Suppose that in 6 minutes, 54 gallons of water came out of a pipe. What was the rate in gallons per minute?

The expression 2ab + [tex]c^2[/tex]  represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.

The equivalent expression [tex]a^2 +b^2+2ab[/tex] use the length of the figure to represent the area.

[tex]2ab +c^2=a^2+b^2+2ab[/tex]

Subtracting 2ab from both sides

[tex]c^2=a^2+b^2[/tex]

Figure of a square with some shaded triangles.

Area of the triangle formula is 1/2 times base times height

base =a and height =a

Area of one triangle = 1/2ab

There are 4 shaded triangles

Area of 4 shaded triangles = 4 x 1/2ab

Area of the square = side times side

Now we find the area of outer square. side length is a+b

Area of outside square = (a + b)(a + b) = [tex](a+b)^2[/tex] = [tex]a^2 +b^2+2ab[/tex]

Using the length of the figure to represent the area.

Thus, now set both the areas equal to each other.

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Your question seems incomplete, the probable complete question is

The area of the shaded region, obtained by finding the area of the composite figure is the difference between the area of the square and the area of the triangle and semicircle composite figure.

5. The area of the shaded region is about 205.8 cm squared. The correct option is therefore;

D. 205.8 cm squared

A composite figure is a figure that is composed two or more regular figures.

The area of the shaded region can be found by considering the unshaded region as a composite figure consisting of a triangle and a semicircle.

The area of the unshaded semicircle = π × 24²/8 = 72·π

The area of the triangular part of the unshaded region = (1/2) × 24 × 12 = 144

Area of the square = 24 × 24 = 576

Therefore, the area of shaded region = 576 - (72·π + 144) ≈ 205.8

The area of the shaded region ≈ 205.8 cm squared

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Answer:

1836.50 square inches of the bulletin board is NOT covered with art work.

Step-by-step explanation:

The question focuses on the area covered by the paintings and the board, since area is defined as:  the amount of space enclosed within the boundaries of a flat, two-dimensional shape, such as a square, circle, or rectangle.

Step 1:  First, we need to know the total area of the five paintings.  

A = lw, where

We can allow 8.5 to be the length and 11 to be the width:

A = 8.5 * 11

A = 93.5 square inches

Multiplying 93.5 by 5 shows us the the total area covered by the five pieces of artwork is 467.50 square inches as 93.5 * 5 = 467.50

Step 2:  Now we need to find the area of the bulletin board.

A = s^2, where

48 is s in the area formula:

A = 48^2

A = 2304 square inches

Thus, the area of the bulletin board is 2304 square inches.

Step 3:  Finally, subtracting the total area of the five pieces of artwork from the area of the bulletin board will tell us how much of the bulletin board is NOT covered with art work:

2304 - 467.50 = 1836.50 square inches

Thus, 1836.50 square inches of the bulletin board is not covered with art work.

An equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4,-3) is: C. y + 3 = 1/4(x + 4) .

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-3 - 1)/(0 + 1)

Slope (m) = -4

m₁ × m₂ = -1

-4 × m₂ = -1

m₂ = -1/-4

Slope, m₂ = 1/4

At data point (-4, -3) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 3 = 1/4(x + 4)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The best representation of the mean number of sports played by middle school students is 2.75 sports and the MAD is about 0.84 sports.

To find the best representation of the mean number of sports played by middle school students, we need to calculate the median of the given data.

The median represents the central tendency of the data and is less affected by extreme values.

Arranging the means of the samples in ascending order, we have:

1, 1, 2, 2.5, 3, 3, 3.5, 4

Since there are eight values, the median will be the average of the fourth and fifth values:

(2.5 + 3) / 2 = 2.75

Variability in the Distribution

Summing up the absolute deviations:

1.75 + 1.75 + 0.75 + 0.25 + 0.25 + 0.25 + 0.75 + 1.25 = 6.75

To find the MAD, we divide the sum of the absolute deviations by the total number of data points:

MAD = 6.75 / 8 = 0.84

Therefore, the MAD is about 0.84 sports.

