What is the rotational symmetry of the figure?

p=?

r=8

i=816

t=2years

we know that

p=I×100/t×r

p=816×100/8×2

p=81600/16

p=5100

it the answer

The height and radius of the cup are 4.41 cm and 2.07 cm respectively

To minimize the amount of paper used, we need to minimize the surface area of the cup. Let h be the height and r be the radius of the cone. Then we have:
\(Volume of cone = \frac{1}{3}  πr^{2} h = 36 cm^{3}\)

Solving for h, we get:
\(h = \frac{108}{(πr^2)}\)

Now we can express the surface area of the cone as:
\(Surface area = πr^2+ πr\sqrt{r^{2}+h^{2}  }\)

Substituting the expression for h, we get:

\(Surface area = πr^2+πr \sqrt{(r^{2} +(\frac{108}{(πr^2)^{2}) } )}\)

To minimize this function, we take its derivative with respect to r and set it equal to zero:
\(\frac{d}{dx} (Surface area) =  \frac{2πr - 108r }{[(r^2+(\frac{108}{πr^2}))^{0.5}  }] - \frac{108π}{r^2 }  = 0\)

Simplifying, we get:
\(2r^3 - \frac{108^2}{π} = 0\)

Solving for r, we get:
\(r = (\frac{54}{π})^{\frac{1}{3} }\)

Substituting this value into the expression for h, we get:
\(h = \frac{108}{\frac{54}{π} ^{(\frac{2}{3}π )} }\)

Thus, the height and radius of the cup that will use the smallest amount of paper are:
height = 4.41 cm
radius = 2.07 cm (rounded to two decimal places)

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Answer:

Can you add the picture maybe?

The multiplication table is an illustration of pattern

The expression that shows the number that comes next in the pattern is 25 + 11

The rule of the pattern is:

\(T_n =(n -1)^2 + 2(n - 1) + 1\)

The next term of the pattern is: n = 6.

So, we have:

\(T_6 =(6 -1)^2 + 2(6 - 1) + 1\)

Simplify the expressions in bracket

\(T_6 =5^2 + 2(5)+ 1\)

Further, simplify

\(T_6 =25 + 10+ 1\)

Add 10 and 1

\(T_6 =25 + 11\)

Hence, the expression that shows the number that comes next in the pattern is 25 + 11

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Answer: 8

Step-by-step explanation:

Answer:

10x² + 14x - 48

Step-by-step explanation:

F: (5x)(2x) = 10x²

O: (5x)(6) = 30x

I:  (-8)(2x) = -16x

L:  (-8)(6) = -48

combine the two middle terms to get 14x

10x² + 14x - 48

To minimize the total cost and produce 12,210 units, approximately ¼ unit should be made on machine A and approximately 12,209.75 units should be made on machine B.

To minimize the total cost, we need to determine the number of units that should be made on each machine, given the cost functions and the total units required. Let’s denote the number of units made on machine A as x and on machine B as y.

The cost function for machine A is C(x) = 10x + 6x², and for machine B, it is C(y) = 160 + 13y. The total cost is given by C(x, y) = C(x) + C(y).

Since the total units required are 12,210 units, we have the constraint x + y = 12,210.

To minimize the total cost, we can use the method of optimization. We need to find the values of x and y that satisfy the constraint and minimize the total cost function C(x, y).

We can rewrite the total cost function as:

C(x, y) = 10x + 6x² + 160 + 13y.

Using the constraint x + y = 12,210, we can express y in terms of x: y = 12,210 – x.

Substituting this into the total cost function, we have:

C(x) = 10x + 6x² + 160 + 13(12,210 – x).

Simplifying the expression, we get:

C(x) = 6x² - 3x + 159,110.

To minimize the cost, we take the derivative of C(x) with respect to x and set it equal to zero:

C’(x) = 12x – 3 = 0.

Solving for x, we find x = ¼.

Substituting this value back into the constraint, we have:

Y = 12,210 – (1/4) = 12,209.75.

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The weight in pounds of the fourth dog, is 55 lbs.

What is weight?

The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.

As given, Ben is walking with three dogs that weigh an average of 75 pounds each. Ben begins to walk with a fourth dog, and the average weight of the dogs decreases to 70 pounds.

The total weight of the first three dogs is 225 pounds.

This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:

\(\frac{d+225}{4} = 70\\d + 225 = 280\\d = 280 - 225\\d = 55 lbs\)

Therefore, the weight of the fourth dog is 55 lbs.

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Answer:

3 days.

Step-by-step explanation:

Simple ratio:

8/2=12/x

4/1=12/x

4x=12

x=3

Hope this helps!

Answer:

Step-by-step explanation:

When two angles add to 90°

Answer:

(6/11, 16/11)

Step-by-step explanation:

While it's fairly obvious that you're supposed to "solve this system of equations," it'd be clearer if you were to say so specifically.  Also, reduce ambiguity by using parenthes:  You meant either (5/3)x or 5/(3x).  Which one?  I'm assuming it's (5/3)x.

