First, complete the sentence to show how the figure can be decomposed
into triangles and rectangles with the fewest number of pieces.
Then find the area of the divisions.

All five answers are (1) 285.7 ft2 (2) 1056 cm2 (3) 105 mm3 (4) 108 cm3 (5) 628 mm3 in accordance with the provided assertion.

In mathematics, volume refers to the amount of space present within a specific 3D object. As an example, the dimensions of a fish aquarium are three feet long, one foot broad, and two feet height.

By increasing the length, width, and height, or 3x1x2, which also equals six, the volume is determined. Consequently, the fish tank has a 6 cubic foot size.

(1) The lateral area of a cone can be calculated using the formula L = πrℓ, where r is the radius and ℓ is the slant height. Using the given values, we have:

L = π(7)(13) ≈ 285.7 ft²

Rounding to the nearest tenth, the answer is 285.7 ft².

(2) A = B + (1/2)Pl, where B is the base area, P is the base circumference, l is the slope height, and A is the surface area, can be used to determine the surface area of a square pyramid. Since the pyramid's foundation is square, we have:

B = (24)² = 576 cm²

The perimeter of the base is 4 times the base length, so we have:

P = 4(24) = 96 cm

Now we can use the formula to find the surface area:

A = 576 + (1/2)(96)(16) = 1056 cm²

Therefore, the surface area of the square pyramid is 1056 cm².

(3) The volume of a rectangular prism can be calculated using the formula V = lwh,

where

l is the length

w is the base

h is the height

V is the volume.

Substituting the given values, we have:

V = (5)(7)(3) = 105 mm³

Therefore, the volume of the rectangular prism is 105 mm³.

(4) The formula V = (1/3)Bh, where B is the base area, h is the height, and V is the volume, can be used to determine the volume of a square pyramid. Since the pyramid's foundation is square, we have:

B = (9)² = 81 cm²

Now we can use the formula to find the volume:

V = (1/3)(81)(4) = 108 cm³

Therefore, the volume of the square pyramid is 108 cm³.

(5) The volume of a cone can be calculated using the formula V = (1/3)πr2h, where r is the radius, h is the height, and V is the volume. Substituting the given values, we have:

V = (1/3)π(10)²(6) ≈ 628.3 mm³

Rounding to the nearest whole number, the answer is 628 mm³.

Therefore, the volume of the cone is 628 mm³.

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The conversion of 72 kilograms is equal to approximately 158.73 pounds (rounded to two decimal places).

A kilogram (symbol: kg) is the base unit of mass in the International System of Units (SI).

It is currently defined based on the fixed numerical value of the Planck constant, h,

Which is equal to 6.62607015 × 10-34 in the units of J·s.

A pound (symbol: lb) is a unit of mass used in the imperial and US customary systems of measurement.

The international avoirdupois pound (the common pound used today) is defined as exactly 0.45359237 kilograms.

To convert 72 kilograms to pounds,

You can use the following formula:

1 kilogram = 2.20462 pounds

Multiplying both sides by 72,

We get:

72 kilograms = 72 x 2.20462 pounds

Simplifying the calculation,

We get:

72 kilograms = 158.73264 pounds

Therefore,  the conversion of 72 kilograms is equal to approximately 158.73 pounds (rounded to two decimal places).

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The probability that the moderate number of moths in 60 traps is more significant than 0.4 is approximately 0.9738 or 97.38%.

(a).

The mean number of moths =  60 traps

Now, the properties of normal distribution and central limit theorem are used.

mean of the individual moth counts = 0.5.

The standard deviation = the Standard deviation of the individual moth counts, divided by the square root of the sample size.

standard deviation = (0.7 / [tex]\sqrt{60}[/tex])

standard deviation = 0.0905

the mean number of moths and standard deviation of the average number of moths in 60 traps are 0.5 and 0.0905.

(b) .