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Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.

We have,

A postulate is a statement or proposition that is accepted as true without proof.

It is an assumption or starting point in a logical argument that is considered to be self-evident or evident based on previous experience or observation.

In mathematics,

Postulates are used to define the basic concepts and axioms that form the foundation of a particular system of thought.

They are often used as the starting point for deriving other mathematical concepts and theorems.

Postulates are also known as axioms or assumptions.

Thus,

Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.

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Answer:

  (3) 60°

Step-by-step explanation:

You want the measure of the third angle (E) in triangle EFG, given that two of the angles have measures 75° (angle F) and 45° (angle G).

The angle sum theorem tells you the sum of angles in any triangle is 180°. This means ...

  E + F + G = 180

  E + 75 + 45 = 180

  E = 60 . . . . . . . . . . . . . subtract 120 from both sides and simplify

The measure of angle E is 60°.

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Answer:

Step-by-step explanation:

The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.

The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.

This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.

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In solving the sequence using the provided rules, we have:

A) Sequence 1: 13, 16, 19, 22, 25.

    Sequence 2: 15, 13, 11, 9, 7.

    Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B) Sequence 1: 1, 5, 17, 53, 159.

Sequence 2:  6, 15, 33, 69, 141.

Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (159, 141).

Using the given rules, we can solve the sequence as follows:

A. Rule 1: Add 3 starting from 13

The first five terms in Sequence 1 would be:

13, 13 +3 = 16, 16 +3 = 19, 19 + 3 = 22, 22 + 3 = 25.

13, 16, 19, 22, 25

Using Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9

The first five terms in Sequence 2 would be:

25 - 2(5) = 25 - 10 = 15

25 - 2(6) = 25 - 12 = 13

25 - 2(7) = 25 - 14 = 11

25 - 2(8) = 25 - 16 = 9

25 - 2(9) = 25 - 18 = 7

The ordered pairs for each numerical pattern would be:

(13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B.  Rule 1: Multiply by 3, then add 2, starting from 1

The first five terms in Sequence 1:

1, (1 * 3) + 2 = 5, (5 * 3) + 2 = 17, (17 * 3) + 2 = 53, (53 * 3) + 2 = 159

Using Rule 2: Multiply by 2, then add 3, starting from 6

The first five terms in Sequence 2:

6, (6 * 2) + 3 = 15, (15 * 2) + 3 = 33, (33 * 2) + 3 = 69, (69 * 2) + 3 = 141

The ordered pairs for each numerical pattern would be:

(1, 6), (5, 15), (17, 33), (53, 69), (159, 141)

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Descartes must be thinking of the number 0.

Now, Let's call the number Descartes is thinking of "x".

Hence, According to the problem, if Descartes multiplies "x" by 9, he gets "x" back. In other words, 9 times "x" is equal to "x".

So we can write this as an equation:

⇒ 9x = x

Now we need to solve for "x". We can start by subtracting "x" from both sides of the equation:

⇒ 9x - x = 0

⇒ 8x = 0

divide both sides by 8 to get:

⇒ x = 0

Thus,  Descartes must be thinking of the number 0.

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The vector representing the radius at the given position is  -13i - j  - 5k.

The magnitude of the radius vector is 13.96 units.

The vector representing the radius at the given position is calculated as follows;

center of the sphere = (11, 5, 2)

The point of the radius = ( -2, 4, -3 )

The radius vector = ( - 2 - 11) , ( 4 - 5), ( -3 - 2)

r = ( -13, - 1, - 5)

r = -13i - j  - 5k

The magnitude of the radius vector is calculated as follows;

| r | = √ x² + y² + z²

where;

| r | = √[ ( -13²) + ( -1)² + ( -5 )² ]

| r | = √ ( 169 + 1 + 25 )

| r | = √ ( 195 )

| r | = 13.96 units

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The approximate height difference between the birdhouse and the tree house is 3 ft.

