Can someone help me with 12 & 13. And show your work!

The calculated volume of the sphere is 44602.24 ft³

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

Radius = 22 ft

The volume of a sphere can be expressed as;

V = 4/3πr³

Where

r = 22

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

V = 4/3π * 22³

Evaluate

V = 44602.24

Therefore the volume of the sphere is 44602.24 ft³

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Question

Determine the volume of the following spheres with the given dimensions. to break the code find the mean of all your answers. round your answers to the hundreth place. use 3.14 for an approximation for pi.

Radius = 22 ft

Consecutive Interior Angles.

They are on the same side of a line that cuts through two other lines.

The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is

B) C=360 degrees s over A

The relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:

s = A / 360 * C

Make C the subject of the formula

s = AC / 360

360s = AC

rearranging

AC = 360s

C = 360 degrees s / A

C = (s / A) * 360°

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Answer:

[tex]\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}[/tex]

Step-by-step explanation:

In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.

This is because:

Therefore, this can be expressed as:

[tex]\dfrac{s}{C}=\dfrac{A}{360^{\circ}}[/tex]

Cross multiply:

[tex]360^{\circ} \cdot s=C \cdot A[/tex]

Now, divide both sides by A to isolate C:

[tex]\dfrac{360^{\circ} \cdot s}{A}=C[/tex]

Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:

[tex]\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}[/tex]

Answer:

3. Substitution because it said angle HKI = angle GKH, so we substitutioned that angle for the other one. I'm not sure about 4. If you provide us with the answer choices for that one, then I could help

Answer:

[tex]a_{n}[/tex] = - 7n + 47

Step-by-step explanation:

there is a common difference between consecutive terms , that is

33 - 40 = 26 - 33 = - 7

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 40 and d = - 7 , then

[tex]a_{n}[/tex] = 40 - 7(n - 1) = 40 - 7n + 7 = - 7n + 47

Answer:

3(5)^6

Step-by-step explanation:

There is 6, 5's in the expression meaning our answer has to be 3(5)^6.

:)

Answer:

the answer for the question given above is equal to 46875

The figures are similar because the ratio of segment BC to segment EF is equal to the of segment AB to segment DE.

The scale factor is equal to 3/2.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following:

Scale factor = BC/EF = AB/DE

Scale factor = 9/6 = 6/4

Scale factor = 3/2 = 3/2 (similar)

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The graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Option C

The function C(x) = (1/4)√x + 2 represents the side length of the smaller granola bar, where x is the area of the larger granola bar in square inches. To determine which graph shows C(x), we need to analyze the characteristics of the function.

First, let's consider the behavior of the function C(x) = (1/4)√x + 2:

Square Root Function: The term √x indicates that the function involves the square root of x. This means that as x increases, C(x) will also increase, but at a decreasing rate.

Scaling Factor: The coefficient (1/4) scales the square root of x. It affects the steepness of the function and causes C(x) to increase more slowly compared to a simple square root function.

Vertical Shift: The constant term (+2) shifts the entire function vertically upward by 2 units. This means that the graph will be raised by 2 units compared to a standard square root function.

Based on these characteristics, we can conclude that the graph of C(x) will be an increasing curve with a flattened slope compared to a simple square root function, and it will be shifted upward by 2 units.

Among the answer choices, the graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Without the actual graphs provided, it is difficult to specify the exact choice, but it should exhibit these features described above.

It is essential to refer to the available graphs or visually analyze the functions to determine the correct graph that shows C(x). Option C is correct.

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The formulas that represent the linear function in this problem are given as follows:

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The line has a slope of 2/3, hence:

y = 2x/3 + b.

When x = 1, y = 2, hence the intercept b is obtained as follows:

2/3 + b = 2

b = 6/3 - 2/3

b = 4/3.

Hence the slope-intercept equation of the line is given as follows:

f(x) = 2x/3 + 4/3.