By using the central limit theorem

The average number of moths in 60 traps = 0.4

The z-score formula is to be calculated by using:

Z = (sample mean - population mean) / (standard deviation/sqrt (sample size))

Substituting the given values, we have:

Z = (0.4 - 0.5) / (0.7 / sqrt(60))

Z = -1.94

The probability of a Z-score greater than -1.94 is approximately 0.9738.

Hence, we can conclude that the probability that the average number of moths in 60 traps is greater than 0.4 is approximately 0.9738.

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Answer:

Step-by-step explanation:

The function to represent the population of bacteria after t days can be written as:

P(t) = P0 * (1 + r)^t

where P0 is the initial population (7500), r is the daily growth rate (14% = 0.14), and t is the number of days.

Substituting the values, we get:

P(t) = 7500 * (1 + 0.14)^t

Simplifying, we get:

P(t) = 7500 * 1.14^t

To find the percentage rate of change per hour, we need to convert the daily growth rate to an hourly growth rate. Since there are 24 hours in a day, the hourly growth rate, denoted by h, is given by:

h = (1 + r)^(1/24) - 1

Substituting the value of r, we get:

h = (1 + 0.14)^(1/24) - 1

= 0.005521

So, the percentage rate of change per hour is:

h * 100% = 0.5521%

Rounding to the nearest hundredth of a percent, we get:

h * 100% ≈ 0.55%

Note that:

The vertical angles are given as follows:

∠CFB vs ∠AFD

∠CFA vs ∠DFB

The complimentary pair of angles is :

∠CFE vs ∠EFA.

Complementary angles are a pair of two angles whose sum equals 90 degrees. In other words, when two angles are complementary, one angle is said to be the complement of the other.

For example, if angle A and angle B are complementary, then A + B = 90 degrees.

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Full Question:

See the attached

As per measurement, 30 inches is equivalent to 2.5 feet.

Measurement is an essential aspect of our daily life, and it helps us to quantify things precisely. The measuring units are used to determine the size, weight, or any physical quantity of an object. It is essential to know the conversions between the measuring units to make the necessary calculations accurately.

In this context, let's discuss the conversion of inches to feet.

Inches and feet are two common units of measurement used for length or distance. Inches are the smaller unit, and feet are the larger unit. One foot is equivalent to 12 inches. Therefore, to convert inches to feet, we divide the given number of inches by 12.

Let's consider we need to convert 30 inches to feet.

30 inches / 12 inches per foot = 2.5 feet

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The scale factor used to produce Figure 2 from Figure 1 is 5 over 3.

Scale factor is a numerical value used to represent the proportional change between two similar objects. This value is often used to compare the size of objects in different measurements, such as inches to millimeters or feet to meters. Furthermore, the scale factor can be used to find the area, volume, or surface area of an object, as the measurements are proportional to the scale factor. This is especially useful when objects are enlarged or reduced, as it allows for the accurate calculation of the changed measurements.

This is because Figure 2 has legs that are 5 units long and Figure 1 has legs that are 3 units long. The ratio of the legs of Figure 2 to the legs of Figure 1 is 5/3, which is the scale factor used to produce Figure 2 from Figure 1.

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The correct answer is C, 3

The question is, "Jada earns twice as much money per hour as Diego. Diego earns twice as much money per hour as Lin. Select all the graphs that could represent how much Jada, Diego, and Lin earn for different amounts of time worked."

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David has drawn a total of 177 cm of lines.

We can use the Pythagorean theorem, which tells us that in a right triangle, the square of the length of the hypotenuse (the diagonal line) is equal to the sum of the squares of the lengths of the other two sides (the lines along the long edge and the width).

In this case, the length of the hypotenuse is the distance from the starting corner to the end of the diagonal line, which we can calculate as follows:

d = √(77² + 36²) ≈ 85.99 cm

Therefore, David has drawn a total of 77 cm + 36 cm + 85.99 cm = 198.99 cm of lines. However, we should subtract the length of the starting corner to the end of the first line, which is 77 cm, since it was counted twice (once as part of the diagonal line and once as part of the line along the long edge).

