The An eclateral triangular pyramid has a set height of 13 trenger base has a perimeter of 4.8 inches and an area of 13 spre me Find the surface area of the pyramid. C 1-0​

If the area of the base is 19. 6 ft^2 and the height of the pyramid is 11. 6 ft, the volume of the pyramid is approximately 79.1 cubic feet.

The formula for the volume of a pyramid is given by:

V = (1/3) × base area × height

In this case, we are given that the pyramid has a square base, so the base area is simply the area of a square with side length s:

base area = s^2 = 19.6 ft^2

We are also given the height of the pyramid:

height = 11.6 ft

Substituting these values into the formula for the volume of a pyramid, we get:

V = (1/3) × base area × height

= (1/3) × 19.6 ft^2 × 11.6 ft

≈ 79.1 ft^3 (rounded to the nearest tenth)

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Step-by-step explanation:

[tex]8 ^{2} [/tex]

is your answer please make me brainalist and keep smiling

8*8=64 then

8 is your answer

Answer: Square root of 64 is 8

The IQR in problem 3 is equal to 10.

The IQR tells us about the measure of the spread of the data contained in the box plot.

In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the given box plot, the five-number summary for the given data set include the following:

Mathematically, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):

Interquartile range (IQR) of data set = Q₃ - Q₁

Interquartile range (IQR) of data set = 75 - 65

Interquartile range (IQR) of data set = 10.

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The next four equivalent fractions of 8/13 are:

Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.

In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.

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Step-by-step explanation:

The only number there :   6/5 is the constant of proportionality

The value of x in the right angle triangle is 84.8 ft.

A triangle is said to have a right angle if one of its angles measures 90 degrees. This type of triangle is also referred to as a right triangle. The other two angles are acute, which means they have a degree value below 90. The hypotenuse, which is the triangle's longest side, is the side that faces the right angle. The legs, or catheti, are the other two sides.

Cos32 = x/100

x = 100 Cos 32

x = 100 * 0.848

x = 84.8 ft

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Answer:

1/2

Step-by-step explanation:

A fair coin have two sides,giving it a chance to land on any side while tossed.

Answer:

Theoretical probability: 0.19336

Chance of success: 19.34%

Hope this helps <3

To find an expression for the width of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

In this case, we know that the area is given by the expression +7x² + 11x + 2 and the length is given by the expression (x + 2). So we can substitute these values into the formula and solve for the width:

+7x² + 11x + 2 = (x + 2) x width

Expanding the right-hand side, we get:

+7x² + 11x + 2 = xwidth + 2width

Rearranging terms, we get:

+7x² + 11x + 2 - xwidth - 2width = 0

Factoring out the width, we get:

width*(x - 2) + 2*(x - 1) = 0

Dividing both sides by (x - 2), we get:

width = -2*(x - 1)/(x - 2)

Therefore, an expression for the width of the rectangle is:

width = -2*(x - 1)/(x - 2)

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Therefore, Mr. Evans' last week's pay was **$399.05** rather than $388.70.

The minimum wage is the lowest remuneration that businesses are required by law to give its workers. As of 2022, the federal minimum wage in the US is $7.25 per hour. State minimum wage rates must be higher than federal minimum wage rates in order for states and local municipalities to set their own minimum pay rates.

The steps below can be used to find out if Mr. Evans made $388.70 last week:

1. Divide the $9.20 hourly rate by 40 to determine the total salary for the first 40 hours of labour.

2. Multiply the $9.20 hourly rate by 1.5, and then multiply the resulting number by 2.25 to determine the total pay for the remaining 2.25 hours worked.

3. To determine your total salary for the week, add the two sums you calculated in stages 1 and 2.

These actions result in:

First 40 hours of pay: $9.20 multiplied by 40 equals $368.

Total salary for the final 2.25 hours is ($9.20 x 1.5) x 2.25, which comes to $31.05.

$368 plus $31.05 is $399.05 in total pay for the week.

Therefore, Mr. Evans' last week's pay was **$399.05** rather than $388.70.