The line goes through points (1,2) and (4,4), hence the point-slope equations to the line are given as follows:

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Answer:  log w²v⁵

Step-by-step explanation:

2log w + 5log v                        >Use exponent log rule

log w² + log v⁵                         >There is addition between, use

                                                   multiplication rule

log w²v⁵

The length of the arc LM is 8.72 cm.

We have,

The length of an arc is the distance that runs through the curved line of the circle making up the arc.

The length of an arc is expressed as;

l = tetha/360 × 2πr

tetha = R

R = 100°

and, radius = 5 units

so, we get,

l = 100/360 × 2 × 3.14 × 5

l = 8.72 cm (1.dp)

therefore the length of the arc LM is 8.72 cm

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The required sum of mixed fraction answer is 12 35/24.

Given that 6 5/8 + 6 5/6.

To find the sum of two or more mixed fractions, add the whole part of two fractions, add the fraction part of two fractions, then add these sums.

The sum (s1) of whole parts of two fractions is

s1= 6 + 6 = 12.

The sum(s2) of fraction parts of two fractions is

s2 = 5/8 +5/6.

L.C.M of 8 and 6 is 24.

Multiply each fraction by 12/12 gives,

s2 = 5/8 × 24/24 + 5/6 × 24/24.

s2 = 15/24 + 20/24.

s2 = 35/24.

The sum of mixed fractions is s1 + s2

Sum = 12 + 35/24

Thus, the required sum of mixed fraction is 12 35/24.

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The base 10 equivalent of the base 7 number 463421 is 83174.

To convert a number from base 7 to base 10, we multiply each digit of the base 7 number by the corresponding power of 7 and sum up the results.

For the number 463421 in base 7:

= 4 x 7⁵ + 6 x 7⁴ + 3 x 7³ + 4 x 7² + 2 x 7¹ + 1 x 7⁰

= 4 x 16807 + 6 x 2401 + 3 x 343 + 4 x 49 + 2 x 7 + 1 x 1

= 67228 + 14406 + 1029 + 196 + 14 + 1

= 83174

Therefore, the base 10 equivalent of the base 7 number 463421 is 83174.

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Answer:3x-4y=8

Step-by-step explanation:

There are 1365 different ways for Andre to select the blue fabrics for his quilt.

To determine the number of different ways Andre can select the blue fabrics for his quilt, we can use the concept of combinations.

Andre wants to select 4 different fabrics from a pool of 15 options for the blue portion of the quilt. This can be calculated using the formula for combinations:

C(n, r) = n! / (r! × (n-r)!)

where n is the total number of options and r is the number of selections.

In this case, we have:

n = 15 (number of options for blue fabrics)

r = 4 (number of fabrics to be selected)

Plugging in these values into the combination formula, we get:

C(15, 4) = 15! / (4! × (15-4)!)

Simplifying the equation, we have:

C(15, 4) = 15! / (4! × 11!)

Now, let's calculate the factorial terms:

15! = 15 × 14 × 13 × 12 × 11!

4! = 4 × 3 × 2 × 1

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Substituting these factorial terms into the equation:

C(15, 4) = (15 × 14 × 13× 12 × 11!) / (4 × 3 × 2 × 1 × 11!)

Simplifying further:

C(15, 4) = (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1)

C(15, 4) = 1365

Therefore, there are 1365 different ways for Andre to select the blue fabrics for his quilt.

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Using the bearing and trigonometry in the problem, the distance of the waterfall from the lake is 7.94km

To determine the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the distance in a south direction.

To find the distance between the waterfall and the lake, we can use the concept of right triangles and trigonometric functions.

Since the bearing is given as 236°, we can subtract this angle from 180° to find the angle formed by the south direction and the line connecting the lake and the waterfall:

180° - 236° = -56°

Now, we can consider the south direction as the reference direction (0°) and the line connecting the lake and the waterfall as the hypotenuse of a right triangle.