So, the total length of lines that David has drawn is 77 cm + 36 cm + 85.99 cm - 77 cm = 177 cm.

Pythagoras' theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

This can be expressed as:

a² + b² = c²

where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.

Pythagoras' theorem can be used to solve a variety of problems involving right triangles, such as finding the length of a missing side or determining whether a triangle is a right triangle. It is also the basis for the distance formula in two and three-dimensional Euclidean space.

Pythagoras' theorem has applications in many fields, including physics, engineering, and computer graphics, and it is one of the most important and widely used theorems in mathematics.

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Answer: 131.39

Step-by-step explanation:

the expression equivalent to 7k+13-4K+10+5k-6 is 8k + 17. correct option: (B) 14+72

How to do and what is expression equivalent?

Simplifying the expression by combining like terms, we get:

7k + 13 - 4k + 10 + 5k - 6

= (7k - 4k + 5k) + (13 + 10 - 6)

= 8k + 17

Therefore, the expression equivalent to 7k+13-4K+10+5k-6 is 8k + 17. correct option would be : (B)

Two expressions are equivalent if they represent the same mathematical value for all possible values of the variables. In other words, if you substitute any value for the variables in both expressions, the resulting values will be the same.

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Answer:  $29830

Step-by-step explanation:

Every year the amount he has (in the bank lets say) goes up by 5.6%. This can be explained as multiplying by 1.056, as it basically take the one and adds 0.056 which is equivalent to 5.6%. If we are trying to find the end value after 19 years, we would have multiplied our original value by 1.056, 19 times. We can find how much that is by calculating 1.056 to the power of 19, which equals 2.8159. This is how much the money would have increased over the 19 years. Dividing the final value by 2.8159 will get us the original value. $84,000 / 2.8159 = ~ $ 29830. I have already rounded up so this should be the answer.

It has to be smaller than $7800

I am not sure if this answer is right.

Answer:

7800-936=6864

Step-by-step explanation:

x/12 7800/100

100x=93600

936

Samuel found the difference between the polynomials is 8x² + 6y² + 6x.

What is the polynomials?

An expression that contains coefficients, variables, non-negative integer exponents, and constants is known as a polynomial.

To find the difference between the polynomials, we need to subtract the second polynomial from the first polynomial.

(15x² + 11y² + 8x) - (7x² + 5y² + 2x)

First, we can simplify the coefficients of the like terms by subtracting them:

15x² - 7x² + 11y² - 5y² + 8x - 2x

Simplifying further, we get:

8x² + 6y² + 6x

Therefore, the difference between the polynomials is 8x² + 6y² + 6x.

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Answer:

False, it took her 2 hours and 24 minutes

Step-by-step explanation:

The equation 12h = 5 is not correct because it would mean that Helen completed her run in 5 hours, which is not possible since she only ran 12 miles.

To find the correct number of hours, we can use the formula:

Distance = rate x time

Where distance is the total distance Helen ran (12 miles), rate is her speed (5 miles per hour), and time is the number of hours it took her to run.

We can rearrange the formula to solve for time:

Time = distance / rate

Plugging in the values we have:

Time = 12 miles / 5 miles per hour

Simplifying, we get:

Time = 2.4 hours

Therefore, it took Helen 2.4 hours (or 2 hours and 24 minutes) to complete her run.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

The binomial probability formula calculates the probability of obtaining a specific number of successes in a fixed number of independent trials, each with the same probability of success

The binomial probability formula is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, each with the same probability of success.

The formula is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where:

P(X=k) is the probability of obtaining k successes

n is the total number of trials

p is the probability of success in each trial

(n choose k) represents the number of ways to choose k successes from n trials, and is calculated as n! / (k! * (n-k)!)

Therefore, the uses of binomial probability formula has been explained

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The binomial probability formula is widely used in various fields, including statistics, probability theory, and genetics, to analyze and predict outcomes in situations with binary events.

