What is the smallest positive integer $n$ such that $\sqrt[4]{56 \cdot n}$ is an integer?

Given:

In ΔGHI, GI is extended through point I to point J.

\(m\angle GHI=(3x+13)^\circ,m\angle IGH=(x+8)^\circ,m\angle HIJ=(6x-5)^\circ\)

To find:

The measure of angle GHI.

Step-by-step explanation:

According to exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of measure of two opposite angles.

Using exterior angle theorem, we get

\(m\angle HIJ= m\angle GHI+m\angle IGH\)

\((6x-5)^\circ=(3x+13)^\circ+(x+8)^\circ\)

\((6x-5)^\circ=(4x+21)^\circ\)

\(6x-4x=21+5\)

\(2x=26\)

Divide both sides by 2.

\(x=13\)

Now,

\(m\angle GHI=(3x+13)^\circ\)

\(m\angle GHI=(3(13)+13)^\circ\)

\(m\angle GHI=(39+13)^\circ\)

\(m\angle GHI=52^\circ\)

Therefore, the measure of angle GHI is 52 degrees.

Answer:

depends on the size of the house

let's say the house is 10 square meter then you would need 5 gallons

let's the house is 60 square meter then you would need 30 gallons

Step-by-step explanation:

whatever the square meter just divide it with 2 and that should be your answer

Answer:

1134

Step-by-step explanation:

Again I chose to separate the top half from the bottom.

top half: B*h=12*10*7=840

bottom half:21*7*2=294

add these two together 840+294=1134

find: one location where we might see fractals in everyday life.

solution: Fractals is a non regular geometric shape that has same degree of non regularity on all scales.

in everyday life one of the most common examples of fractals is branches of trees, electricity, clouds and so many.

Layla should by not more than 4 outfits in order not to exceed her budget

The inequality expression is n  ≤ 4

price of a new bicycles = $418.55

2 bicycle reflectors = $19.39

a pair of bike gloves = $27.23

new biking outfits = $38.86 each

Nora's total money to spend at a bicycle store = $38.86

Layla's spending will never exceed the total spending at the bike shop, so it will be less than or equal to the total of other items

We write the expression as;

$640 ≤ $418.55 + 2 * $19.39 + $27.23 + n * $38.86

where n represents the number of the new biking outfits

$640 - ( $418.55+ 2 * $19.39 + $27.23 ) ≤. + n * $38.86

( $640 - ( $418.55 + 2 * $19.39 + $27.23 ) ) /  $38.86≥ n

( $640 - $484.56 ) /  $38.86 ≥ n

( $155.44) /  $38.86  ≥ n

4  ≥ n

Layla should by not more than 4 outfits in order not to exceed her budget

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Answer:

2

Step-by-step explanation:

If we have the length and the breadth of a rectangle then we can draw a unique rectangle because we know already that all the vertex angles are equal to 90 degrees. Hence, only two measurements are required.

According to the information, Hannah donated b/50 books in total.

First, we need to find the average number of books donated by each student. We can do this by dividing the total number of books donated by the number of students:

Hannah donated 3 times this amount, so we can multiply the average by 3 to find how many books she donated:

Simplifying this expression, we get:

Therefore, Hannah donated b/50 books in total.

Note: This question is in Spanish. Here is the question in English:

Hannah's school organized a book donation. There are 150 students in her school who donated a total of b books. Hannah donated 3 times the average number of books donated by each student. How many books did Hannah donate?

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Answer:

Charlie owns 9,315 ft2 of the land area

Step-by-step explanation:

There are 34,500 ft2 of land shared between Mabel, Adeline, and Charlie.

Mabel owns 26% of the land area, that is:

26*34,500 ft2 / 100 = 8,970 ft2

Adeline owns 47% of the land area, or:

47*34,500 ft2 / 100 = 16,215 ft2

The land owned by Mabel and Adeline is: 8,970 ft2 + 16,215 ft2 = 25,185 ft2

Since the total area land is 34,500 ft2, Charlie owns:

34,500 ft2 - 25,185 ft2 = 9,315 ft2

Charlie owns 9,315 ft2 of the land area

The rotation of the image given 180° clockwise around the point (-2, 1) gives the image in the second option.

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

The coordinates of the given image are :

(-1, 1), (-2, 1), (-1, 4) and (-2, 4).

Point of rotation is (-2, 1).

The points are not rotated around the origin.

To make it seem like around the origin, subtract the point of rotation from the points.

So the new points are :

(1, 0), (0, 0), (1, 3) and (0, 3)

Now rotate the image with the new coordinates around the origin 180° clockwise.

Rotation is -180°, which is equivalent to rotation of 180° counterclockwise.

Coordinates (x, y) when rotated 180° clockwise becomes (-x, -y).

