Use the figure below. Which angles are vertical angles?
2

(a) The closed form for ∑2 is 2.

(b) The closed form expression for ∑3 is 24.

(c) The closed form for the sum ∑n = 0(― 1)² ― 1 is n(1 - n) / 2.

(d) The value of -3 matches the manual computation of the four terms.

Our closed form solution is correct.

To find the closed form for ∑2, we can use the formula for the sum of the first n terms of an arithmetic series:

∑2 = n(a + l) / 2

In this case, a = 2 (the first term) and l = 2 (the last term) since we are summing a series of 2's.

We also know that there is only one term, so n = 1.

Substituting these values into the formula, we have:

∑2 = 1(2 + 2) / 2

= 4 / 2

= 2

The formula for the sum of the first n terms of an arithmetic series is:

∑n = n(a + l) / 2

In this case, we have a = 3 (the first term), l = 13 (the last term), and n = 3 (the number of terms).

Substituting these values into the formula, we get:

∑3 = 3(3 + 13) / 2

= 3(16) / 2

= 48 / 2

= 24

The formula we developed in class is:

∑n = n(a + a + (n - 1)d) / 2

In this case, we have a = 0 (the first term) and d = -1 (the common difference).

Substituting these values into the formula, we get:

∑n = n(0 + 0 + (n - 1)(-1)) / 2

= n(0 - n + 1) / 2

= n(1 - n) / 2

To test the closed form solution for ∑3 = 0(― 1)² ― 1, we substitute n = 3 into the closed form expression we derived in part (c):

∑3 = 3(1 - 3) / 2

= 3(-2) / 2

= -6 / 2

= -3

Now, let's manually compute the sum of the first four terms of ∑3 = 0(― 1)² ― 1:

0(― 1)² ― 1 + 1(― 1)² ― 1 + 2(― 1)² ― 1 + 3(― 1)² ― 1

= 0 - 1 - 2 - 3

= -6

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Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.

To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.

First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.

Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.

To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).

(1/3) * 69 ≈ 23

Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.

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Answer:

Step-by-step explanation:

208

Answer:

x ≤ 2

Step-by-step explanation:

x+5 ≤ 7

x ≤ 7 - 5

x ≤ 2

Answer:

cos h° = x/z

Step-by-step explanation:

SOH CAH TOA

Answer:

Papina found 27 more shells than Camila.

Step-by-step explanation:

Let x = the number of seashells that Camila found.

That means that

4x = the number of seashells that Papina found.

Papina's shells + Camila's shells = 45

4x + x = 45

Combine like terms.

5x = 45

Divide by 5.

x = 9

Camila found x shells. That is 9 shells.

Papina found 4x shells.

4x

= 4(9)

= 36

Papina found 36 shells.

36 - 9

= 27

Papina found 27 more shells than Camila.

The average value of f(x) over [2, 6] is given by the definite integral,

\(\displaystyle f_{\rm ave[2,6]} = \frac1{6-2} \int_2^6 3\ln(2+x^3)\cos(x) \, dx\)

and is approximately -1.67284.

The approximate average value of the function in the closed interval [2,6] is -1.628.

It is given that the f is the function given by:  \(\rm f(x) = 3ln(2+x^2)cosx\)

It is required to find the average value of f in the closed interval [2,6]

It is defined as the mathematical approach to calculating the smaller parts or components.

We have function f:

\(\rm f(x) = 3ln(2+x^2)cosx\)

For the average value in [2,6]

We integrate the function with lower limit 2 and higher limit 6.

\(\rm \int_{2}^{6}f(x) =\int_{2}^{6}( 3ln(2+x^2)cosx)\\\)

The average value of the above function:

\(\rm =\frac{1}{6-2} \int_{2}^{6}( 3ln(2+x^2)cosx)\\\)

Further solving:

\(\rm =\frac{3}{4} \int_{2}^{6}( ln(2+x^2)cosx)\\\)

Further solving and applying limits we get:

\(=\frac{3}{4}\times-2.2304\)

= -1.628

Thus, the approximate value of the function in the closed interval [2,6]

is -1.628.

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The propane tank has a cylindrical shape. The general formula for the total surface area of a cylinder is given by:

where, r = 5.2 ft.

h = 16 ft.

Hence:

Steve needs to cover the entire tank twice, so:

ANSWER

Steve will cover 1385ft²

The range of the function is {0.01, 0.1, 1, 10, 100}. With an increase in the value of the domain, the range of the function is increasing.

What is a function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

Given function is

f(x) = 10^x.

Given domain is {-2, -1, 0, 1, 2}.

Now putting x = -2, -1, 0, 1, 2 in the function f(x) = 10^x.

When x = -2:

f(-2) = 10^(-2)

f(-2) = 0.01.

When x = -1:

f(-1) = 10^(-1)

f(-1) = 0.1.

When x = 0:

f(0) = 10^(0)

f(0) = 1.

When x = 1:

f(1) = 10^(1)

f(1) = 10

When x = 2:

f(2) = 10^(2)

f(2) = 100

The range of the function is {0.01, 0.1, 10, 100}

The values of the range increase with the increase of domain.

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Answer:

18 foot ladder will reach at 14.4 feet up the wall.

Step-by-step explanation:

Triangles formed by the ladder against wall and the ground are similar,

ΔABC ~ ΔDEC

Therefore, their corresponding sides will be proportional.

\(\frac{AB}{DE}= \frac{BC}{EC}= \frac{AC}{DC}\)

\(\frac{AB}{DE}= \frac{BC}{EC}\)

\(\frac{18}{10}=\frac{BC}{8}\)

BC = \(\frac{18\times 8}{10}\)

     = 14.4

Therefore, 18 foot ladder will reach at 14.4 feet up the wall.