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The total areas of each composite shape are:

1) 121 in²

2) 150m²

3) 14.03 ft²

4) 538.36 cm²

1) Formula for area of a rectangle is:

Area = Length * width

Thus:

Area of composite shape = (9 * 8) + (7 * 7)

= 121 in²

2) Formula for area of rectangle is:

Area = Length * width

Area = 12 * 5 = 60 m²

Area of triangle = ¹/₂ * base * height

Area = ¹/₂ * 12 * 15

Area = 90 m²

Area of composite shape = 60 + 90 = 150m²

3) Area of triangle = ¹/₂ * 3 * 7 = 10.5 ft²

Area of semi circle = ¹/₂ * πr²

= ¹/₂ * π * 1.5²

= 3.53 ft²

Total composite area = 10.5 ft² + 3.53 ft²

Total composite area = 14.03 ft²

4) Total composite area = (¹/₂ * π * 7.5²) + (30 * 15)

= 538.36 cm²

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Answer:  (x + 3) (x - 3) (x^2 + 9) (x^2 - 9)

Step-by-step explanation: We can use the difference of squares formula to factor x^4 - 81 as (x^2 + 9)(x^2 - 9).

Then, we can use the difference of squares formula again to factor x^2 - 9 as (x + 3)(x - 3).

Therefore, the complete factorization of x^4 - 81 is (x + 3)(x - 3)(x^2 + 9)(x^2 - 9).

Answer:

B,C,D

Step-by-step explanation:

Answer:

number 2

number 3

number 4

Step-by-step explanation:

Answer:

The square root of 40 is approximately 6.324555320336759.

Rounded off would be 6

The triangle ABC ≅ triangle DEC using the SSS criteria.

Given that, BA ≅ ED. Also C is midpoint of BE and AD thus,

BC = CE

AC = CD

Now, for the triangle ABC and triangle DEC we have:

BA = ED (Given)

C is the midpoint of BE and AD (given)

BC = CE (C is the midpoint)

AC = CD (C is the midpoint)

Thus, the triangle ABC ≅ triangle DEC using the SSS criteria.

BA = ED (Given). C is the midpoint of BE and AD (given). BC = CE (C is the midpoint). AC = CD (C is the midpoint), The triangle ABC ≅ triangle DEC using the SSS criteria.

Two triangles that are similar in shape but not necessarily in size are said to be similar triangles. This indicates that the respective sides and angles in the two triangles are proportional to one another. There are numerous uses for similar triangles in geometry, such as discovering missing side lengths or angles or resolving problems with indirect measurements. Other shapes besides triangles, like circles, rectangles, and polygons, are also included in the concept of resemblance.

Given that, BA ≅ ED. Also C is midpoint of BE and AD thus,

BC = CE

AC = CD

Now, for the triangle ABC and triangle DEC we have:

BA = ED (Given)

C is the midpoint of BE and AD (given)

BC = CE (C is the midpoint)

AC = CD (C is the midpoint)

Thus, the triangle ABC ≅ triangle DEC using the SSS criteria.

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The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.

We are given the diameter of the sphere, which is 8 cm. The radius, r, is half the diameter, so:

r = 8/2 = 4 cm

Substituting this value of r into the formula for the volume of a sphere, we get:

V = (4/3)π(4³) ≈ 268.08

Rounding this to the nearest whole number, we get:

V ≈ 268

Therefore, the volume of the sphere to the nearest whole number is 268 cm³, which is option D.

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The congruent arcs arcAB and arcCD, indicates that the chords AB and CD are also congruent, which indicates that quadrilateral ABCD is an isosceles trapezium and ∠A = ∠C

An isosceles trapezoid is a trapezoid that has congruent base angles and congruent non parallel sides.

The quadrilateral ABCD is a trapezoid, therefore;

BD is parallel to AC

The measure of the arcs AB and CD are the same;

arcAB = arcCD

The converse of the chord and intercepted arc theorem indicates that the lengths of the chords, AB and CD are the same, therefore;

The trapezoid ABCD is an isosceles trapezoid

Which indicates that the base angles ∠A and ∠C are congruent

∠A ≅ ∠C

Therefore; ∠A = ∠C

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Answer:

The homeowner’s insurance company will pay for the damages after the homeowner pays the deductible of $1,175 for each claim. Therefore, the amount that the homeowner’s insurance company will pay for the damages is $42,500 - $1,175 = $41,325.