It is less than the approximate difference in height between the swing set and the tree house.

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

We have:

height of birdhouse = 14[tex]\frac{9}{16}[/tex] ft

height of tree house = 11[tex]\frac{13}{16}[/tex] ft

Thus, the approximate height difference between the birdhouse and the tree house will be:

14[tex]\frac{9}{16}[/tex] ft - 11[tex]\frac{13}{16}[/tex]  = 2[tex]\frac{3}{4}[/tex] ft

                   = 2.75 ft

                  = 3 ft

To determine if it is greater than or less than the approximate difference in height between the swing set and the tree house, we have to find the approximate difference in height between the swing set and the tree house. That is:

height of swing set = 8[tex]\frac{1}{4}[/tex] ft

height of tree house = 11[tex]\frac{13}{16}[/tex] ft

difference = 11[tex]\frac{13}{16}[/tex] - 8[tex]\frac{1}{4}[/tex]

                    = 3[tex]\frac{1}{2}[/tex]

                    = 3.5

                    = 4 ft

Therefore, it is less than the approximate difference in height between the swing set and the tree house

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When a dilation is performed on a triangle, the angles and side lengths of the preimage and image are related in a specific way. The correct answer is B. The angles are congruent, and the side lengths are proportional.

In a dilation, each corresponding angle of the preimage and image triangles is congruent. This means that if an angle in the preimage triangle measures 60 degrees, the corresponding angle in the image triangle will also measure 60 degrees.

However, the side lengths of the preimage and image triangles are not necessarily congruent. Instead, they are proportional. This means that the ratio of corresponding side lengths remains constant throughout the dilation. For example, if one side of the preimage triangle is twice as long as another side, the corresponding side in the image triangle will also be twice as long as its corresponding side.

It's important to note that the center of dilation and the scale factor determine the specific proportions between the side lengths. The scale factor represents the ratio of corresponding side lengths in the preimage and image triangles.

Therefore, in a dilation, the angles are congruent, and the side lengths are proportional.

The right answer is B. The angles are congruent and the side lengths are proportional.

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Answer:

Să rezolvăm această problemă pas cu pas. Să denotăm vârsta Denisei ca D, vârsta mamei sale ca M și vârsta tatălui ei ca F. Din informațiile date, putem scrie următoarele ecuații:

M = D + 27 (Denisa are cu 27 de ani mai puțin decât mama ei) F = M + 1 (mama Denisei are cu un an mai puțin decât tatăl ei) F = 5D (Denisa este de cinci ori mai tânără decât tatăl ei)

a) Din ultima ecuație, putem vedea că Denisa este F - D cu ani mai tânără decât tatăl ei. Înlocuind F cu 5D, înțelegem că Denisa este 5D - D = 4D cu ani mai tânără decât tatăl ei.

b) Pentru a determina vârsta Denisei, putem rezolva sistemul de ecuații. Din prima ecuație, obținem acel M = D + 27. Înlocuind acest lucru în a doua ecuație, obținem acel F = D + 27 + 1 = D + 28. Înlocuind acest lucru în a treia ecuație, obținem acel D + 28 = 5D. Rezolvând pentru D, obținem acel D = 7.

Deci Denisa are 7 ani.

Answer:

Denisa are 7 ani

Step-by-step explanation:

Except You can invest your 401(k) into a wider variety of asset types than you can with an IRA. All are the advantages. Option B

A) You don't pay taxes on your investments' growth each year: One of the main advantages of a 401(k) plan is the tax advantage it provides.

Contributions to a traditional 401(k) are made on a pre-tax basis, meaning that the money you contribute is not subject to income tax. Additionally, the growth of investments within the 401(k) account is tax-deferred until you make withdrawals in retirement.

