6. Find the volume of a cone with a radius of 5 ft and a height of 12 ft. (1 point)
O 300 ft³
O 314 ft³
O 100 ft³
O224 ft³

Answer:

Step-by-step explanation:

To find the missing side lengths in the given right triangles, use trigonometric ratios.

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the first triangle ABC, we have been given the angle, the side opposite the angle and the side adjacent the angle.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the tangent ratio:

[tex]\implies \tan 18^{\circ}=\dfrac{15}{x}[/tex]

[tex]\implies x\tan 18^{\circ}=15[/tex]

[tex]\implies x=\dfrac{15}{\tan 18^{\circ}}[/tex]

[tex]\implies x=46.165253...[/tex]

[tex]\implies x=46.2\;\;\sf(nearest\;tenth)[/tex]

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

Triangle LMN is a right triangle. Interior angles of a triangle sum to 180°.

Therefore, as m∠M = 50° and m∠MLN = 90°, then m∠MNL = 40°.

As KN is perpendicular to NM and m∠MNL = 40° then m∠KNL = 50°.

As KL is parallel to NM, then m∠K = 90°.  Therefore, m∠KLN = 40°.

(Refer to the attached diagram).

For right triangle LMN, we have been given the angle (∠M) and the side adjacent to the angle (LM). To find an expression for the length of the side opposite the angle (LN), use the tangent ratio:

[tex]\implies \tan 50^{\circ}=\dfrac{LN}{45}[/tex]

[tex]\implies LN=45\tan 50^{\circ}[/tex]

LN is the hypotenuse of right triangle KLN.

If we use ∠KNL as θ, then side KN is adjacent to the angle.

Therefore, to find the KN use the cosine ratio:

[tex]\implies \cos 50^{\circ}=\dfrac{KN}{LN}[/tex]

[tex]\implies \cos 50^{\circ}=\dfrac{KN}{45\tan 50^{\circ}}[/tex]

[tex]\implies KN=45\tan 50^{\circ}\cos 50^{\circ}[/tex]

[tex]\implies KN=34.471999...[/tex]

[tex]\implies KN=34.5\;\; \sf (nearest\;tenth)[/tex]

As KL is the side opposite ∠KNL, to find KL use the sine ratio:

[tex]\implies \sin 50^{\circ}=\dfrac{KL}{LN}[/tex]

[tex]\implies \sin50^{\circ}=\dfrac{KL}{45\tan 50^{\circ}}[/tex]

[tex]\implies KL=45\tan 50^{\circ}\sin50^{\circ}[/tex]

[tex]\implies KL=41.0821297...[/tex]

[tex]\implies KL=41.1\;\;\sf (nearest\;tenth)[/tex]

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

From inspection of the second triangle ABC, we have been given the angle, the side adjacent the angle and the hypotenuse.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the cosine ratio:

[tex]\implies \cos 70^{\circ}=\dfrac{x}{46}[/tex]

[tex]\implies x=46\cos 70^{\circ}[/tex]

[tex]\implies x=15.732926...[/tex]

[tex]\implies x=15.7\;\;\sf(nearest\;tenth)[/tex]

If all 4 posts are painted, 44 square feet must be painted.

We know that the formula for the surface area of the cylinder is:

A = 2πrh + 2πr²

Here, the dimensions of the each cylindrical post:

the diameter d = 1 foot and the height is 3 feet high.

So, the radius r = 0.5 ft and height h = 3 ft

Let us assume that the surface area of one post be A₁

Using above formula of surface area of cylinder,

A₁ =  2πr(h + r)

A₁ =  2 × π × 0.5 × (3 + 0.5)

A₁ =  2 × 3.14 × 0.5 × (3.5)

A₁ =  10.99

A₁ ≈ 11 sq.ft.

So, the total surface area of  4 cylindrical posts would be,

A = 4 × A₁

A = 4 × 11

A = 44 sq.ft.

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Answer:

To find the sum of two complex numbers on the complex plane, we can simply add their real and imaginary parts separately. The real part of a complex number is the x-coordinate on the complex plane, while the imaginary part is the y-coordinate.

