Find the volume of the solid generated by rotating the figure around the given axis. If
necessary, use 3.14 for and round your answer to the nearest hundredth.
TU
2
5

Answer:

a) .12 × $2,400 = $288

b) $2,400 + $288 = $2,688

Answer:

Step-by-step explanation:

The exact value of cos(2θ) given the information and using trigonometric identity is 1519.

To find the exact value of cos(2θ), we can use the double-angle formula for cosine:

cos(2θ) = cos²(θ) - sin²(θ)

First, let's find the values of sin(θ) and cos(θ) using the given information about θ:

Given:

tan(θ) = 9/40

θ : lies in the fourth quadrant (3π/2 < θ < 2π).

In the fourth quadrant, both sin(θ) and cos(θ) are negative.

Since:

tan(θ) = sin(θ)/cos(θ),

we can write:

9/40 = sin(θ)/cos(θ)

Using the properties of trigonometric functions, we can rewrite this as:

sin(θ) = -9

cos(θ) = -40

Now, let's calculate cos²(θ) and sin²(θ):

cos²(θ) = (-40)² = 1600

sin²(θ) = (-9)² = 81

Finally, we can substitute these values into the double-angle formula for cosine:

cos(2θ) = cos²(θ) - sin²(θ)

        = 1600 - 81

        = 1519

Therefore, the exact value of cos(2θ) is 1519.

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Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

In this context, "surplus" refers to the excess or additional amount beyond the ideal diameter of 24 inches that the actual diameter of the cake possesses.

It represents the difference between the actual diameter and the desired or expected diameter, taking into consideration the specified margin of error.

When a chef aims to purchase a cake with a margin of error of 3 inches, the surplus indicates the extent to which the cake's diameter surpasses the desired size.

It is a measure of how much larger the cake is compared to the ideal diameter, considering the acceptable range within the margin of error.

The surplus can be positive or negative, depending on whether the actual diameter is larger or smaller than the ideal diameter.

If the actual diameter is greater than 24 inches, the surplus will be a positive value, indicating the excess size of the cake.

Conversely, if the actual diameter is smaller than 24 inches, the surplus will be a negative value, representing the shortfall in size.

By quantifying the surplus, the chef can assess the degree to which the actual cake deviates from the ideal size and make an informed decision based on their specific requirements and preferences.

The surplus helps ensure that the cake's dimensions align with the desired specifications and meets the chef's expectations within the specified margin of error.

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Answer:

goat= 45 birr

sheep = 50 birr

Answer:

Goats =45

sheep =50

Step-by-step explanation:

3 sheep ÷375=7

looking to open the Naeem:

looking to open the Naeem

looking to open the Naeem:

how ❓️ ❓️,

The area of the shaded region is equal to 45 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

By substituting the given side lengths into the formula for the area of a rectangle, we have the following;

Area of rectangle = 8 × 6

Area of rectangle = 48 square units.

Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;

L₁ = 8 - 5 = 3 units.

L₂ = 6 - 4 = 2 units.

Area of right triangle = 1/2 × 3 × 2

Area of right triangle = 3 square units.

For the area of the shaded region, we have:

Area of the shaded region = 48 square units - 3 square units.

Area of the shaded region = 45 square units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

see explanation

Step-by-step explanation:

using any of the tangent, sine, cosine ratios in the right triangle.

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{6}[/tex] , then

Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{7}{6}[/tex] ) ≈ 49.40° ( to 2 decimal places )

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

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{6.32}[/tex]

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{6.32}[/tex]

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{2}{6}[/tex]

The data set is not approximately periodic. The correct option is A.

The values do not repeat after a certain interval. For example, the value of 36 is not repeated after 6 days, 12 days, or any other interval. Therefore, the data set is not periodic.

A periodic function is a function that repeats its values after a certain interval. For example, the function f(x) = sin(x) is periodic with a period of 2π. This means that the values of f(x) repeat every 2π units of x.

The data set in the question does not repeat its values after a certain interval. Therefore, the data set is not periodic.

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Answer:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Step-by-step explanation:

Total expenses for this year: $214.00

The child fee will be: $x

and the adult fee will be $(x+2)

Last year the number of children was 44

and the number of adults was 33

this year also has the same number of children and adults.

which means the entrance fee total for children will be $44x and for adults will be $33(x+2).