Using the cosine function, we can calculate the length of the side adjacent to the angle (-56°), which represents the distance between the waterfall and the lake:

cos θ = adjacent / hypothenuse

Adjacent = Hypotenuse * cosθ

Let's substitute the values into the formula:

Adjacent  = 14.2 km * cos(-56°)

To calculate the cosine of -56°, we can use the fact that the cosine function is an even function:

cos(-56°) = cos(56°)

Adjacent side = 14.2 cos(56)

Adjacent side = 7.94km

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Answer:

The waterfall is approximately 8.91 km away from the lake

Step-by-step explanation:

To find the distance between the waterfall and the lake, we can use trigonometry and the given information about the bearing and the southward direction.

Since the waterfall is 14.2 km south of the lake, the line connecting the waterfall and the lake forms a right triangle with the south direction being the adjacent side, the distance between them being the hypotenuse, and the angle formed between them being the bearing of 236°.

To find the distance between the waterfall and the lake, we can use the cosine function, which relates the adjacent side, hypotenuse, and angle:

cos(236°) = adjacent side / hypotenuse

Let's denote the distance between the waterfall and the lake as "d." The adjacent side represents the southward direction.

cos(236°) = d / 14.2 km

Solving for "d":

d = cos(236°) * 14.2 km

Using a calculator:

d ≈ -8.91 km

Since distance cannot be negative, we take the absolute value:

|d| ≈ 8.91 km

Therefore, the waterfall is approximately 8.91 km away from the lake.

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Answer:

13.48 - 8.263 = 5.217

Answer:5.217

Step-by-step explanation: caculate it

The y-intercept of the function is (0, c)

The coefficients b determine the horizontal shift of the parabola compared to the parent function

If a is negative, the parabola opens downward

The y-intercept of the function is (0, c).

This means that when x = 0, the y-value is equal to c.

The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.

The coefficient b determines the horizontal shift of the parabola compared to the parent function.

The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.

A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.

If a is negative, the parabola opens downward.

The coefficient a determines the shape of the parabola.

If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.

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Answer:

To find the answer, we can use the formula:

number of won games / total number of games played = percentage won

Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:

number of won games / x = 0.65

To solve for x, we can cross-multiply:

number of won games = 0.65x

We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:

If the team played 22 games, then the number of won games is:

number of won games = 0.65 * 22 = 14.3

This is not a whole number value, so we can rule out choice A.

We can repeat this process for each answer choice. When we try choice C, we get:

number of won games = 0.65 * 18 = 11.7

This is also not a whole number value, so we can rule out choice C.

When we try choice D, we get:

number of won games = 0.65 * 14 = 9.1

This is also not a whole number value, so we can rule out choice D.

Therefore, the only remaining answer choice is B, which gives us:

number of won games = 0.65 * 20 = 13

This is a whole number value, so the team could have played 20 games in total last season.

Answer:

Height = 64 feet

Step-by-step explanation:

(***It's very important to model these kinds of problems.  I attached a picture modeling the problem so show how modeling makes it easier to solve the problem)

We know that the building is vertical, and the ground is horizontal.  Thus, the ground and the building make a right angle.  

Therefore, the top of the building, the base of the building, and the surveyor form a right triangle, where

Because we're working with a right triangle, we can now find h, the heigh of the building using one of the trigonometric ratios.

We know that the angle of elevation is made by the ground and the distance between the surveyor and top of the building.

When the 65° (angle of elevation) is our reference angle, the height of the building is the opposite side and the distance between the base of the building and the surveyor is the adjacent side.

Thus, we can use the tangent ratio, which is:  tan (θ) = opposite / adjacent:

We can now plug in 65 for θ and 30 for the adjacent side.  This will allow us to find the opposite side, which is the heigh of the building:

tan (65) = h / 30

30 * tan(65) = h

64.33520762

64 = h

Thus, the height of the building to the nearest foot is 64 feet.

The probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.

We know that, probability of an event

= Number of favourable outcomes/Total number of outcomes.

Here, area of a rectangle = Length × Breadth

= 15×8

= 120 square units

Area of a triangle = 1/2 × Base × Height

= 1/2 ×(√10²-6²)×6

= 0.5×8×6

= 24 square units

Area of a trapezium = 1/2 (Sum of parallel sides)×Height

= 1/2 ×(5+7)×2

= 12 square units

Area of a square = side² = 2²

= 4 square units

(a) Probability of landing in trapezium or Square = 12/120 + 4/120

= 16/120

= 2/15

(b) Probability of landing inside the rectangle but outside the triangle = 16/120

= 2/15

Therefore, the probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.