In this case, the two complex numbers are (-4-4i) and (4+2i). To find their sum, we add their real and imaginary parts separately:

Real part: -4 + 4 = 0

Imaginary part: -4 + 2 = -2

So, the sum of (-4-4i) and (4+2i) is 0 - 2i, which can be represented as a point on the complex plane with x-coordinate 0 and y-coordinate -2.

Step-by-step explanation:

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%. Albinism and hemophilia are both recessive genetic conditions, meaning that both parents must have the recessive gene in order for a child to be born with either condition. Since neither Clara nor Charles have either condition, the probability that their first child will be a boy with both albinism and hemophilia is 0%.

The probability that the first child of Clara and Charles will be a boy with both albinism and hemophilia is 0%, since neither Clara nor Charles have either of these recessive genetic conditions.

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Answer:

Step-by-step explanation:

You want the value of x that makes f(x) = 60, when f(x) is the exponential function with an initial value of 100 and a decay factor of 0.95.

The form of an exponential function is ...

  f(x) = (initial value) · (decay factor)^x

For the given initial value and decay factor, the function is ...

  f(x) = 100 (0.95^x)

Solving for x, we find ...

  f(x)/100 = 0.95^x

  log(f(x)/100) = x·log(0.95)

  x = log(f(x)/100)/log(0.95)

For f(x) = 60, the value of x is about ...

  x = log(60/100)/log(0.95) ≈ 9.959

The value of x is about 9.959.

The recursive rule for the sequence is T(n) = T(n - 2) - T(n - 1)

From the question, we have the following parameters that can be used in our computation:

100, 3 , 97 ,-94 , 191

The above definitions imply that we simply subtract the current from the previous term to get the next term

Using the above as a guide,

So, we have the following representation

T(n) = T(n - 2) - T(n - 1)

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Answer:i don't realy now so 5 point 3

The equation of the new graph is f(x) = 9^(x - 2)

From the question, we have the following parameters that can be used in our computation:

f(x) = 9^x

Also, we have

shifted 2 units to the right,

This is represented as

(x, y) = (x - 2, y)

Substitute the known values in the above equation, so, we have the following representation

f(x) = 9^(x - 2)

Hence, the function is f(x) = 9^(x - 2)

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Samantha used 120 grams of 25% sugar syrup.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.

Let Samantha used y grams of 25% sugar syrup.

Then, she used (120 - y) grams of 10% sugar syrup.

We know that the final concentration of sugar syrup is 15%, which means that 15% of the total 120 grams of the syrup is sugar.

This can be expressed as:

0.15 x (y + (120 - y)) = 0.15 x 120

Expanding and simplifying the equation, we get:

0.15y + 0.15 x 120 - 0.15y = 18

0.15 x 120 = 18

Solving for y, we get:

y = 120 x 18 / (0.15 x 120)

= 120 x 18 / 18

= 120.

Hence, Samantha used 120 grams of 25% sugar syrup.

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Answer:

work hard you can get it

Step-by-step explanation:

lol

The 8 painters will take 12 hours and 9.6 minutes to paint the office. The result is obtained by comparing the two variables, worker and time duration.

If the they work at the same rate, find the time needed for the 8 painters to finish their job!

Let's say

We convert the unit of time in hours.

t₁ = 7 h 36 min

t₁ = (7 + 36/60) h

t₁ = (7 + 0.6) h

t₁ = 7.6 hours

If they work at the same rate, the number of workers and time durations of each day are directly proportional. So,

w₁/w₂ = t₁/t₂

5/8 = 7.6/t₂

t₂ = 8/5 × 7.6

t₂ = 12.16 hours

In hours and minutes,

t₂ = 12 h + (0.16 × 60) min

t₂ = 12 h 9.6 min

Hence, to paint the office, the 8 painters will take 12 hours and 9.6 minutes.

