The table shows the number of pages Peter read in different numbers of minutes.Minutes 2 10 18 26Number ofPages Read 6 30 54 78Based on the information in the table, how long will it take Peter to read 42 pages?A. 14 minutesOB. 32 minutesOC. 102 minutesOD. 126 minutes

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

When two lines are parallel to each other, their slopes are EQUAL.

This means if the slope of the green line is

Then the slope of the red line is also

Answer:

The relationship between the areas of the three squares is that square A plus square B equals the area of square C.

The sum of the square of a and b is equal to the area of square of c

Data;

This theorem is used to calculated a missing side from a right angle triangle when we have the value of at least two sides.

Given that

\(c^2 = a^2 + b^2\)

This indicates a relationship such that the sum of square of two sides is equal to the area of the square of one side. I.e the area of the square of c is equal to the sum of the square of both a and b.

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Answer:

y=-5/2x+16

Step-by-step explanation:

:)

Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = \(\sqrt{(15.4)^2+(7.2)^2}=17mm\)

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

This is an right angle ∆ and the side lengths containing a right angle are 9 and 11.

By Pythagoras theoram,

\( {p}^{2} + {b}^{2} = {h}^{2} \)

where p is the perpendicular, b is the base and h is the hypotenuse.

Plugging the values,

\( {9}^{2} + {11}^{2} = {h}^{2} \)

Then,

\(h = \sqrt{ {9}^{2} + {11}^{2} } \)

\(h = 14.12(approx.)\)

The x of the right angled ∆ = 14.12

Answer:

the top angle is 11 and the angle on the left is 9 so the X will be rounded to the nearest hundreth since it's the biggest angle so 11×9=109 so yea I THINK its 100 since it's rounding

a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$

\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}

100 sin 35° = 80 sin 55°=57.73 mT

herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.

Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.

To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.

Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.

Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.

To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.

(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus

:$$c^2 = a^2 + b^2$$

where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$

c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$

Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.

Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$

Therefore, the bearing of the boy's current position from the starting point is N51°E.

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Answer:

1. 363 to 2

2. 363:2

3. 363/2

Step-by-step explanation:

1. First of all, there are 365 days in a year.

* Note that the question says there are only 2 days where sports aren't played.

2. As said in the question there are 3 ways to write a ratio: a to b; a : b; a/b. Now, let's think that what are a and b in this scenario? a= says without games= 2; and b= days in a year= 365.

3. Now fill in the variables with the numbers for each form of a ratio.

a. 363 to 2

b. 363:2

c. 363/2

Step-by-step explanation:

The way you can think about volume is that we have some cross sectional area times the height of the solid.

27.

The volume of a square based pyramid is

\(v = {s}^{2} ( \frac{h}{3} )\)

where h is the height of the pyramid

s is the side length of the square base.

S=7

h=12

\(v = {7}^{2} ( \frac{12}{3} ) = 49 \times 4 = 196\)

28. The volume of a rectangular prism

\(v = l \times w \times h\)

where l is length

w is width

h is height

\(v = 11 \times 11 \times 8 = 968\)

29.

Use the same formula in 27

\(v = 100(3) = 300\)

30.

Volume of a Cylinder is

\(v = \pi {r}^{2} h\)

where r is the radius of the circle

where h is the height

r is half of the diameter

The diameter is 22, thus the radius is 11.

\(v = {11}^{2} (8)(\pi)\)

\(v = 968\pi\)

pi is approximately 3.14

\(v = 3041.06\)

31. Volume of A Sphere

\( \frac{4}{3} \pi {r}^{3} = v\)

The radius is half of diamter, thus r=7

\( \frac{4}{3} \pi( {7}^{3} ) = 1436.76\)

Answer:

P is complementary to x

Step-by-step explanation:

Complementary means adding to 90 degrees

P+x = 90 degrees

So P is complementary to x

Answer:

( A) ∠ P

∠P is complementary angle to ∠ X .

Step-by-step explanation:

P + X = 90°

P is complementary to X.

Answer:

Step-by-step explanation:

ok I’ll do an image hopes this helps

Answer:

KN be better

sons of if his

Jacobi get area of pizza is 52.987 in²

5 friends getting equally share each one area of pizza is 40.27 in²

Any point in a plane that is a certain distance away from another point forms a circle. The fixed point is known as the center of the circle and the fixed distance is known as the radius of the circle.

The formula for calculating a circle's sector's area is (∅/360°) ×π×r²

Jacobi get area of pizza =(75/360°) × π×9²=52.987in²

5 friends getting pizza with each central angle measuring=360°-75°/5

=57°

5 friends getting each one area of pizza = (57/360°) × π×9²

40.27in².