The binomial probability formula is used to calculate the probability of obtaining a specific number of successes in a fixed number of independent Bernoulli trials. In other words, it helps us determine the likelihood of achieving a certain outcome in a series of experiments, where each experiment can result in one of two possible outcomes (success or failure).
The formula is given by P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where P(X=k) represents the probability of getting exactly k successes, n is the total number of trials, p is the probability of success in a single trial, and (n choose k) is the binomial coefficient.
For example, let's say you flip a fair coin 10 times and want to know the probability of getting exactly 7 heads. In this case, n = 10 (number of trials), k = 7 (number of successes), and p = 0.5 (probability of heads). Plugging these values into the binomial probability formula will give you the desired probability.
The binomial probability formula is widely used in various fields, including statistics, probability theory, and genetics, to analyze and predict outcomes in situations with binary events.

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To find the weight of a baby at age 5 months, we can substitute x=5 in the given function:

f(5) = 1.5(5) + 7

f(5) = 7.5 + 7

f(5) = 14.5

Therefore, the weight of a baby at age 5 months is 14.5 pounds. Answer: D.

Answer:

The period of a spring-mass system is the time it takes for the weight to complete one full cycle of motion (i.e., go up and down once).

In this problem, we are told that the weight goes up and down 60 times in 90 seconds. Therefore, the time it takes for the weight to complete one cycle of motion is:

90 seconds / 60 cycles = 1.5 seconds/cycle

To find the period of the motion in minutes, we need to convert the time per cycle from seconds to minutes:

1.5 seconds/cycle * 1 minute/60 seconds = 0.025 minutes/cycle

Therefore, the period of the motion is 0.025 minutes/cycle or 25 milliseconds/cycle. In this case, it is 1/40 minutes.

Answer: i think B.1/40 minutes

Step-by-step explanation: hope this helps0^0

Another name for a regression line is Least squares line

Answer:Best-Fit-Line

Step-by-step explanation:

--Or line of best fit

HOP THIS HELPS!!!

The side lengths that cannot form a triangle are: 2 ft, 3 ft, 8 ft.

The letter "F" has one reflectional symmetry. This symmetry can be seen by drawing a line that divides the letter "F" into two equal parts, such that the left and right sides are mirror images of each other.

This line of symmetry would run vertically down the middle of the letter "F", passing through the crossbar. The letter "F" has one reflectional symmetry. A reflectional symmetry is a type of symmetry where one half of an object is a mirror image of the other half. In the case of the letter "F", a line can be drawn vertically down the middle of the letter, passing through the crossbar, such that the left and right sides of the letter are mirror images of each other. This line is called a line of symmetry. Therefore, the letter "F" has one reflectional symmetry.

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The figure which is missing in the question is attached here-with the answer

From the given information the quadrilateral QUAD is a rectangle because opposite sides are of the same length and the adjacent sides are perpendicular to each other.

What is a quadrilateral?

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry. A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees. The diagonals are obtained by joining the opposing vertices of the quadrilateral.

From finding the lengths of the sides of the quadrilateral, we can see that two sides of the quadrilateral have the same length and the other two sides have the same length.

QU

length = √20

slope = 2

UA

length = √5

slope = -1/2

AD

length = √20

slope = 2

DQ

length = √5

slope = -1/2

Now the lines QU and UA are perpendicular to each other since the product of slopes is -1.

So QU ⊥ UA

similarly,

AD ⊥ UA

AD ⊥ DQ

Also, the lines QU and AD as well as the lines UA and DQ are parallel to each other as the slopes are the same.

Therefore from the given information the quadrilateral QUAD, is a rectangle because opposite sides are of same length and the adjacent sides are perpendicular to each other.

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Department of Education is usually determined by the sales tax rate and the amount of the purchase.

The main sources of funding for the Department of Education come from income taxes and sales taxes.

The amount of income taxes collected by the Department of Education is usually determined by the tax code and the amount of income earned.