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Answer:

D = 90 FT

Step-by-step explanation:

40 / d = 20 / 45

cross multiply

45 × 40 = 20d

1800 = 20d

divide both sides by 20

1800 / 20 = 20d / 20

d = 90 ft

The Surface Area of Cone is 706.5 cm².

We have dimension of Cone

height = 12 cm

Radius = 9 cm

Now, l = √9² + 12² = √81 + 144 = 25 cm

So, the Surface Area of Cone

= πrl

= 3.14 x 9 x 25

=  706.5 cm²

Thus, the Surface Area of Cone is 706.5 cm².

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The equation of the circle is (x - 2)² + (y - 3)² = 36

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

The circle

Where, we have

Center = (a, b) = (2, 3)

Radius, r = 6 units

The equation of the circle is represented as

(x - a)² + (y - b)² = r²

So, we have

(x - 2)² + (y - 3)² = 6²

Evaluate

(x - 2)² + (y - 3)² = 36

Hence, the equation is (x - 2)² + (y - 3)² = 36

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The solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.

Given the inequalities that include 3 in the following inequalities

x > 1.4, x < 2.6, x > 4.2, x < 5.1 and x < 8.2.

To find the solution set which include 3, write the solution set which consists of integer.

The solution set of x > 1.4 is { 2, 3, 4, 5, 6,     ........}

The solution set of x < 2.4 is { 2, 1. 0, -1, ...............}

The solution set of x > 4.2 is { 5, 6. 7, 8, ...............}

The solution set of x < 5.1 is { 5, 4, 3, 2, 1, ...............}

The solution set of x < 8.2 is { 8, 7, 6, 5, 4, 3, ...............}

Hence, the solution set which include 3 are x > 1.4, x < 5.1 and x < 8.2.

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The average utility price in Orlando for the 6 month period, and the way it compares to the national average is d. $ 308. 83 ; higher than the national average .

The information for Orlando is April, the cost was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.

The average is:

= ( 288 + 310 + 325 + 294 + 293 + 343 ) / 6

= 1, 853 / 6

= $ 308. 83

This average is higher than the national average of $ 308. 83.

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Full question is:

The average national utility price is $270.48. Over a 6-month period, what is the average utility price in Orlando? How does this compare with the national average?

A graph titled Orlando, Florida, has month on the x-axis and utility price on the y-axis. In April, the cost was 288 dollars; May, 310 dollars; June, 325 dollars; July, 294 dollars; August, 293 dollars; September, 343 dollars.

a. $370.60; higher than the national average

b. $292.17; higher than the national average

c. $38.35; lower than the national average

d. $308.83; higher than the national average

The measure of angle BDC is 42° and the measure of angle BAC is 21°.

Given that, the measure of arc BC of circle = 42°.

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

From the given circle,

The measure of arc BC = Angle BDC = 42°

Here, Angle BDC = 2×Angle BAC

42° = 2×Angle BAC

Angle BAC = 21°

Therefore, the measure of angle BDC is 42° and the measure of angle BAC is 21°.

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Answer:

x = 8 units

Step-by-step explanation:

Because this is a right triangle, we can find x using the Pythagorean theorem, which is given by:

a^2 + b^2 = c^2, where

In the triangle, the 6 unit side and the x unit sides are the legs while the 10 unit side is the hypotenuse.

Thus, we can solve for x by plugging in 6 for a and 10 for c in the theorem and solving for a (aka x, simply a in the theorem):

a^2 + 6^2 = 10^2

a^2 + 36 = 100

a^2 = 64

a = 8

x = 8

Thus, x is 8 units.

If Jeremy wants to try to prove ∠3 ≅ ∠6, then the statement that Jeremy can write is ∠1 ≅ ∠4

That's it :)