(13+3x) + 166 = 180​

The least number of blocks with which he can do is 168 blocks.

What is the least Common Multiple (LCM)?

The Least Common Multiple (LCM) is a method for determining the smallest common multiple of two or more numbers. A common multiple is a number that is the product of two or more numbers.

Least number of blocks = LCM of 6cm, 7cm, and 8cm.

Multiples of 6 - 6,12,18,24,30,36,42,48,54,60

Multiples of 7 - 7,14,21,28,35,42,49,56,63,70

Multiples of 8 - 8,16,24,32,40,48,56,64,72,80

Common Multiples - 168

Least Common Multiple - 168

So the least number of blocks with which he can do is 168 blocks.

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x= 90° - 63° = 27° (NO perpendicular to AOB)

angle DOB = (90°+90°) -128° (angles on a straight line)

= 180° - 128°

= 52°

y= 180° - x - 63° - angle DOB (angles on a straight line)

=180° - 27° - 63° - 52°

= 38°

I'm not sure of the answer tho^^ good luck!

(a) The two vectors and the path on a quadrant I plot: Given vectors: S = 2m  i  + 10m  j ;E = 8m  i  + 4m  j .Plotting the given vectors on the Cartesian plane, we get, Graphical representation of the given vectors
(b) A point on the path is a fraction f of the way between the start and the end. Write this as a vector equation involving f.If a point on the path is a fraction f of the way between the start and end points, then the position vector of this point can be given as:
P(f) = fE + (1 - f)S
= f(8m  i  + 4m  j ) + (1 - f)(2m  i  + 10m  j )
= (8f + 2 - 6f) m i  + (4f + 10 - 6f) m j
= (6f + 2) m i  + (6 - 2f) m j
So, the required vector equation is P(f) = (6f + 2) m i  + (6 - 2f) m j .
(c) Evaluate your expression from part (b) for f=0, P(0), and f=1, P(1).

Explain whether these results confirm if your expression in part (b) is reasonable or not.
For f = 0, P(0) = (6 × 0 + 2) m i  + (6 - 2 × 0) m j  = 2 m i  + 6 m j
For f = 1, P(1) = (6 × 1 + 2) m i  + (6 - 2 × 1) m j  = 8 m i  + 4 m j
These results are reasonable since P(0) is the starting vector S and P(1) is the ending vector E, which is as expected.

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The probability that at least one of A, B, or C happens is approximately 0.5968, or 59.68%.

To calculate the probability that at least one of A, B, or C happens, we can use the principle of inclusion-exclusion.

The probability that at least one of the events occurs is equal to the sum of the probabilities of the individual events minus the sum of the probabilities of the intersections of any two events plus the probability of the intersection of all three events. This can be expressed mathematically as:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

Since A, B, and C are independent events, we know that the probability of any intersection of two or more of them is simply the product of their individual probabilities. Therefore, we can substitute the given probabilities into the equation:

P(A ∪ B ∪ C) = 0.2 + 0.24 + 0.32 - (0.2 x 0.24) - (0.2 x 0.32) - (0.24 x 0.32) + (0.2 x 0.24 x 0.32)

Simplifying the expression gives:

P(A ∪ B ∪ C) = 0.5968

In other words, in about 60% of the trials, at least one of the events A, B, or C will occur. This probability can be useful in determining the likelihood of a certain outcome in a probability experiment or in making decisions based on uncertain events.

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Answer:

6 9/10, 6 3/4, 6 19/80

Step-by-step explanation:

it is the ordre r r my duuuud

Answer:  120

120 x 0.85 = 102

Have a good day!

Answer: 120

Step-by-step explanation: (102 x 100) / 85

Answer:

4(11+7) - 9.8

4 (18) - 9.8

72 - 9.8

= 62.2

The least common multiple (LCM) of 60 and 90 is 180.

The LCM of 220 and 1400 is 3080.

The LCM of 3273∙11 and 23∙5∙7 is 127155.

To find the LCM of 60 and 90, we can list their multiples and find the smallest common multiple, which is 180.

For the numbers 220 and 1400, we can find their prime factorizations (220 = 4 × 5 × 11, 1400 = \(2^{3}\) × 10 × 7). Then, we take the highest power of each prime factor and multiply them together to get the LCM, which is \(2^{3}\) × 10 × 7 × 11 = 3080.

For the numbers 3273∙11 and 23∙5∙7, we multiply together all the distinct prime factors and their highest powers to obtain the LCM, which is 3273∙11∙23∙5∙7.

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Answer:

Step-by-step explanation:

\(y=-3(x^2+10x+25)-1\\ \\ y=-3x^2-30x-76\\ \\ dy=-6x-30\\ \\ d^2y=-6\\ \\ \text{Since the second derivative is always negative, when the first derivative is equal to zero the function will be at a global maximum.}\\ \\ dy=0=-6x-30\\ \\ x=-5\\ \\ f(-5)=-1\\ \\ \text{So the global maximum occurs at the point (-5,-1)\)

The inverse of the conditional statement "If p then q" is, "p and not q".