Answer:

Step-by-step explanation:

1 min= 20%+5%=25%

Therefore 2 min = 25%+5%=30%

3 min=30%+5%=35%

4min =40% therefore your coodinates will be like(1,25),(2,30),(3,35),(4,40) etc

Answer:

True. Hope this helps

Step-by-step explanation:

speed=distance÷time

A.V.S=440÷11=40m/s

hope it helps.. Please mark brainliest.

Answer:

40 m/s

Step-by-step explanation:

Find:

We are asked to find the unit rate, How many meters per 1 second?

Know:

440 meters in 11 seconds

Solve:

440 meters in 11 seconds

  ? meters in 1 second

   440/11  = 40 meters per second

Answer:

The average speed of the person is 40 m/s

Answer:

The radius is 8 inches

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

Assuming you mean 320 pi for the volume

320  pi = pi r^2 ( 5)

320 =5pi r^2

Divide each side by 5pi

320 pi / 5pi = 5 pi r^2 / 5pi

64 = r^2

Take the square root of each side

sqrt(64) = sqrt(r^2)

8 = r

The radius is 8 inches

Answer:

\(\Huge \boxed{\mathrm{4.51 \ inches}}\)

\(\rule[225]{225}{3}\)

Step-by-step explanation:

\(V=\pi r^2 h\)

The volume is 320 in³.

The height is 5 in.

\(320=\pi r^2 * (5)\)

Solving for \(r\).

Dividing both sides by 5.

\(64=\pi r^2\)

Dividing both sides by \(\pi\).

\(20.371833=r^2\)

Taking the square root of both sides.

\(r= 4.513517\)

The radius is 4.51 inches.

\(\rule[225]{225}{3}\)

Answer:

x^2+7x+10

Step-by-step explanation:

x×x=x^2

5×x=5x

2×x=2x

5x+2x=7x

5×2=10

Answer:

11

4

Step-by-step explanation:

3 hrs to travel 45 miles downstream

4 hrs to travel 28 miles upstream

speed of boat in still water= s

speed of the current= c

added up the 2 equations, we get:

\(\large\bf{\underline{Given:}}\)

__________________________________________

\(\large\bf{\underline{To\:find:}}\)

\(\bf{Let\:the\:total\:no.\:of\: kitten\:x}\)

__________________________________________

\(\large\bf{\underline{Therefore}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\bf{⟹30\%\:of\:x=3}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\bf{⟹\frac{30}{100}\times x= 3}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\bf{⟹x= 3\times \frac{100}{30}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\bf{⟹x=10}\)

__________________________________________

\(\large\bf{\underline{Hence}}\)

\(\bf{There\:are\:10\: kittens\:in\:the\: litter}\)

Answer:

n ≤ 1 or n ≥ 7

Step-by-step explanation:

solve each part separately

86n + 13 ≤ 99 ( subtract 13 from both sides )

86n ≤ 86 ( divide both sides by 86 )

n ≤ 1

n + 90 ≥ 97 ( subtract 90 from both sides )

n ≥ 7

solution is n ≤ 1 or n ≥ 7

Answer:

sorry I can't know the answer

Step-by-step explanation:

again sorry

Answer:

alright so I'll give an example, say if theres like 5x+6x. you can add these because they have the same variable so it would equal 11x. However if you had something like 5x+6n you cannot add cause yhey have different variables. If you have something like 5x^2+6x you still cannot combine because one has a different variable.

The graph of the solution to the given inequality on the number line plotted is attached.

Inequalities are the mathematical expressions in which both sides are not equal.

In inequality, unlike in equations, we compare two values.

The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is q < 69.5​.

The result can be shown in multiple forms.

Inequality Form:q<69.5

Interval Notation:(−∞,69.5)

Therefore, the graph the solution to the given inequality on the number line plotted below.

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A.AAA know this becouse i took the test

Answer:

4

Step-by-step explanation:

count up from -5 to -1

so -5,-4,-3,-2,-1 and there are four numbers excluding-5

The area of the shaded sector of the circle is 7.27 m^2

The area of a circle is the amount of two-dimensional space taken up by the circle. It can be calculated by using the formula A = πr2, where A is the area, π is 3.14, and r is the radius of the circle. The radius is the distance from the center of the circle to any point on the circle. The diameter of a circle, which is the distance from one side to the other, is twice the radius. Therefore, the area of a circle can also be calculated by using the formula A = πd2/4, where d is the diameter of the circle.

The area of the shaded sector of the circle is 7.27 m^2.

This can be calculated using the formula A = (π/180) x r^2 x θ, where r is the radius (18 m in this case), and θ is the angle in degrees (110° in this case).

Therefore, A = (π/180) x (18^2 x 110) = 7.27 m^2.

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Answer:

The equation equals 0

Step-by-step explanation:

12 ( 1/3 ) + 5 - 9

4 + 5 - 9

9 - 9

= 0

Answer:

K5.60.

Step-by-step explanation:

What are supplementary angles?

Supplementary angles are angles that sum up to give 180°

What are vertically opposite angles?

Vertically opposite angles are angles that are vertically opposite each other which equals the same.

So, since angle 2 is vertical to a 123° angle, angle 2 is also 123° because they are vertically opposite angles.

So, since supplementary angles are angles that sum up to give 180°, angle 1 = 180° - angle 2 which is 123°.

Angle 1 = 180° - 123° = 57°

Therefore angle 1 = 57°

Hope this helps you <3

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