In addition to income taxes and sales taxes, the Department of Education also collects taxes from other sources. These include inheritance taxes, property taxes, and excise taxes. Inheritance taxes are taxes collected on the transfer of property from one person to another upon death.

Property taxes are taxes collected on the value of real estate, such as land and buildings. Excise taxes are taxes collected on the purchase of certain items, such as cigarettes and alcohol.

By understanding how taxes work, you can locate the Department of Education funding in your tax breakdown.

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The required conversion of 10 miles per hour to kilometers per hour is given by 16.0934 kilometers per hour.

Conversion of miles to kilometer is :

One miles is equal to 1.60934 kilometers

Now substitute the required value we get,

10 miles = ( 10 ) × ( 1.60934 ) kilometers

⇒ 10 miles = ( 10 × 1.60934 ) kilometers

⇒ 10 miles = 16.0934 kilometers

Required conversion is :

10 miles per hour = 16.0934 kilometers per hour

Therefore, converted value of 10 miles per hour is equal to 16.0934 kilometers per hour .

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Answer:

x² + y² = z²

Step-by-step explanation:

The side of the bottom square is y.

The side of the left square is x.

The side of the right square is z.

These sides are also the legs and hypotenuse of the right triangle.

We use the Pythagorean Theorem.

x² + y² = z²

Answer:

a) r = 2

b)
GP a₆ = 384

AP a₆ = 32

Step-by-step explanation:

First term a₁ = 12 for both progressions

r = common ratio, d = common difference

nth term of geometric progression = a₁ x rⁿ⁻¹
nth term of arithmetic progression = a₁ + (n - 1)d

Second term of GP = Fourth term of AP

=> 12r¹ = 12 + 3d

==> 12r = 12+ 3d  (1)

Third term of GP = 10th term of AP

=> 12r² = 12 + 9d (2)

3 x (1) => 3(12r = 12 + 3d) => 36r  = 36 +  9d (3)

(2) - (3) gives12r² -36r = 12 - 36
12r² - 36r = 12 + 9d - (36 + 9d)

12r² -36r = -24

12r² -36r + 24 = 0

Dividing by 12 gives
r² - 3r + 2= 0

We can factor r² - 3r + 2 as (r - 1)(r-2)

r² - 3r + 2= 0
=>  (r - 1)(r-2) = 0

=> r = 1 or r = 2

r cannot be 1 since all terms of the GP will be equal with a common ratio of 1

Therefore r = 2  (Part a)

Using equation (1) we get:
12r = 12+ 3d
12 x 2 = 12 + 3d

24 = 12 + 3d

3d = 24 - 12 = 12

d = 12/3 = 4

So the common ratio, r,  is 2. Common difference d = 4

6th term of GP =12 x r⁵ =  12 x 2⁵ = 12 x 32 = 384

6th term of Ap = 12 + 5d = 12 + 5(4) = 12 + 20 = 32

m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.

Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.

To determine the unknown angle measures of △DEF, we can use the fact that the sum of the angles of a triangle is 180°. Thus, if we know two angle measures in the triangle, we can use them to calculate the third.

Let's denote the two known angle measures as m∠D and m∠F. We can use the following equation to solve for the unknown angle measure:

m∠D + m∠F + m∠E = 180°

We can rearrange the equation to solve for m∠E:

m∠E = 180° - m∠D - m∠F

Therefore, once we know the measures of m∠D and m∠F, we can calculate the measure of m∠E.

For example, if m∠D = 40° and m∠F = 65°, then the measure of m∠E would be:

m∠E = 180° - 40° - 65° = 75°

Therefore, m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.

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Step-by-step explanation:

36 because since theres 36 people each person gets one for each

60 INCH TV MATE 60

the answer is 60 inch its a trick question just find out the inches there trying to trick you its 60 inch mate enjoy <3 Mark me brainliest

Answer:

1. Tv Length: 12 in

2. Tv Width: 5 in

3. Sorry I don't understand 3

4. I have a 60-inch Tv.

Hope this helps!

I