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Answer: $140 each weekend

Step-by-step explanation:

$1250 - $130 = $1,120

$1,120 divided by 8 weekends = $140

The solution to the expression ⁴√(-15/16) is (-15/16)^1/4

From the question, we have the following parameters that can be used in our computation:

⁴√(-15/16)

The above expression means that we calculate the 4th root of -15/16

-15 and 16 do not have perfect fourth roots

This means that the expression can only be rewritten as

(-15/16)^1/4

It cannot be evaluated

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Answer:

Step-by-step explanation:

The transformations that have been applied to the parent function y = 1/x^2 are:

shift 3 units to the right

shift 5 units down

reflection over the x-axis

So the correct options are:

shift 3 to the right

shift 5 down

reflection over the x-axis

Answer:

40%

Step-by-step explanation:

32 out of 80 as a percentage it is 40%

Answer:

using the equation of the straight line we solve

You can estimate that the used cars Mr. Ford reviewed were worth roughly $2,200 less now than when they were new, had an average price of around $22,000 when new, and typically lose $2,200 of value per year. (option 1, 2, 3)

To calculate this, you can substitute the x-values from the table into the equation and solve for y. For example, when x is 3,

which is the price of the car when it was 3 years old. This same formula can be used to calculate the price of the car at other age values and shows that the car loses an average of $2,200 of value per year. At 5 years old, the equation would be

which is the average value of the used car at that age.

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Complete Question:

Mr. Ford wants to better understand the value of used cars over time. He reviewed some used-car ads and recorded the relationship between age and price in a table. Finally, he calculated a line of best fit. Used cars Age in years (x) 3 6 4 2 6

Price (y) $15,000 $8,000 $12,000 $5,000 $19,000 $10,000

The equation for the line of best fit is y = -2,200x + 22,000.

Based on the equation, what estimates can you make about the used cars Mr. Ford reviewed?

Select all that apply.

The z statistic that is associated with the class's average is 1.25.

In the given question the population of all standardized ex scores has a mean of 500 and a standard deviation of 100 . Twenty-five students in a professor's class take the ex , and their average score is 525.

We have to find z statistic that is associated with the class's average.

n = 25

μ = 500

σ = 100

[tex]\bar X[/tex] = 525

Then ,

z statistic = [tex]\frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt n} }[/tex]

putting the value in the formula:

z statistic = (525-500)/(100/\sqrt 25)

z statistic = (25)/(100/5)

z statistic = (25)/(20)

z statistic = 1.25

Therefore,

The z statistic that is associated with the class's average is 1.25.

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The surface area of the right triangular prism with legs of 5 centimeters and 12 centimeters, a hypotenuse of 13 centimeters, and a height of 2 centimeters is 108 square centimeters.

Surface area refers to the total area of the surface of a three-dimensional object. When it comes to a right triangular prism, the surface area includes the area of all six faces.

Let's call the height of the triangular prism "h" and label the legs of the triangle "a" and "b". Using these values, we can find the area of the base of the triangular prism. The area of a right triangle is equal to 1/2 times the product of the legs, so the area of the base is

=> (1/2) * a * b = (1/2) * 5 * 12 = 30 square centimeters.

Next, we need to find the surface area of each of the three lateral faces. Each of these faces is a rectangle, so we can find the area by multiplying the height of the prism by the length of one of the sides of the triangle base.

The length of one side of the triangle base is equal to the hypotenuse, which is 13 centimeters. So, the surface area of each of the three lateral faces is

=> h * 13 = 2 * 13 = 26 square centimeters.

Finally, we can find the total surface area by adding the surface area of the base and the surface area of the three lateral faces.

The surface area of the base is 30 square centimeters, and the surface area of each lateral face is 26 square centimeters, so the total surface area is

=> 30 + 3 * 26 = 30 + 78 = 108 square centimeters.

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The error made by the student in the exponential function, y = 48,000(1.03)^x is that the function represented an exponential growth rather than an exponential decay.

An exponential function is written in the form y = abˣ.

In the exponential function, the exponent, x is a variable.

Annual decreasing rate of the fish population = 3% or 0.03

Original population = 48,000

Let the number of years = x

Exponential function: 48,000 (1 - 0.03)^x

= 48,000(0.97)^x

Thus, to represent an exponential decay, the exponential function should have been written as y = 48,000(0.97)^x.