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Answer:

the answer to the question is 1

Answer:

-26 Is the correct answer

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

First we'd need to solve 5 x 6. When we solve 5 x 6 we'd get the answer 30. Then do 7 - 3, when we solve that we'd get the answer of 4. Now we add 4 with 2 and we'd get 6. Now we get the 30 and divide it with 6 and get our answer as 5. Therefore our final answer is 5.

I hope this helps, have a blessed day! :)

Answer:

2 .3   and  5  

Step-by-step explanation:

Answer:

its c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I think it's d because the end of the table is on 12 so its less and more than 12.

The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.

To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.

The change in the function between x = 2 and x = 6 is:

f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6

The change in the input variable between x = 2 and x = 6 is:

6 - 2 = 4

So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:

(√10 - √6) / 4

To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:

(√10 - √6) / 4 ≈ 0.29

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Answer:

x ^3 cubed is  x  and -8 cubed is 2

Step-by-step explanation:

The difference between 3n³ + 4n² - 9 and -2n³ + 4n - 9 is 5n³ + 4n² - 4n

Given,

The two expressions are:

a = 3n³ + 4n² - 9

b = -2n³ + 4n - 9

We have to find a - b:

That is,

(3n³ + 4n² - 9) - ( -2n³ + 4n - 9)

Open the bracket and multiply (-) with the terms.

That is,

3n³ + 4n² - 9 + 2n³ - 4n + 9

Now solve the expression:

We get,

3n³ + 4n² + 2n³ - 4n

Add 3n³ and 2n²

Then,

5n³ + 4n² -4n

Therefore, the difference between 3n³ + 4n² - 9 and -2n³ + 4n - 9 is 5n³ + 4n² - 4n

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Answer:

(B)A number line going from 48 to 51. An open circle is at 50. Everything to the left of the circle is shaded.

Step-by-step explanation:

Amount of Money Earned - Amount of Money saved < $20

Therefore:

e - 30 < $20

e<20+30

e<$50

Since e is less than, we use an open circle and shade everything to the left.

The correct option is B.

Answer:

B

Step-by-step explanation:

Got it right

Answer:

x=12

Step-by-step explanation:

Lines A and B are parallel, with a transversal passing through them.

The properties of two parallel lines and a transversal tells us that angles 5x and 4x+12 must be equal, because they are a pair of alternate exterior angles.

To solve for x, we do 5x=4x+12

Subtract 4x on both sides

x=12

Answer: 12

Step-by-step explanation:

Therefore, the smaller of the two acute angles is 8°.

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. Here are some general steps to solve trigonometry problems:

Understand the problem: Read the problem carefully and identify what is being asked for.

Draw a diagram: Draw a diagram of the triangle and label the sides and angles.

Identify the known values: Identify what is given in the problem, such as the lengths of the sides or the measure of an angle.

Choose the appropriate formula: Choose the formula that relates the known values to the unknown value that you need to find.

Solve for the unknown value: Use algebraic manipulation and/or your calculator to solve for the unknown value.

Check your answer: Check your answer to make sure it makes sense and that it satisfies any given constraints.

Let's start by using the trigonometric identity cos(x) = sin(90° - x) for the left-hand side of the equation:

\(cos(4x) =\)\(sin(90^{0} - 4x)\)

Now we can substitute this into the original equation and simplify:

\(sin(90^{0} - 4x) = sin(6x + 10)\)

Using the identity sin(a) = sin(b) implies a = b + 2kπ or a = π - b + 2kπ for some integer k, we can set the angles inside the sine function equal to each other and solve for x:

90° - 4x = 6x + 10 + 2nπ or 90° - 4x = π - (6x + 10) + 2nπ

where n is an integer.

Solving for x in the first equation, we get:

10x = 80° + 2nπ

x = 8° + (2n/10)π

Solving for x in the second equation, we get:

10x = 80° + π + 2nπ

x = (8° + π/10) + (2n/10)π

Since we want the acute angle of the right triangle, which is less than 90°, we only need to consider the values of x that satisfy 0° < x < 22.5°. From the two equations above, we see that x can take on values between 8° and 9° or between 89° and 90°. Therefore, the smaller of the two acute angles is 8°.

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Answer:

16.5 m/s

Step-by-step explanation:

The sentence with the correct punctuation would be Alex ran well in the race, but lost by a whisker.

Punctuation marks are those symbols that are used to create meaning in both spoken and written works or sentences.

Examples of punctuation marks include the following:

A comma can be used to separate two clauses in a sentence. That is 'Alex ran well in the race' as the first clause and but lost by a whisker as the second clause.

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Answer:

RSM? Anyway. 40º FOR SURE. Remember the degrees sign! :D

Step-by-step explanation:

x = 180º - 75º - 65º

x = 40º

This is because the 75º angle is the same throughout the whole side. It can't change because it's a T R I A N G L E. Really hope this helps!!

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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