What is conditional statement?

"If...then" is how a conditional statement is expressed. If we consider p and q to be the two statements, then p and q can be written under several conditions, such as;

If the "If" component (p) and the "then" part (q) of a conditional statement are both negated, this is known as a conditional statement in reverse. The conditional statement in geometry is known as p → q. Where stands for NOT or negating the statement, the inverse is written as  ~ p → ~  q.

In logic, "p and not q" is identical to the negation of "if p then q."

Therefore, the inverse of the conditional statement "If p then q" is,  

"p and not q".

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A parametric representation using spherical-like coordinates for the upper half of the ellipsoid \(\[4(x)^2 + 9y^2 + 36z^2 = 36\]\) can be obtained by expressing the coordinates in terms of spherical coordinates.

To find a parametric representation, we can express the coordinates (x, y, z) in terms of spherical coordinates (ρ, θ, φ). In spherical coordinates, ρ represents the radial distance from the origin, θ represents the azimuthal angle in the xy-plane, and φ represents the polar angle from the positive z-axis.

For the upper half of the ellipsoid, we need to restrict the values of ρ, θ, and φ. Since the ellipsoid is symmetric about the xy-plane, we can restrict ρ to positive values and φ to the range of 0 to π/2.

Using the equation of the ellipsoid, we can express ρ, θ, and φ in terms of x, y, and z as follows:

\(\[\rho = \frac{6}{\sqrt{4\cos^2\theta\sin^2\phi + 9\sin^2\theta\sin^2\phi + 36\cos^2\phi}}\]\[\theta = \arctan\left(\frac{y}{2x}\right)\]\[\phi = \arctan\left(\sqrt{\frac{4}{3}\left(1 - \frac{x^2}{9} - \frac{y^2}{36}\right)}\right)\]\)

With these expressions, we can generate a parametric representation for the upper half of the ellipsoid by varying the values of θ and φ within their respective ranges and calculating the corresponding values of x, y, and z.

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The response rate of the survey conducted by Megan to study bullying in high school is 0.4 or 40%

How to Calculate Response Rate?

The response rate can be calculated by dividing the number of completed survey responses by the number of people who viewed or started the survey.

To convert this to a percentage, multiple your final number by 100.

According to the giving question:

The number of completed survey responses = 400

The number of people who started the survey = 1,000

∴ Response rate = 400/1,000

                           = 0.4 or 40%

Hence the response rate is 0.4 or 40%.

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The value of cos45 will be equal to ( 1 / √2 ).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

Let the two sides of the triangle is having a unit length then the hypotenuse of the triangle will be √2.

Apply cosine law for the triangle:-

cos45 = Base / Hypotenuse

cos45 = 1 / √2

Therefore, the value of cos45 will be equal to ( 1 / √2 ).

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In the coordinate plane, the unit circle is a circle with a radius of 1 centered at the origin. When we refer to the terminal side of an angle in standard position, we mean the side that ends at a point on the unit circle.

Quadrant IV is the bottom-right quadrant of the coordinate plane, where both the x-coordinate and the y-coordinate are positive.

Therefore, a point on the unit circle lying on the terminal side of an angle in standard position in Quadrant IV would have positive x and y coordinates. This is because both coordinates are positive in Quadrant IV.

It is important to note that the x-coordinate of the point corresponds to the cosine of the angle, and the y-coordinate corresponds to the sine of the angle. In Quadrant IV, the cosine is positive, while the sine is positive.

By understanding the properties of the unit circle and the characteristics of each quadrant, we can determine the correct completion of the statement: A point on the unit circle lies on the terminal side of an angle in standard position in Quadrant IV when both the x-coordinate and the y-coordinate are positive.

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The abelian groups (up to isomorphism) of order 360 are:

1. C360: The cyclic group of order 360.2. C2 x C2 x C3 x C3 x C5: The direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

To find all abelian groups of order 360, we need to consider the prime factorization of 360, which is 2^3 × 3^2 × 5. The abelian groups will be direct products of cyclic groups whose orders divide 360.

First, we consider the cyclic groups. Since the order of an element in a cyclic group divides the order of the group, we can have cyclic subgroups of orders 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Now, we can combine these cyclic subgroups to form the abelian groups. We can take direct products of the cyclic groups to obtain different possibilities. The order of the resulting group will be the product of the orders of the cyclic subgroups.

In this case, we can form the following abelian groups of order 360:

C360: This is the cyclic group of order 360 itself.

C2 x C2 x C3 x C3 x C5: This is the direct product of cyclic groups of orders 2, 2, 3, 3, and 5.