Then our system is:

(5/3)x - 2y = -2

      x  +  y =  2

Let's eliminate y through addition/subtraction.  Multiply the 2nd equation through by +2:

(5/3)x - 2y = -2

     2x  + 2y = 4

------------------------

(11/3)x       =  2

Multiplying both sides by 3 eliminates the fractional coefficient:

11x = 6

Then x = 6/11.  Now we must solve for y:

-(6/11) + y = 2

Multiplying 2 by 11/11 yields:

-(6/11) + y = 22/11.

This simplifies to y = 16/11

Thus, the solution of this system is

(6/11, 16/11)

18 months of All-Star Library membership cost $76 in total.

For the given equation.

The sign-up fee for the library-all-star-members club = $40.

Let 'x' be the total number of months.

Let 'y' be the total cost.

Monthly fee = $2.

Then, the linear equation models is-

y = 2x + 40

Given that a particular club member has been a part of it for 19 months, we replace x with the number 19 as follows:

y = 2x + 40

y = 2 * 18 + 40

y = = 36 + 40

y = 76.

Thus, 18 months of All-Star Library membership cost $76 in total.

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The complete question is-

3. In order to become a member of the library-all-star-members club, there is a $40 sign-up fee and a $2 monthly fee. Write an equation in slope-intercept form that models this situation. Use equation you wrote in problem 3 to find the total cost of being an all-star library member for 18 months.

The given numbers are:(10 1010 1010)2 and (1 1111 0001)2To find the sum of two binary numbers, we can add them using binary addition.

Similarly, to find the product of two binary numbers, we can multiply them using binary multiplication.Therefore, using binary addition:1 1 1 1 1 0 0 0 1 0(10 1010 1010)2+ (1 1111 0001)2-------------------1 0 0 1 0 1 1 0 1 1(11 1010 1011)2Therefore, the sum of the given binary numbers is (1 0 0 1 0 1 1 0 1 1)2To find the product of two binary numbers,

we use binary multiplication.(10 1010 1010)2 × (1 1111 0001)2---------------------------(10 1010 1010)2(×) (1) (1 0101 0101 0)2(×) (1 1111 0001)2--------------------------(10 1011 0001 1 0 1 0)2Therefore, the product of the given binary numbers is (10 1011 0001 1 0 1 0)2.Note: To represent the binary number, (10 1011 0001 1 0 1 0)2, it is better to split it into groups of 4 starting from the right side. Therefore, it can be written as (1 0101 1000 1110 1010)2.

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Answer: f(x) and g(x) both represent y of the equations

Step-by-step explanation: f(x) and  g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.

Answer: 1. Not a right triangle 2. Right Triangle 3. Right triangle 4. Right triangle 5. Not a right triangle

Step-by-step explanation:

the right triangle has to have a pattern to go by, so only evens or only odd sides.

The numeric value of ms within is = 19.

To find the numeric value of ms within:

Given: Swithin = 70, sample size = 17 and number of groups = 3.

So, 17 × 3 = 51

70 - 51 = 19

Therefore, the numeric value of ms within is = 19.

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The variation between the sample means is small.

The variation between the sample means provides insight into the spread or dispersion of the data. In this case, if the variation between the sample means is small, it indicates that the mean name lengths across the seven samples are relatively similar and close together. This suggests that there is not much variability or difference in the average name lengths among the different samples of students. Therefore, the variation between the sample means is small, indicating a certain level of consistency in the mean name length across the samples.

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\(\text{Given that,}\\\\ (x_1,y_1) = (-7,-4) ~~ \text{and slope}~ m = 3\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y +4 = 3(x+7)~~~~~;[\text{Point-slope form.}]\\\\\implies y = 3x +21 -4\\\\\implies y = 3x +17~~~~~~~~~~~;[\text{Slope-intercept form.}]\\\\\text{Hence the answers are A and F.}\)

Answer:

53 cm

Step-by-step explanation:

the distance from opposite corners of the rectangle, divide the rectangle into 2 congruent right triangles with legs 45 and 28 and the diagonal (d) , the hypotenuse.

using Pythagoras' identity in one of the right triangles , then

d² = 45² + 28² = 2025 + 784 = 2809 ( take square root of both sides )

d = \(\sqrt{2809}\) = 53

the distance from corner to corner is 53 cm

Answer:

53

Step-by-step explanation:

u see this is how Pythagorean theorem works a^2 + b^2 = c^2 so yep thats how i got 53 i hope this helps please give brainliest have a good morning/afternoon/night have a great day!!! :D.   THANK YOU FOR BRAINLIEST!!!!

Answer:

the 9th term would be  -15

Step-by-step explanation:

Answer:

the 6 inch is a better deal because it is 55 cents per inch while the 12 inch is 60 cents per inch

The goal of a hypothesis test is to determine if the data can refuse an assumption a parameter or a population.