44x + 33(x+2) = 214

--> 44x + 33x + 66 = 214

--> 77x = 214 - 66 = 148

--> x = 148/77 = 1.92

So children's price is $1.92 and adults price is $1.92 + 2

hence:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Answer: The answer is A.

Step-by-step explanation: The surface area of a triangular prism is given by A = b h + ( b 1 + b 2 + b 3 ) l units 2 where is the base of a triangular face, is the height of a triangular face, , , and are the sides of the triangular base, and is the length of the prism.

The number of boxes of lawn seed that will be needed will be 4.

From the information, an area is formed by a square, ABCB, and a semi circle. BD is the diameter of the semi circle.The radius of the semi circle is 4m. The area is going to be covered completely with lawn seed.

The area of the square is s²

= 4²

= 16 m²

The area of the semi-circle is (πr²)/2:

= (π*4²)/2

= 8π m²

The total area is 16 + 8π m²

The number of boxes of lawn seed needed is (16 + 8π)/25 = (8 + 4π)/25

≈ 3.44 boxes

≈ 4 boxes

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Answer:

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

In ΔNOP, we are given:

Use the law of cosines to find side o:

Now, use the law of sines to find ∠N:

So,  ∠N is approximately 10°.

The distance from X to Z will be 386 km when rounded to 3 significant figures.

The distance from Y to XZ will be 141 km when rounded to 3 significant figures.

To obtain the distances, we need to extend the distances traveled by the airplane and this yields another triangular form. Angle Y = 105°, z = 200 km, and Z = 30°.

y/Sine Y = z/Sine Z

y/Sine 105° = 200/Sine 30°

y = 200 × 0.966/0.5

386 km to 3 significant figures

Also for the distance from Y to XZ,

We assume that the distance from Y to XZ is d

Sine 45°/1 = d/200

d = 200 sine 45°

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Answer:

Step-by-step explanation:

Given quadrilaterals JKLM and NPQR are similar with K=100°, M=85°, JK=12, LM=(5y+1), MJ=20, RN=10, NP=(x+4), PQ=7, QR=8, you want to identify the true statments.

Corresponding angles are congruent, so we have ...

  ∠K≅∠P = 100°

  ∠M≅∠R = 85°

Corresponding sides have the same ratio. The larger : smaller ratio here appears to be 2 : 1.

  JK : NP = 12 : (x+4)   ⇒   x+4 = 6   ⇒   x = 2

  KL : PQ = ? : 7   ⇒   KL = 14

  LM : QR = (5y+1) : 8   ⇒  5y+1 = 16   ⇒   y = 3

  MJ : RN = 20 : 10 . . . . . establishes the ratio for the others

The true statements are ...

__

Additional comment

It can be helpful to write a list of the specific correspondences (based on the similarity or congruence statement).

<95141404393>

Answer:

please see answers below

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ².

angles in a triangle add up to 180°.

Sine rule:   a/SIN A  =  b/SIN B  =   c/SIN C

angle C = 90° (little square means 90).

if angle A is 30, then angle B must be 180 - 90 - 30 = 60°.

using the Sine rule:

a/Sin A  =  c/Sin C

multiply both sides by Sin A:

a = (c Sin A) / Sin C

= (12 Sin 30) / Sin 90

= 6.

so a = 6.

Using Pythagoras (In a right-angled triangle, a ² + b ² = c ²),

c² = a² + b²

b² = c² - a²

= 12² - 6²

= 144 - 36

= 108

so b² = 108

b = √108

angle B is correct

The experimental probability of not spinning a 1 is 21/25.

To find the experimental probability of not spinning a 1, we need to calculate the ratio of the total number of times a number other than 1 was spun to the total number of spins.

From the bar graph, we can see that the number 1 was spun 8 times. Therefore, the total number of spins is the sum of the frequencies for all the bars:

8 + 6 + 9 + 11 + 9 + 7 = 50.

To find the total number of times a number other than 1 was spun, we need to subtract the frequency of 1 from the total number of spins: 50 - 8 = 42.

The experimental probability of not spinning a 1 is given by:

Probability(not spinning a 1) = (Number of times not spinning a 1) / (Total number of spins)

Probability(not spinning a 1) = 42 / 50

Simplifying the fraction, we get:

Probability(not spinning a 1) = 21 / 25

Therefore, the experimental probability of not spinning a 1 is 21/25.