New coordinates after rotation about origin are :

(-1, 0), (0, 0), (-1, -3) and (0, -3).

Now add the point of rotation (-2, 1) again.

Points are :

(-3, 1), (-2, 1), (-3, -2) and (-2, -2).

Image with these points is the second option.

Hence the required image is the second option.

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Answer:

x1 = -4

x2 = 6

Step-by-step explanation:

The 2 vertical lines are "absolute values" meaning whatever they contain has to be positive

For Example

|-3| = 3

So we can ignore if the answer we get is positive or negative because it will forced to be a positive

|3 x 4| = 12

|x - 2| = 4

x1 = 6

x2 = -2

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

x² - 22x + y² - 6y + 121 = 0

Step-by-step explanation:

General Form of Equation

Solving

Answer:

(x+11)2+(y−3)2=81

mark me brainliest

Step-by-step explanation:

Answer:

2+2=4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

3√2 and 3 are the values of x and y respectively from the figure.

The given diagram is a right triangle with an acute angle of 45 degrees

We need to determine the values of variables x and y.

Applying the trigonometry identity, we will have:

sin 45 = opposite/hypotenuse
sin45 = 3/x

x = 3/sin45

x = 3/(1/√2)
x = 3√2

Similarly:

tan 45 = opposite/adjacent
tan 45 = 3/y

1 = 3/y

y = 3

Hence the values of x and y from the figure is 3√2 and 3 respectively

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Answer:

First, let's calculate the total number of chairs in the six rooms with 20 chairs each:

20 chairs/room x 6 rooms = 120 chairs

Next, let's calculate the total number of chairs in the four rooms with 30 chairs each:

30 chairs/room x 4 rooms = 120 chairs

Now we can add the total number of chairs in both sets of rooms:

120 chairs + 120 chairs = 240 chairs

To find the mean (average) number of chairs per room, we divide the total number of chairs by the total number of rooms:

240 chairs / 10 rooms = 24 chairs per room

Therefore, the mean number of chairs per room is 24.

================================================

Work Shown for problem 1

P(pink, then violet) = P(pink)*P(violet given 1st was pink)

= (4/14)*(2/13)

= 8/182

= 4/91

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

Work Shown for problem 2

P(gray, then gray)

= P(gray)*P(gray given 1st was gray)

= (3/14)*(2/13)

= 6/182

= 3/91

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

Work Shown for problem 3

P(not yellow, not yellow)

= P(not yellow)*P(not yellow given 1st was not yellow)

= (9/14)*(8/13)

= 72/182

= 36/91

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

Work Shown for problem 4

P(yellow, not yellow)

= P(yellow)*P(not yellow given 1st was yellow)

= (5/14)*(9/13)

= 45/182

Answer:

Step-by-step explanation:

Answer:

Explanation:

Here, we want to get the probability that a randomly chosen member of the student government Board is a sophomore or lives in off-campus housing

What we need to do here is to sum the count of sophomores and students living in off-campus housing, then divide it by the total number of students

Mathematically, we have that as;

We are subtracting the 1/17 because we have sophomores who live off campus:

P(A) refers to the probability of selecting a sophomore

P(B) refers to the probability of off-campus housing

P(A n B) refers to the probability of a sophomore who lives off campus

Answer:

the unknown number c must be greater than 5.4286 in order for the inequality to be true. We can write this in interval notation as (5.4286, ∞).

Step-by-step explanation:

The inequality can be written as:

7c - 8 > 30

To solve for c, we can first add 8 to both sides:

7c > 38

Then, we can divide both sides by 7:

c > 38/7

So the solution is:

c > 5.4286

Therefore, the unknown number c must be greater than 5.4286 in order for the inequality to be true. We can write this in interval notation as (5.4286, ∞).

Answer:

Commutative

Step-by-step explanation:

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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Answer:

1/2 is 1 example

Step-by-step explanation:

what

A fraction that is less than 5/8 is 4/8

The fraction is given as:

Fraction = 5/8

A fraction less than 5/8 will have the same denominator but a smaller numerator compared to 5/8

Take for instance, the numerator can be

1 to 4

So, we have;

Smaller fraction = 4/8

Hence, a fraction that is less than 5/8 is 4/8

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According to the solution we have come to find that, If we start with x = 0, then the orbit of x under f will be {0, b, 0, b, ...}, with the period of 2.

Positive integers are whole numbers that are greater than zero, such as 1, 2, 3, 4, 5, and so on. They are also called natural numbers.

For the function f(x) = -x + b, the orbit of x is the set of values that we obtain by repeatedly applying the function f to x. We can write the orbit of x as {x, f(x), f²(x), f³(x), ...}.