I hope that helps! (´▽`ʃ♡ƪ)

Step-by-step explanation:

Answer:

9) Keep the denominators the same, and subtract the numerators. Then simplify if necessary.

[tex] \frac{3x + 2}{x + 5} - \frac{2x - 3}{x + 5} [/tex]

[tex] = \frac{3x + 2 - (2x - 3)}{x + 5} [/tex]

[tex] = \frac{3x + 2 - 2x + 3}{x + 5} [/tex]

[tex] \frac{x + 5}{x + 5} = 1[/tex]

10) Find the LCD. Rewrite each rational expression as an equivalent expression with the LCD as the denominator. Add the numerators and write the sum over the LCD. Then simplify if necessary.

[tex] \frac{4x}{x - 2} + \frac{x - 4}{x - 5} [/tex]

[tex] = \frac{4x(x - 5) + (x - 4)(x - 2)}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{4 {x}^{2} - 20x + {x}^{2} - 6x + 8 }{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8 }{ {x}^{2} - 7x + 10} [/tex]

Answer:

four less than three times a number

The probability that at most 70 switches fail during the first year is low, at around 1.3%.

The problem involves the use of the exponential distribution to model the lifetime of a certain type of electrical switch. Specifically, we are given that the average life of these switches is beta = 3.

The exponential distribution is often used to model the time between occurrences of a certain event, such as the failure of a component. In this case, we can use it to model the time between failures of the electrical switches.

To answer the question, we need to find the probability that at most 70 switches fail during the first year. Let X be the number of switches that fail during the first year. We know that X follows a Poisson distribution with parameter lambda = (1/3)*300 = 100.

This is because the expected number of failures per year for each switch is 1/3 (since the average life is 3 years), and there are 300 switches installed.

Therefore, we can use the Poisson distribution to calculate the probability that at most 70 switches fail during the first year:

P(X <= 70) = e^(-100) * (100^0/0!) + e^(-100) * (100^1/1!) + ... + e^(-100) * (100^70/70!)

This can be calculated using a calculator or software such as Excel. The answer is approximately 0.013, or 1.3%. This suggests that the switches are fairly reliable, and that it is unlikely that a large number of them will fail in a short period of time.

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The average number of visitor per concert in 2020 as compare to average number of visitors in 2019 is equal to 591 ( approximately ).

Average number of visitors per concert in 2019 was 584,

And the average number of visitors per concert in 2020 increased by 1.2%,

The average number of visitors per concert in 2020 as follows,

Average number of visitors per concert in 2020

= Average number of visitors per concert in 2019 + Increase in average number of visitors per concert

Increase in average number of visitors per concert

= 1.2% of the average number of visitors per concert in 2019

= (1.2/100) x 584

= 7.008

This implies,

The increase in the average number of visitors per concert from 2019 to 2020 is approximately 7.008.

Adding this increase to the average number of visitors per concert in 2019 gives us,

Average number of visitors per concert in 2020

= 584 + 7.008

= 591.008

Rounding this to the nearest whole number, we get,

Average number of visitors per concert in 2020 ≈ 591

Therefore, the average number of visitors per concert in 2020 is approximately 591.

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The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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Answer:

X2 - X1 = 7 - 1 = 6

Y2 - Y1 = 8 - 3 = 5

L = (6^2 + 5^2)^1/2 = 7.81

2/3 L = 5.21      length of segment

Tan θ = 5 / 6 = .833    slope of line

θ = 39.8 deg

5.21 * sin 39.8 = 3.34

5.21 * cos = 39.8 = 4.00        gives length of line segments

x2 = 1 + 4 = 5      

y2 = 3 + 3.34 = 6.34

(5, 6.34) = point 2/3 up the line

Check (length of line)

[(5 - 1)^2 + (6.34 - 3)^2]^1/2 =

l = 5.21      correct length for line segmet

The total amount of money in the account at the end of 5 years, compounded monthly, is $2,329.48.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To find the total amount of money in the account, we can use the formula for compound interest:

A = [tex]P*(1 + r/n)^{(n*t)}[/tex]

where:

A is the total amount of money in the account

P is the principal or initial amount of money in the account

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time period in years

In this case, P = $2,000, r = 0.03 (since 3% is equivalent to 0.03), n = 12 (since the interest is compounded monthly), and t = 5.