C) Your employer may match some of your 401(k) contributions: Many employers offer a matching contribution to their employees' 401(k) plans. This means that for every dollar you contribute to your 401(k), your employer will contribute a certain percentage, up to a specified limit.

D) You can contribute more money into a 401(k) than into an IRA: 401(k) plans generally allow for higher contribution limits compared to Individual Retirement Accounts (IRAs).

In 2021, the annual contribution limit for a 401(k) is $19,500 (with an additional $6,500 catch-up contribution for individuals aged 50 or older).

In contrast, the annual contribution limit for an IRA is $6,000 (with an additional $1,000 catch-up contribution for individuals aged 50 or older). The higher contribution limits of a 401(k) allow individuals to save more for retirement on a tax-advantaged basis.

In summary, the correct answer is B. The ability to invest in a wider variety of asset types is not an advantage of a 401(k) plan. However, the other options listed (A, C, and D) are all advantages of a 401(k) plan.

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Answer:

21

Source:

trust me bro

The number 1.3 is both a rational and an irrational number.

The number 1.3 is a rational number because it can be expressed as the quotient of two integers, namely 13/10.

The number 1.3 an irrational number because it cannot be expressed as the ratio of two integers, without repeating or terminating decimals, and its decimal representation goes on forever without repeating.

So we can conclude that the number 1.3 is both rational and irrational number.

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If a top travels 8 centimeters each time it is spun and it is spun 7 times, the total distance it travels is 56 centimeters.

The total distance is determined by multiplication of the distance traveled per spin and the number of spins.

Multiplication involves the multiplicand, the multiplier, and the product.

The traveling distance per spun = 8 centimeters

The number of spinning of the top = 7 times

The total distance = 56 centimeters (8 x 7)

Thus, using multiplication, the total distance the top travels after the 7th spin is 56 centimeters.

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In a case whereby a boat travels with velocity vector (25, 25√3) the directional bearing of the boat is ON 30° E.

The given velocity vector are; 25 and  25√3)

horizontal  components =25

vertical components =25√3

Then the angle

Tan(θ) = {vertical component / horizontal component }

= 25√3 / 25

= √3 / 1

= √3

Tangent √3= 60 degrees, Then the directional bearing of angle 60 degrees is 30° E

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Based on the given values, the value of A is given as 5

To find the value of A, we need to solve the equation for the expected value, E(X) = 5.75, using the provided probabilities and x values.

The expected value formula is:

E(X) = Σ[x * P(x)]

Plugging in the given values:

5.75 = (4 * 0.15) + (A * 0.55) + (8 * 0.3)

To solve for A, we can first simplify the equation:

5.75 = 0.6 + 0.55A + 2.4

Now, combine constants and subtract from the left side:

2.75 = 0.55A

Finally, divide by 0.55 to find the value of A:

A = 2.75 / 0.55 ≈ 5

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Answer:

P(d) = 0; 14 days

Step-by-step explanation:

First part of answer:  Setting P(d) = 0 would allow us to find the day Sandra finishes since P represents the pages remaining the book will be finished when there are 0 pages left to read.

Second part of answer:  We can solve the equation P(d) = 0 = 420 - 30d to see how it would take 14 days to finish the book and have 0 pages left to read:

Step 1:  Subtract 420 from both sides:

(0 = 420 - 30d) - 420

-420 = -30d

Step 2:  Divide both sides by -3 to solve for d:

(-420 = -30d) / -30

14 = d

Answer:

Step-by-step explanation:

The exact solutions for the equation 2sec²x - tan²x = -1 in radians are:

x = π/4 + πk, where k is an integer

x = 3π/4 + πk, where k is an integer

These solutions represent all the values of x that satisfy the given equation.

The similar triangles for this problem are given as follows:

RST and VUT.

Then the measure VT is given as follows:

VT = 5.4 units.

Similar triangles are triangles that share these two features listed as follows:

Hence the similar triangles for this problem are given as follows:

RST and VUT.