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A) first multiply 18 x 7 = 116, then subtract 500 - 116 = 384, so the answer is 384

B) first divide 384 from 18 which should give you 18, so the answer is 18

Answer:

70 cm³

Step-by-step explanation:

let the total volume be x

copper : zinc = 3:2

copper ==>

3/5 *x = 42

make x the subject if formula

x = 42*5/3

:. x = 70 cm³✅✅

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The statement that, the value 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1 is true.

Given an equation,

3√2 sec θ + 7 = 1

We have to find that whether 3π/4 is a solution for the given equation or not.

Solving the given equation, we get,

3√2 sec θ + 7 = 1

3√2 sec θ = 1 - 7

3√2 sec θ = -6

sec θ = -6 / 3√2

sec θ = -2 / √2

sec θ = -√2

Now, we know that, sec θ = 1/ cos θ

So the equation becomes,

1/ cos θ = -√2

cos θ = -1/√2

Thus the solutions for the given equation are all values of θ such that cos θ = -1/√2.

cos 3π/4 =  cos (π - π/4) = -cos (π/4) = -1/√2

So 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1.

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The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

m∠1 = 111°: m∠4 = 61°; m∠6 = 141°; m∠7 = 47°

m∠2 = 69°; m∠3 = 119°; m∠5 = 39°; m∠8 = 133°

Step-by-step explanation:

The Polygon Exterior Angle Sum Theorem states the sum of the measures of the exterior angles of a polygon always equals 360°.  

Step 1:  Find x by setting sum of exterior angles equal to 360:

m∠1 + m∠4 + m∠6 + m∠7 = 360

(5x + 11) + (3x + 1) + (8x - 19) + (3x - 13) = 360

(5x + 3x + 8x + 3x) + (11 + 1 - 19 - 13) = 350

19x - 20 = 360

19x = 380

x = 20

Step 2:  Check validity of answer by plugging in 20 for x in the equations representing the measures of angles 1, 4, 6, and 7 and checking that we get 360:

(5(20) + 11) + (3(20) + 1) + (8(20) - 19) + (3(20) - 13) = 360

(100 + 11) + (60 + 1) + (160 - 19) + (60 - 13) = 360

(111 + 61) + (141 + 47) = 360

172 + 188 = 360

360 = 360

Thus, x is indeed 20.

Step 3:  Find the measures of angles 1, 4, 6, and 7 by plugging in 20 for x in the equations representing the measures of the angles.

Plugging in 20 for x in (5x + 11) to find m∠1:

m∠1 = 5(20) + 11

m∠1 = 100 + 11

m∠1 = 111°

Plugging in 20 for x in (3x + 1) to find m∠4:

m∠4 = 3(20) + 1

m∠4 = 60 + 1

m∠4 = 61°

Plugging in 20 for x in (8x - 19) to find m∠6:

m∠6 = 8(20) - 19

m∠6 = 160 - 19

m∠6 = 141°

Plugging in 20 for x in (3x - 13) to find m∠7:

m∠7 = 3(20) - 13

m∠7 = 60 - 13

m∠7 = 47°

In polygons, an interior angle and its corresponding exterior angle are always supplementary and thus the sum of their measures always equals 180°.

Step 4:  Identify the interior angles and their corresponding exterior angles:

∠2 is the interior angle, and its corresponding exterior angle is ∠1.

∠3 is the interior angle, and its corresponding exterior angle is ∠4.

∠5 is the interior angle, and its corresponding exterior angle is ∠6.

∠8 is the interior angle, and its corresponding exterior angle is ∠7.

Step 3:  Find the measures of angles 2, 3, 5, and 8 by subtracting the measures of angles 1, 4, 6, and 7 from 180:

Finding the measure of ∠2:

m∠1 + m∠2 = 180

m∠2 = 180 - m∠1

m∠2 = 180 - 111

m∠2 = 69°

Finding the measure of ∠3:

m∠4 + m∠3 = 180

m∠3 = 180 - m∠4

m∠3 = 180 - 61

m∠3 = 119°

Finding the measure of m∠5:

m∠6 + m∠5 = 180

m∠5 = 180 - m∠6

m∠5 = 180 - 141

m∠5 = 39°

Finding the measure of m∠8:

m∠7 + m∠8 = 180

m∠8 = 180 - m∠7

m∠8 = 180 - 47

m∠8 = 133°

Step 5:  Check validity of answer.