Statistical hypothesis test: A statistical hypothesis test is a technique for determining whether the available data are sufficient to support a specific hypothesis. We can make probabilistic claims about population parameters through hypothesis testing.

The purpose of a hypothesis test is to ascertain whether the data can refute a parameter or population assumption.

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Using limit definition of big O, we can show that (x²+1)/(x+1) is O(x) as the limit of (x²+1)/(x+1) as x approaches infinity is finite. Therefore, (x²+1)/(x+1) grows no faster than a linear function, which implies that it is O(x).

To show that (x²+1)/(x+1) is o(x), we need to prove that the limit of the ratio of the function and x as x approaches infinity is equal to 0. That is, we need to prove

lim (x²+1)/(x+1) / x as x → ∞ = 0

To evaluate this limit, we can use L'Hopital's rule. Taking the derivative of the numerator and denominator with respect to x gives

lim (2x) / 1 as x → ∞ = ∞

Since the limit of the ratio is not equal to 0, we can conclude that (x²+1)/(x+1) is not o(x). In fact, (x²+1)/(x+1) is actually O(x), which means it grows no faster than x.

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In order for a function to be considered o(x) as x approaches 0, the limit of the absolute value of the function divided by x must approach 0.

However, in this case, the limit is equal to 1, indicating that the function does not satisfy the condition for being o(x) as x approaches 0.

To prove that (x^2 + 1)/(x + 1) is o(x) as x approaches 0, we need to show that the absolute value of (x^2 + 1)/(x + 1) divided by x approaches 0 as x approaches 0.

Let's calculate the limit:

lim(x→0) |(x^2 + 1)/(x + 1) / x|

We can simplify the expression inside the absolute value by multiplying the numerator and denominator by (x - 1):

lim(x→0) |(x^2 + 1)/(x + 1) / x| = lim(x→0) |(x^2 + 1)/(x + 1) * (1/x)|

Now, we can simplify further by canceling out x terms:

lim(x→0) |(x + 1) / (x + 1)| = lim(x→0) |1| = 1

The limit is equal to 1, not 0.

Therefore, (x^2 + 1)/(x + 1) is not o(x) as x approaches 0.

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Answer:

13pts

Step-by-step explanation:

If you're asking how many pints 6 qt and 1 or is then I believe it is 13 pt

The chain rule for the function: dh/dx = df/dx * du/dx * dv/dx, where df/dx, du/dx and dv/dx are the derivatives of f, u and v with respect to x.

The chain rule is a rule used to calculate the derivative of a composite function. It states that the derivative of the composite function is equal to the product of the derivatives of each of its component functions. In the case of the function dh/dx, where h(x) = f(x, u(x), v(x)), the chain rule can be written as:

dh/dx = df/dx * du/dx * dv/dx

This means that the derivative of h with respect to x is equal to the product of the derivatives of f with respect to x, u with respect to x, and v with respect to x. This can be broken down further, where df/dx is the derivative of f with respect to x, du/dx is the derivative of u with respect to x, and dv/dx is the derivative of v with respect to x.

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Answer:

10 cubic inch is the volume of container

There are 15,504 ways to randomly select a team of 5 people from a group of 20 people

If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:

C(20, n) = 20! / (n! * (20 - n)!)

where C(20, n) represents the number of ways to select n people from a group of 20 people.

For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:

C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504

Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.

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When two sides of a triangle measure 18 meters and 13 meters, the measures that could represent the perimeter of the triangle is B. 37 meters

The perimeter of a triangle is the sum of the lengths of its three sides. So, if two sides of a triangle measure 18 meters and 13 meters, the third side must be less than 18 meters + 13 meters = 31 meters.

Therefore, the perimeter of the triangle must be less than 31 meters + 31 meters = 62 meters. Only 37 meters is less than 62 meters, so the answer is (b).

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The sum of the first fifteen terms of the given sequence is 220.

The given sequence can be expressed as: \($2, 8, 14, \dots$\), in which each term is six more than the preceding term. This is an arithmetic sequence, where the common difference between terms is 6. The formula to calculate the sum of the first n terms of an arithmetic sequence is given by \($S_n = \frac{n}{2}(a_1 + a_n)$\), where \($a_1$\) is the first term and \($a_n$\) is the nth term.

In the given sequence, the first term \($a_1$\) is 2 and the 15th term \($a_n$\) is 42. So, plugging these values to the formula gives us, \($S_{15} = \frac{15}{2}(2+42) = \frac{15\times 44}{2} = 220$\).

Therefore, the sum of the first fifteen terms of the given sequence is 220.

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Answer:

$16,750

Step-by-step explanation:

It took a lot of plugging in and guessing

The formula used was 16750(1+.04)^1

That equaled 17420

17420-16750 is 670

Hope this helps