So, plugging in the values, we get:

A = [tex]2000*(1 + 0.03/12)^{(125)}[/tex]

A = [tex]2000(1.0025)^{60}[/tex]

A = $2,329.48 (rounded to the nearest cent)

Therefore, the total amount of money in the account at the end of 5 years, compounded monthly, is $2,329.48.

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After Tuesday, Andy still had 5/18 of his candy bar left.

What is the fraction?

A fraction is a mathematical representation of a part of a whole, where the whole is divided into equal parts. A fraction consists of two numbers, one written above the other and separated by a horizontal line, which is called the fraction bar or the vinculum.

If Andy ate 7/12 of his candy bar on Monday, then the fraction of the candy bar that was left after Monday is:

1 - 7/12 = 5/12

So, on Tuesday, he ate 1/3 of the remaining candy bar, which is:

(1/3) * (5/12) = 5/36

Therefore, the fraction of the candy bar that was still there after Tuesday is:

5/12 - 5/36 = (15/36) - (5/36) = 10/36 = 5/18

Hence, after Tuesday, Andy still had 5/18 of his candy bar left.

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The sample mean for 100 pell grant recipients is more likely to be within $80 of $2,600 for State A, given the relatively smaller population size and the use of the t-distribution.

To compare the two states, we need to calculate the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 for each state.

For State A, with only 4,000 pell grant recipients, the sample size of 100 is relatively large, but not enough to use the normal distribution. Therefore, we need to use the t-distribution, which has fatter tails than the normal distribution, making it more likely to produce extreme values. This means that the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 is higher for State A than for State B.

For State B, with a larger population of 200,000 pell grant recipients, the sample size of 100 is a small fraction of the population, allowing us to use the normal distribution. However, as the distribution is narrower than the t-distribution, the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 is lower for State B than for State A.

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The Gabrielsons ran a total of 30 kilometers in the family relay race.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

It seems that there are five family members who participated in the relay race, and the distance run by each of them in kilometers is listed as follows:

11, 4, 8, 2, 5

To find the total distance run by the family, we simply add up the distances:

11 + 4 + 8 + 2 + 5 = 30

Therefore, the Gabrielsons ran a total of 30 kilometers in the family relay race.

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Therefore, the shortest driving distance from the greenhouse to the animal shelter is approximately 6.08 units (rounded to two decimal places).

Distance is a measure of the physical space between two objects or points. It refers to the length of the path travelled by an object moving from one point to another, and is typically measured in units such as meters, kilometers, feet, miles, or other similar units of length. Distance can be calculated using various methods such as using the distance formula in mathematics or using measuring tools such as rulers, tape measures, or GPS devices. Distance is an important concept in physics, engineering, geography, and many other fields that involve measurements of space and motion.

Here,

We can use the distance formula to calculate the shortest driving distance between the coordinates (2,3) and (3,-3):

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where

x₁ = 2

y₁ = 3

x₂ = 3

y₂ = -3

Substituting the values, we get:

d = √((3 - 2)² + (-3 - 3)²)

d = √(1² + (-6)²)

d = √(1 + 36)

d = √(37)

=6.08 feet

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If $18,000 is invested at 5. 2% compounded then the full sum of the investment after 7 long years is roughly $24,810.89.

we are able to utilize the equation for compound intrigued:

A = P(1 + r/n)[tex]^{nt}[/tex]

where A is the entire sum of the venture after t a long time, P is the foremost speculation sum, r is the yearly intrigued rate as a decimal, n is the number of times the intrigued is compounded per year, and t is the number of a long time.

In this case, P = $18,000, r = 0.052 (since the intrigued rate is 5.2%), n = 1 (since the intrigued is compounded every year), and t = 7 (since we need to discover the full sum after 7 a long time). Substituting these values into the equation, we get: A = 18000(1 + 0.052/1)[tex]^{1*7}[/tex]

= 18000(1.052)[tex]^{7}[/tex]

= $24,810.89 (adjusted to the closest cent)

thus, the full sum of the venture after 7 a long time is roughly $24,810.89.

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