We can find the sum of all the interior angles of a polygon using the formula 180(n-2), where

Since there are 4 sides, the sum of the interior angles of this polygon equals 180 as 180(4-2) = 360

We can check the validity of our answers for Step 3 by seeing if their sum is 360:

m∠2 + m∠3 + m∠5 + m∠8 = 360

(69 + 119) + (39 + 133) = 360

188 + 172 = 360

360 = 360

Thus, we've correctly found the measures of the interior angles.

In my community, there are several situations where hypothesis testing can be applied. Here are three examples: Traffic Flow Optimization, Recycling Program Assessment, and Crime Prevention Strategy Evaluation

For the purpose of this response, let's choose Situation 1 (Traffic Flow Optimization) and go through the four steps.

1. Problem Statement: The local authorities want to determine if implementing a new traffic signal timing system will significantly reduce the average travel time for commuters passing through a busy intersection during peak hours.

2. Null Hypothesis (H0): The new traffic signal timing system has no effect on the average travel time for commuters passing through the intersection.

Alternative Hypothesis (H1): The new traffic signal timing system significantly reduces the average travel time for commuters passing through the intersection.

3. Level of Significance: α = 0.05

4. Rejection Region: The rejection region will depend on the specific test statistic used. Let's assume we are using a t-test to compare the mean travel time before and after implementing the new traffic signal timing system. In this case, we would calculate the t-statistic and determine the critical value(s) based on the degrees of freedom and the chosen level of significance. The rejection region would be in the tails of the t-distribution corresponding to the critical value(s).

Possible Type I Error: Rejecting the null hypothesis when it is actually true, indicating that the new traffic signal timing system is effective when it is not. In this case, it would mean concluding that the new system significantly reduces travel time when, in reality, it has no effect.

Possible Type II Error: Failing to reject the null hypothesis when it is actually false, indicating that the new traffic signal timing system is ineffective when it is actually effective. In this case, it would mean not detecting a significant reduction in travel time when the new system does indeed have a positive impact.

It's worthy of note that the specific test statistic and rejection region may vary depending on the nature of the data and the chosen statistical test. The above steps provide a general framework for conducting hypothesis testing in the given situation.

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Answer:

5446cm²

Step-by-step explanation:

the surface area = the 2 isosceles triangles + the 2 sides + the base

= 2 (24/2 X 35) + 2(37 X 47) + (47 X 24)

= 5446cm²

Answer: 5,446 cm²

Step-by-step explanation:

First, we will find the area of the two triangle sides.

       A = 2 * ([tex]\frac{bh}{2}[/tex])

       A = bh

       A = (35 cm)(24 cm)

       A = 840 cm²

Next, we will find the area of the three rectangular sides. We have two that are congruent and a third that is not.

       A = 2 * (LW)

       A = 2 * ((47 cm)(37 cm))

       A = 2 * 1,739 cm²

       A = 3,478 cm²

       A = LW

       A = (24 cm)(47 cm)

       A = 1,128 cm²

Lastly, we will add all of these faces together.

       840 cm² + 3,478 cm² + 1,128 cm² = 5,446 cm²

Answer:

  {3, 4, 5}

Step-by-step explanation:

You want the integer values that satisfy the inequality 3 ≤ x < 6.

The interval of interest has an open circle at 6, which means x=6 is not included in the solution set. (The "or equal to" condition is missing there.) The integers that are included are shown in the attachment.

  {3, 4, 5} . . . . possible integer values of x

<95141404393>

Answer:

The answer James

Step-by-step explanation:

James=2/5hours

J=2/5×60=2×12=24 minutes

Sandle=4/12×60=4×5=20 minutes

Answer:

Step-by-step explanation:

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

a. The two-digit number  is 19

b. The number is 22

C. The number is 44

(a) To solve this problem, we are looking for a two-digit number less than 20, odd  and with a sum of digits equal to 10.

the only number that satisfies these conditions is 19.

(b) We need to find a two-digit even number

the only number that meets these criteria is 22.

(c) We are searching for a two-digit number less than 80, even, with identical digits and a multiple of 4.

the only number that satisfies all these conditions is 44

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