If we start with a positive value of x, then the first iterate f(x) will be negative, since f(x) = -x + b and b is a fixed number. The second iterate f²(x) will be positive, since f²(x) = f(f(x)) = f(-x + b) = -(-x + b) + b = x. Therefore, the orbit of x under f will be a repeating sequence that oscillates between x and -x + b, with the period of 2. In other words, the orbit of x under f is {x, -x + b, x, -x + b, ...}.

If we start with a negative value of x, then the first iterate f(x) will be positive, since f(x) = -x + b and b is a fixed number. The second iterate f²(x) will be negative, since f²(x) = f(f(x)) = f(-x + b) = -(-x + b) + b = x. Therefore, the orbit of x under f will be a repeating sequence that oscillates between x and -x + b, with the period of 2. In other words, the orbit of x under f is {x, -x + b, x, -x + b, ...}.

If we start with x = 0, then the orbit of x under f will be {0, b, 0, b, ...}, with the period of 2.

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The time required to fill the pool by using both the hoses is 4/5 hours.

Algebra is the study of mathematical expressions, in which letters and other generic symbols are used to represent numbers and quantities in formulas and equations.

Given that,

Time taken by hose A to fill 3/4 of the pool = 1 hour.

And time taken by hose B to fill the 2/4 of the same pool = 1 hour.

From the given information,

Time taken by hose A to fill the whole pool = 1 x (4/3) = 4/3 hours

And time take by hose B to fill the whole pool = 1 x (4/2) = 1 x 2 = 2 hours.

The LCM of 4/3 and 2 is 4, which can be considered as total capacity of pool.

The efficiency of hose A = 4/(4/3) = 3

The efficiency of hose B = 4/2 = 2

Total time taken to fill the whole pool by using both hoses

= 4 / (3+2) = 4 / 5 hours

If both hoses are uses, then it will take 4/5 hours to fill the pool.

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Answer: 1.6

Step-by-step explanation: To find how many gallons it is in 1 hout you take 3.47*60 for one hour. That equals 208.2. Then you take 334 and divide it by 208.2. then round to the nearest hundreth.

Main Answer: The total surface area of cylinder B is approximately 476.7  square units.

Supporting Question and Answer:

How is the surface area of a cylinder calculated?

The surface area of a cylinder is the sum of the areas of its curved surface and two circular bases. It can be calculated using the formula:

A = 2πrh + 2π\(r^{2}\)

where "r" is the radius of the circular base, "h" is the height of the cylinder, and π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.

The first term, 2πrh, represents the area of the curved surface of the cylinder, while the second term, 2π\(r^{2}\), represents the combined area of the top and bottom circular bases.

Body of the Solution: Let the height and radius of cylinder A be "h" and "r" respectively. Then, the height and radius of cylinder B are "2h" and "R" respectively, since cylinder B has twice the height of cylinder A but the same radius.

The total surface area of a cylinder is given by the formula:

Area = 2πrh + 2π\(r^{2}\)

For cylinder A, we know that the surface area is 180, so we can substitute the values and solve for "r" as follows:

180 = 2πrh + 2π\(r^{2}\)

90 = πrh + π\(r^{2}\)

We can rearrange this equation to solve for r:

r² + rh - 90/π=0

Using the quAdratic formula,we get:

r = (-h ± √((h)² + 4(90/π)))/2

r = -h/2 ± √(h² + 4(90/π))/2

Now we have an expression for r in terms of h . We can use this expression to find the radius of cylinder B, since we know that cylinder B has twice the height of cylinder A.

R = 2r= -h ± √(h² + 4(90/π))

We can use this expression to find the surface area of cylinder B:

Surface area of cylinder B = 2πR² + 2πR(2h)

Surface area of cylinder B= 2π( -h ± √(h² + 4(90/π)))² + 4πh( -h± √(h² + 4(90/π)))

We can use the value we found for 2h using the quadratic formula in the expression to get:

Surface area of cylinder B = 476.7 square units (rounded to one decimal place)

Therefore, the total surface area of cylinder B is approximately 476.7  square units.

Final Answer: Therefore, the total surface area of cylinder B is approximately 476.7  square units.

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Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

Let's find the mean, median, and mode for each set of numbers:

Set: 40, 38, 29, 34, 37, 22, 15, 38

Mean: To find the mean, we sum up all the numbers and divide by the total count:

Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125

Median: To find the median, we arrange the numbers in ascending order and find the middle value:

Arranged set: 15, 22, 29, 34, 37, 38, 38, 40

Median = (29 + 34) / 2 = 63 / 2 = 31.5

Mode: The mode is the number(s) that appear(s) most frequently in the set:

Mode = 38 (appears twice)

Set: 26, 32, 12, 18, 11, 14, 21, 12, 27

Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222

Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32

Median = 18

Mode: No mode (all numbers appear only once)

Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15

Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611

Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15

Median = 8

Mode: Mode = 8 (appears 4 times)

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

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