The proportional relationship for the side lengths is given as follows:

6/14 = (x + 2)/(4x - 1).

Applying cross multiplication, the value of x is obtained as follows:

14(x + 2) = 6(4x - 1)

14x + 28 = 24x - 6

10x = 3.4

x = 3.4.

Then the length VT is given as follows:

VT = 3.4 + 2

VT = 5.4 units.

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The decreasing interval of function is (-∞ , 0) .

The decreasing interval in the function is said to be when the value of the derivative f' (x) ≤ 0 .

Decreasing interval is when f(x) is decreasing as x is increasing.

Here the graph is of a parabola the equation of a upper parabola is

f(x) = x²

Now doing derivation of the parabola equation, we get

f'(x) = 2x

As for decreasing interval we will put

f'(x) ≤ 0

Putting the value of f'(x) in the equation

2x ≤ 0

x ≤ 0

Decreasing interval (-∞ , 0)

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The probabilities are: 1a) P(A) = 12, 1b)P(B) = 1.055 + 1,160 = 1,161.055 . 1c) P(A and B) = P(AB) = 1.055

P(A) = 12

P(B) = 1.055 + 1,160 = 1,161.055

P(A and B) = P(AB) = 1.055

To determine if the events A and B are independent, we need to check if P(A and B) = P(A) * P(B).

P(A) * P(B) = 12 * 1,161.055 = 13,932.66

Since P(AB) = 1.055 is not equal to P(A) * P(B) = 13,932.66, the events A and B are not independent.

P(A | B) = P(AB) / P(B) = 1.055 / 1,161.055 ≈ 0.0009098

To convert this probability to a percentage, we multiply by 100:

Percentage chance = P(A | B) * 100 ≈ 0.0009098 * 100 ≈ 0.091%

Therefore, the company should report a percentage chance of approximately 0.091% to the person as an estimate of their risk of developing the disease based on the study.

The reasoning behind this estimation is that among those who have the genetic variation (B), the probability of having the disease (A) is approximately 0.0009098, which corresponds to 0.091% when expressed as a percentage.

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Movie B has approximately 25% more frames than Movie A.

For Movie A the duration is 100 minutes

Frame rate: 24 frames per second

Total frames in Movie A:

Total frames in Movie A = 100×60×24

Movie B:

Duration: 100 minutes

Frame rate: 30 frames per second

Total frames in Movie B:

Total frames in Movie B = 100 × 60 × 30

To find the percent more frames in Movie B compared to Movie A, we can use the following formula:

Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100

Total frames in Movie A = 100 × 60× 24

Total frames in Movie B = 100 ×60 × 30

Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100

Percent more frames = ((100 × 60× 30) - (100 × 60×24)) / (100 × 60× 24)×100

Percent more frames = (180,000 - 144,000) / 144,000 * 100

Percent more frames = 36,000 / 144,000 * 100

Percent more frames = 25%

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Given statement solution :- The correct proportion to make the best estimate for the number of beats in 60 seconds is:

A. 48/40 = 60/x

To make the best estimate for the number of beats in 60 seconds, we need to find the proportion that relates the beats per second in the given scenario to the desired duration of 60 seconds.

Let's set up the proportion using the given information:

Heart beats per second (beats/sec) = 48 beats / 40 seconds

We want to find the number of beats in 60 seconds (x beats / 60 seconds).

The correct proportion would be:

48 beats / 40 seconds = x beats / 60 seconds

Therefore, the correct proportion to make the best estimate for the number of beats in 60 seconds is:

A. 48/40 = 60/x

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Answer:

11.9 sq cm, answer choice C.

Step-by-step explanation:

Area of a parallelogram = base x height.

The base is 4.25 cm, and the height is 2.8 cm. The other measurement is not needed.

area = 4.25 x 2.8 = 11.9 sq cm, answer choice C.

Answer:

can i have a photo, please?

Step-by-step explanation: