- Add the like term

∵ ab = ba

∴ -ab + ba = 0

∴ (a + b)(a - b) = a² - b² ⇒ difference of two squares

- From above the difference of two squares appears when we

 multiply sum and difference of the same two terms

# (a + b) ⇒ is the sum of a and b

# (a - b) ⇒ is the difference of a and b

* Now lets solve the problem

- In (5z + 3)(-5z - 3)

∵ (5z + 3) ⇒ is the sum of 5z and 3

∵ (-5z - 3) ⇒ is the difference of -5z and 3

∵ 5z ≠ - 5z

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

- In (w - 2.5)(w + 2.5)

∵ (w - 2.5) is the difference between w and 2.5

∴ (w + 2.5) is the sum of w and 2.5

∴ They are the sum and difference of the same two terms

∴ The product result in a difference of squares

- In (8g + 1)(8g + 1)

∵ The two brackets are the sum of 8g and 1

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

- In (-4v - 9)(-4v + 9)

∵ (-4v - 9) is the difference between -4v and 9

∵ (-4v + 9) is the sum of -4v and 9

∴ They are the sum and difference of the same two terms

∴ The product result in a difference of squares

- In (6y + 7)(7y - 6)

∵ (6y + 7) is the sum of 6y and 7

∵ (7y - 6) is the difference between 7y and 6

∵ 6y ≠ 7y and 7 ≠ 6

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

- In (p - 5)(p - 5)

∵ The two brackets are the difference of p and 5

∴ They are not the sum and difference of the same two terms

∴ The product result not in a difference of squares

Answer:

option 2 and 4

Step-by-step explanation:

Answer:

1172.08 square inches

Step-by-step explanation:

Total surface area is area of all the surfaces.

Cylinder:

Top surface = πr^2 = π(4)^2 = 16(3.14) = 50.24

Lateral Surface = 2πrh = 2π(4)(9) = 72π = 72(3.14) = 226.08

Rectangular Prism:

2 sides = 2*(11*11) = 242

front and back = 2*(16*11) = 352

bottom = 16 * 11 = 176

Top part (it is top rectangle - bottom of cylinder) = (16*11) - (π(4)^2) = 125.76

Adding all up, we get:

50.24 + 226.08 + 242 + 352 + 176 + 125.76 = 1172.08 square inches

Answer:

D. 9

Step-by-step explanation:

The Pythagorean triple for a 30-60-90 right triangle is (x, x√3, 2x).  The side across from the 30° angle is x, the side across from the 60° angle is x√3, and the side across from the right angle is 2x (which is also the hypotenuse).  If the side across from the 60° angle is given as 9√3, we can set that equal to the identity for that leg:

9√3 = x√3 and solve for x.  Divide both sides by the √3 to get that x = 9

Answer:

The correct answer is option D. 9

Step-by-step explanation:

Points to remember

It a right triangle with angles 30°, 60 and 90° the n the sides are in the ratio,

Shorter leg : longer leg : hypotenuse = 1 : √3 : 2

To find the length of shorter leg

Here it is given that, longer length = 9√3

We have,

Shorter leg : longer leg : hypotenuse = 1 : √3 : 2 =  Shorter leg : 9√3: hypotenuse

Therefore shorter leg = 9√3/√3 = 9

Parameterize [tex]C[/tex]

[tex]x=\cos t[/tex]

[tex]y=\sin t[/tex]

with [tex]0\le t\le2\pi[/tex]. Then the line integral of [tex]\langle2x^3-y^3,4x^3+y^3\rangle[/tex] along [tex]C[/tex] is

[tex]\displaystyle\int_0^{2\pi}\langle2\cos^3t-\sin^3t,4\cos^3t+\sin^3t\rangle\cdot\langle-\sin t,\cos t\rangle\,\mathrm dt[/tex]

[tex]\displaystyle=\int_0^{2\pi}(4\cos^4t-2\cos^3t\sin t+\cos t\sin t^3+\sin^4t)\,\mathrm dt=\boxed{\frac{15\pi}4}[/tex]

By Green's theorem, the line integral is equivalent to

[tex]\displaystyle\iint_{x^2+y^2\le1}\left(\frac{\partial(4x^3+y^3)}{\partial x}-\frac{\partial(2x^3-y^3)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]

[tex]=\displaystyle\iint_{x^2+y^2\le1}(12x^2+3y^2)\,\mathrm dx\,\mathrm dy[/tex]

[tex]=\displaystyle\int_0^{2\pi}\int_0^1(12r^2\cos^2\theta+3r^2\sin^2\theta)r\,\mathrm dr\,\mathrm d\theta[/tex]

[tex]=\displaystyle\int_0^{2\pi}\int_0^1(9r^3\cos^2\theta+3r^3)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{15\pi}4}[/tex]

To evaluate the line integral along the unit circle, we can parametrize the circle using x = cos(t) and y = sin(t). The resulting integral is 6 times the integral of cos squared(t) times cos(t).

To evaluate the line integral, we need to parametrize the unit circle. Let's use x = cos(t) and y = sin(t) as the parameterization. The differential arc length is given by ds = √(dx² + dy²) = dt. Substituting these into the line integral, we get:

∫(2cos³(t) - sin³(t)) dt + ∫(4cos³(t) + sin³(t)) dt = ∫(6cos³(t)) dt

Since the unit circle can be parameterized from 0 to 2π, the integral becomes:

∫[6cos³(t)] dt = 6 ∫[(cos(t))³] dt = 6 ∫[cos³(t)] dt = 6[∫(cos²(t)cos(t)) dt]

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Answer:

  y = 700 +22x

Step-by-step explanation:

The CD account balance is 722 after the first year and increases by $22 each year. The function rule is a linear function with a y-intercept of 700 and a slope of $22 per year.

  y = 700 +22x . . . . . . ending balance after x years

Answer:

  B. (6√2 + 12) inches

Step-by-step explanation:

The length of the kite edge at upper left is ...

  x/sin(45°) = x/(1/√2) = x√2

The length of the kite edge at upper right is ...

  x/sin(30°) = x/(1/2) = 2x

The perimeter of the kite is double the sum of the lengths of these edges:

  P = 2(x√2 +2x) = 2x(√2 +2)

For x=3 in, this is ...

  P = 2·(3 in)(√2 +2)

  P = (6√2 +12) in

_____

The sine of an angle is the ratio of the side opposite to the hypotenuse. Here, the side opposite is x, and the hypotenuse is the kite edge of interest.

  x/hypotenuse = sin(angle)

  hypotenuse = x/sin(angle) . . . . . solve for hypotenuse

Answer:

B

Step-by-step explanation:

I was told to put down A B C or D

And B was right

Answer:

Step-by-step explanation:

h(10) would be the height of the balloon at 10 seconds

Answer:

C

Step-by-step explanation:

at least two have to be in the same place (i think), and that’s the only one that does that

Answer:

  55/56 ≈ 0.982143

Step-by-step explanation:

  nPk = n!/(n-k)!

Your expression is ...

  1 - (6·5·4·3)/(8·7·6·5·4·3) = 1 - 1/(8·7) = 1 - 1/56 = 55/56 ≈ 0.982143

Question 10

cos 45 = x/10

cos 45(10) = x

(1/sqrt{2})*10 = x

10/sqrt{2} = x

Rationalize the denominator.

[10/sqrt{2}] • [sqrt{2}/sqrt{2}] = x

10•sqrt{2} ÷ 2 = x

5• sqrt{2} = x

Final answer:

To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other. The endpoints of the other diagonal are (-7, 7) and (-1, 3). Therefore, Option A is the correct answer.

Explanation:

To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other, meaning they intersect at their midpoints. We can find the midpoint by taking the average of the x-coordinates and the average of the y-coordinates of the given endpoints of the first diagonal.

For the given endpoints (-10, 1) and (2, 9), the midpoint would be ((-10 + 2)/2, (1 + 9)/2), which simplifies to (-4, 5).

Since the diagonals bisect each other, the other diagonal would have the same midpoint. Therefore, the endpoints of the other diagonal would be (-4, 5) and the reflection of (-4, 5) across the midpoint of the given diagonal, which is the midpoint of (-10, 1) and (2, 9). Thus, the correct answer is (-4, 5) and its reflection across (-4, 5), which is (-7, 7) and (-1, 3).

Step-by-step explanation:

In his last 30 throws, Tom hit the target 20 times and missed 10 times.

p = probability he misses the target = ⅓

q = probability he hits the target = ⅔

Using binomial probability:

P = nCr (p)^r (q)^(n-r)

Given n = 3, r = 1, p = ⅓, and q = ⅔:

P = ₃C₁ (⅓)¹ (⅔)³⁻¹

P = (3) (⅓) (⅔)²

P = 4/9

There is a 4/9 probability that he misses exactly 1 of his next 3 throws.

By applying binomial probability, the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target is 4/9.

In order to determine the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target, we would apply binomial probability equation:

[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]

Based on the information given, we can deduce the following points:

Substituting the given parameters into the equation, we have;

P = ³C₁ × (⅓)¹ × (⅔)³⁻¹

P = 3 × (⅓)¹ × (⅔)²

P = 3 × ⅓ × (⅔)²

P = 1 × 4/9

P = 4/9.

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Answer:

  1.1×10^8

Step-by-step explanation:

2% of 5.5 billion is ...

  2×10^-2 × 5.5×10^9 = 11×10^7 = 1.1×10^8

About 1.1×10^8 grains of brown sand are in the bucket.

Answer:

Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].

Step-by-step explanation:

Total number sand grains in the bucket =[tex] 5.5\times 10^9 grain[/tex]

Concentration of brown sand grains = 2.0%

Number of brown brain in the bucket be x

[tex]\%=\frac{\text{Brown sand grains}}{\text{Total sand grains}}\times 100[/tex]

[tex]2.0\%=\frac{x}{5.5\times 10^9 grain}\times 100[/tex]

[tex]x=1.1\times 10^8 grains[/tex]

Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].

Answer:

  B.  12n + 2(25) ≤ 100

Step-by-step explanation:

The inequality you are asked for is intended to express ...

  shirt cost + pant cost (is less than or equal to) Sandy's budget

The cost of n shirts at $12 each will be 12n. The cost of 2 pants at $25 each is 2(25). Then the inequality is ...

  12n + 2(25) ≤ 100 . . . . . matches choice B

Answer with explanation:

Temperature in the living room =68°F

The equation which satisfies ,the  room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies

 t=2 Cos (0.21 m) +68----------(1)

⇒To determine the period of the function

Z= A cos (sx+q)+r

As period of cos x is 2 π.

So,the given function has period

        [tex]=\frac{2\pi}{s}[/tex]            

So, the period of function 1, is given by

        [tex]=\frac{2\pi}{0.21}[/tex]  

⇒The meaning of period of the function is that after every period of   [tex]=\frac{2\pi}{0.21}[/tex] the temperature of the room increases or decreases by an integer equal to 2.

⇒Cosine function has maximum value of 1 , and Minimum value of -1.

-1 ≤ Cos x ≤ 1

So, the Maximum value of function = 2 ×1+68°=70°----Maximum Temperature

And, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature

Final answer:

The period of the cosine function used to model the room temperature controlled by a thermostat is about 29.9155 minutes. This is the time it takes for the temperature to complete one full cycle of oscillation between the maximum of 70°F and the minimum of 66°F.

Explanation:

Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. This function describes a cosine wave, typical for oscillator systems like a thermostat regulating room temperature. To determine the period of the function, we examine the cosine part of the equation.

The general form of a cosine function is y = A cos(Bx + C) + D, where the period is 2π/B. Here, A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift. In Felicity's thermostat function, B = 0.21. The period of the function is therefore 2π/0.21, which is approximately 29.9155 minutes. This period represents the time it takes for the room temperature to go from a maximum value back to that value again after one complete cycle.

The max temperature is 2 + 68 = 70°F, and the min temperature is -2 + 68 = 66°F. These represent the highest and lowest temperatures the room will reach with the current thermostat settings.

For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder.

quotient: [tex]4x + 15[/tex]

Divisor: x-3

Dividend: [tex]4x ^ 2 + 3x + 2[/tex]

Remainder: 47

It must be fulfilled that:

Dividend = Quotient * Divisor + Remainder

Answer:

See attached image

The perimeter of the new garden after extension is 44 feet.

To find the perimeter of the new garden, we need to determine the dimensions after the extension. The original garden measures 3 feet by 15 feet, and the gardener decides to extend it by 1 foot in each direction. This means the new dimensions are 5 feet by 17 feet.

To find the perimeter, we add up all the sides of the rectangle. The formula for the perimeter of a rectangle is:

P = 2(l + w)

where P represents the perimeter, l represents the length of the rectangle, and w represents the width of the rectangle. Plugging in the values, we have:

P = 2(5 + 17) = 2(22) = 44 feet

Therefore, the perimeter of the new garden is 44 feet.

Answer:

+/- 1.9983

Step-by-step explanation:

The critical values for a confidence interval for the population mean, with population standard deviation not known, are obtained from the student's t distribution.

The sample size is given as 64. The degrees of freedom will thus be;

sample size - 1 = 64 - 1 = 63

The confidence level is given as 95%. The level of significance will thus be;

100 - 95 = 5%.

The area in the right-tail will thus be 2.5%. Therefore, we looking for a t-value such that the area to its right is 2.5% and the degrees of freedom being 63. From the t-tables we have;

+/- 1.9983

Answer:

[tex]f^{-1}(x)=25(x-2)^2[/tex]

Step-by-step explanation:

The inverse function can be found by solving ...

  f(y) = x

  (√y)/5 +2 = x

  (√y)/5 = x -2 . . . . . subtract 2

  √y = 5(x -2) . . . . . . multiply by 5

  y = 25(x -2)² . . . . . square both sides

The inverse function is ...

  [tex]f^{-1}(x)=25(x-2)^2[/tex]

_____

About the graph

The inverse of a function is its mirror image across the line y = x.