These are the two abelian groups (up to isomorphism) that can be formed using the prime factorization of 360.

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Answer:

+30 feet

Step-by-step explanation:

"Above" infers a positive sign.

If the model airplane is 30 feet above the ground. The integer represents the situation will be +30 feet.

it is defined integer as a whole number it can be a negative whole number or a positive whole number for example 2, 4, 1, -8, 0.Players' results in golf, football, and hockey competitions, movie or song ratings, and other real-world scenarios where integers are utilized

​

It is given that, the model airplane is 30 feet above the ground.

Additionally, negative numbers can be used to represent elevations. At sea level, there are 0 feet of elevation. Elevations above sea level are considered positive, and those below sea level are considered negative.

​

The integer represents the situation will be +30 feet.

Thus, if the model airplane is 30 feet above the ground. The integer represents the situation will be +30 feet.

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The probability of getting tails on the next toss is 0.5 as the coin is a fair coin and doesn't remember the past results.

The probability of getting heads on a fair coin is 0.50.

The probability of getting tails is also 0.50.

If you toss the coin three times and get heads all three times,

The probability of getting tails on the next toss is 0.5 as the coin is a fair coin and doesn't remember the past results.

A fair coin is a coin where each of the two faces has the same probability of landing on any coin toss. That is, a fair coin will land on tails and heads equally often.

In other words, the probability of getting heads and tails is 0.5.

There are only two possible outcomes of flipping a fair coin.

The probability of each outcome is 0.5.

This is because a fair coin has two equally likely outcomes.

The probability of getting heads on any flip is 0.5.

The same goes for the probability of getting tails on any flip.

This implies that the probability of flipping a fair coin three times and obtaining three heads is

(0.5 x 0.5 x 0.5) = 0.125

Similarly, the probability of flipping a fair coin three times and obtaining three tails is also 0.125.

As each flip is independent, the outcome of the preceding flips does not affect the next flip, and the probability of getting tails on the next toss is 0.5.

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Answer:

B

Step-by-step explanation:

Not much to explain

Work Shown:

\(S = \text{sum of the integers from 1 to n}\\\\ S = 1+2+3+\ldots+n\\\\ S = \frac{n(n+1)}{2}\\\\ S = \frac{30(30+1)}{2}\\\\ S = \frac{30(31)}{2}\\\\ S = \frac{930}{2}\\\\ S = 465\\\\ \text{Therefore, }1+2+3+\ldots+29+30 = 465\)

Answer:

hehehe see how you like it i did it on purpose too

Step-by-step explanation:

Answer:

the blank= 12.82

Step-by-step explanation:

Answer:

12.82

Step-by-step explanation:

x = blank

x / (-2) = -6.41

multiply both sides by -2

x = 12.82

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

6(b+1)

Step-by-step explanation:

6(b+1)

see this and reply me

Sorting involves arranging a set of elements in a particular order (ascending or descending)

The list elements are given as:

3, 2, 4, 5, 1, 6

To sort the list in ascending order, the adjacent elements are compared, and the smaller element is pushed to the left.

So, we have the following steps

See attachment for the complete step that sorts the list

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Answer:

8n - (2n + 11 - 54) =

Step-by-step explanation:

6n + 43, I used a calculator !

Answer:

There are 18 juniors on the track team

Answer:

There are a total of 18 juniors on the track team.

Step-by-step explanation:

Apply the following ratio to the quantity by multiplying.

6:7 = 6 to 7 or 6/7

6/7 × 21 = 126/7 = 18

The distance of the plane from point P by line of sight is 1385. 76 meters

Using the trigonometric identities, we have that these identities are enumerated as;

From the information given, we have that;

The opposite side = 800 m

The angle of elevation = 30 degrees

The distance of the plane from point P is the adjacent side

Using the tangent identity

tan 30 = 800/m

cross multiply the values

m = 1385. 76 meters

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The possible number of ways the 7-question test can be answered: 128

In this question, we have been given a true-false test contains 7 questions.

We need to find the possible number of combinations (ways)  the 7-question test can be answered.

As, it is a true-false test, there are 2 choices per problem.

The number of problems = 7

so,  the possible number of ways  the 7-question test can be answered: 2*2*2*2*2*2*2

= 2^7

= 128

Therefore, in 128 different ways the 7-question test can be answered.

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The piecwise function in the graph  is written as:

We can see that the piecewise function is:

First a constant at y = -2, which ends at x = -2, so this is the first piece.

Then a line x = y, it starts at x = -2 and ends at x = 2, this is the second piece of our function.

Finally, another constant line at y = 2, it starts at x = 2.

Then the piecwise function is written as:

f(x) = -2  if x < -2

f(x) = x   if -2 ≤ x ≤ 2

f(x) = 2  if  2 < x

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