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The smallest possible value for a term in the five-term arithmetic sequence is 1.The sum of a five-term arithmetic sequence is given as 100 and all terms are positive integers. Let's call the first term "a" and the common difference "d".

The five terms can be represented as a, a + d, a + 2d, a + 3d, and a + 4d. The sum of these five terms is 100, which can be represented as:

a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 100

Simplifying the expression, we get:

5a + 10d = 100

Dividing both sides by 5, we get:

a + 2d = 20

Since all terms are positive integers, it follows that "a" and "d" must also be positive integers. The smallest possible value for "a" is 1, and the smallest possible value for "d" is 1. Substituting these values into the expression for "a + 2d" yields:

1 + 2 * 1 = 3

Thus, the smallest possible value for a term in the five-term arithmetic sequence is 1.

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Answer:

9.6a + (-2)

Step-by-step explanation:

(6 + 12.5a) - (8 + 2.9a)  Distribute the negative sign

6 + 12.5a - 8 - 2.9a  Combine like terms

12.5a - 2.9a +6 - 8

9.6a + (-2)

Answer:

B

Step-by-step explanation:

cause the premeter is way around the area

Answer:

B. V = pi*r^2*H/6

Step-by-step explanation:

The formula for the volume of a cone is V=pi*r^2*h/3, where h is the height of the cone, and r is the radius of the base. In this case, the hieght of the cone is equal to half the height of the cylinder, so it's h=H/2

If we substitute, we get

V = pi * r^2 * h / 3 = pi * r^2 * (H / 2) / 3 = pi * r^2 * H / 6

KLMN is a trapezoid where KL=MN and m∠1=m∠2 . It is also given that LM:KN = 8/9 and PKLMN=132.The midsegment is 34 units long.

The trapezoidal shape KLMN, where KL = MN.

m∠1=m∠2

Moreover, LM/KN = 8/9

Additionally, KLMN's perimeter is 132 units.

The midsegment's size (KM).

We can see that in the above case, KM is a transversal in relation to the parallel lines LM and KN. which implies,

∠KML=∠MKN

∠1=∠2

Two base angles are clearly equal. So, KLM and KMN are isosceles triangles.

Using the side ratios of two triangles as an example,

= KL: LM: MN: KN

= 8 : 8 : 8 : 9

The ratio units add out to 8 + 8 + 8 + 9 = 33. Consequently, each ratio's value is,

=[tex]\frac{perimeter}{33} \\\\\frac{132}{33} \\\\=4[/tex]

The segment LM's length is thus,

LM=8×4=32

Additionally, section KN's length is

KN=9×4=36

Taking the average of LM and KN as, one can then determine the length of the midsegment KM.

[tex]KM=\frac{LM+KN}{2} \\\\\\KM=\frac{32+36}{2}[/tex]

KE=34

As a result, the midsegment is 34 units long.

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Answer: 16

Step-by-step explanation:

      The geometric number between 7 and 28 is 16. Geometric numbers are the numbers you get by multiplying by a factor. If we multiply by 2 for this common geometric sequence, we get 16:

1 * 2 = 2, 2 * 2 = 4, 4 * 2 = 8, 8 * 2 = 16,16 * 2 = 32, etc.

         7 < 16 < 28

Answer:

It should be 8...

Step-by-step explanation:

16 / 8 = 2 and there is no higher number 16 that can be divided by. 56 is dividable by 8 so it makes sense.

Also 56 isn't dividable by 16

So, on solving the provided question, we can say that the equation, we have been provided with is x = 48

The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.

A mathematical formula explains the connection between the two sentences on either side of a letter. There is typically just one variable, which also acts as the symbol. As an illustration, 2x - 4 = 2.

the equation, we have been provided with is

x + 2 = 50

x = 50-2

x = 48

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The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.

What is cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.

In the given box it is given sides are 2, 3 and 4 ft.

So the volume of the rectangular prism is V = 2*3*4 = 24 ft².

So the greater surface area in the given description is 6ft, 2ft and 2ft.

Where the surface area will be 12ft ²

Hence The greater surface area with similar volume will be of the side, 6ft, 2ft and 2ft.

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