Answer:

[tex]5x=100[/tex]

[tex]x=20\ books[/tex]

Step-by-step explanation:

I'm going to assume that all books cost the same.

Let

x ------> the number of books he originally wanted to buy

we know that

[tex](x+4)(5)=100+4(5)[/tex]

[tex]5x+20=100+20[/tex]

[tex]5x=100[/tex] -----> equation that can be used to find the number of books he originally wanted to buy

solve for x

[tex]x=100/5[/tex]

[tex]x=20\ books[/tex]

Nick has 21 pencils and Lance has 63 pencils.

Tony spent a total of $100 on books. Since he bought 4 more books than he originally planned, and each book cost $5, let's denote the original number of books he planned to buy as x. Therefore, the total number of books he ended up buying would be x + 4. Given that the cost of each book is $5, we can establish the equation 5(x + 4) = 100 to represent the total expenditure on books.

To find the number of books he originally wanted to buy, we will solve for x in the equation above:

Multiply 5 by the quantity x + 4 to obtain the left side of the equation.

Set that result equal to 100, as this is the total amount spent.

Solve the equation for x by first distributing the 5, which gives us 5x + 20 = 100, and then subtracting 20 from both sides of the equation to get 5x = 80.

Finally, divide both sides by 5 to find the value of x, which results in x = 16.

Therefore, Tony originally planned to buy 16 books.

Answer:  D. 15

Step-by-step explanation:

Given : The revenue each season from tickets at the theme part is represented by [tex]t(x) = 5x[/tex] .

The cost to pay the employees each season is represented by [tex]r(x) = (1.5)x[/tex].

From the given graph , we can see that at 4th season, the profit = 15

Hence, the estimated profit after four seasons. =15

The correct option is d. 15, is the estimated profit after four seasons, rounded to the nearest integer.

Given : The revenue each season from tickets at the theme part is represented by t(x) = 5x .

The cost to pay the employees each season is represented by r(x) = (1.5)x.

From the given graph , we can see that at 4th season, the profit = 15

Hence, the estimated profit after four seasons. =15

Hey there! Thanks for asking your question here on Brainly.

First, we can factor a 5 out of each term in the trinomial. This leaves us with: 5(12x^2 - 31x + 20)

Second, we need to multiply 12 * 20 and find a factor pair of the product, 240, which equals -31. This factor pair would be -15 and -16. This now leaves us with: 5((12x^2 - 16)(-15x + 20))

Third, we need to simplify each binomial in parenthesis. By doing so, what is left inside of each parenthesis should be the same if this step is done correctly. This leaves us with: 5(4x(3x - 4)-5(3x - 4))

Fourth and finally, we construct our new factored trinomial! The outside number stays, as well as one of the inner parenthesis binomials. Use the terms you factored out of the parenthesis in step three to construct another

binomial. This leaves us with: 5(4x - 5)(3x - 4) and the correct answer is C.

Hope this helps! If there's anything else I can help you with, please let me know! :)

Answer:  The correct option is

(D) q → ~p.

Step-by-step explanation:  We are given to select the statement that is logically equivalent to the conditional statement   p → ~q.

We know that

two conditional statements are said to be logically equivalent if the truth tables of both the statements are same.

That is, they have same truth values under similar conditions.

The truth table is given by

p          q        ~p          ~q         p → ~q      p → q        ~p → q     q → p        q → ~p

T          T          F            F           F               T                  T            T             F

T          F          F            T            T               F                  T            T              T

F          T          T            F            T              T                  T            F             T

F          F          T            T            T               T                  F            T             T

So, the truth values of p → ~q is same as the truth values of q → ~p. They must be logically equivalent.

Thus, option (D) is CORRECT.

Answer:

D). q → ~p

Step-by-step explanation:

I just did the assignment on Edge... It's 100% correct...  Hope this helps!!

Also heart and rate if you found this answer helpful...  Have a nice day!!  :)

Answer:

  A. f(0.6)=0

  C. f(5.1)=5

  D. This is the graph of the greatest integer function.

Step-by-step explanation:

The graph maps each x-value to the largest integer less than or equal to that value. That is the definition of the "greatest integer" function.

The "greatest integer" of -3.2 is -4, so B is not a correct choice. The graph does not pass the horizontal line test, so the function is not one-to-one, and E is not a correct choice.

Answer:

C, D, E

Step-by-step explanation:

Answer:

Step-by-step explanation:

Both numbers of the ratio units used to express the ratio in ten years are 2 higher than at present. Thus, each ratio unit must stand for 5 years. That would make their current ages ...

  Sunitha: 7·5 = 35

  Raseeda: 8·5 = 40

_____

If you can't figure the answer right away from the change in ratio units, then you may need to write a couple of equations:

These can be translated to standard form, which may make some methods of solution easier:

These have solution (r, s) = (40, 35).