Find the area of the trapezoid 19 12.6 29.2 14.5

The density of an object is obtained by taking the ratio of the mass of the object and its volume ; \( Density = \frac{Mass}{Volume}\)

There is no picture attached and no picture corresponding to the question could be found.

Therefore, the density of the object is the ratio of its mass and volume.

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Answer:

4 m

Step-by-step explanation:

Answer:

4m

Step-by-step explanation:

The angular speed of the wheel is 0.314 rad/sec and the linear speed of the car is 8.164 feet/second .

Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ/ t

one revolution = 360°

180° = π

360° = 2π

3 revolution = 3× 2π = 6π

1 minute = 60 ×1 = 60s

angular speed = 6× 3.14/60

= 0.314 rad/s

The linear velocity =

V = wr

r = d/2

r = 52/2 = 26 feet

V = wr

V = 0.314× 26

V = 8.164 feet/second

Question: A Ferris wheel at a carnival has a diameter of 52 feet. Suppose it turns at a rate of 3 revolutions per minute. i. What is the angular speed of the wheel.

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Answer:

1048

Step-by-step explanation:

53(20)- 12

1060 - 12

1048

hope this helps

The change in temperature between the two readings as measured by Miguel is 18.7°F  .

In the question ,

the temperature  readings on the Miguel is

Average low temperature = -8.5°F

Average high temperature = 10.2°F

the change in the temperature , is given by the difference between the two reading .

which means

Change in temperature = Average high temperature - Average low temperature .

Substituting the values of average high and average low reading of the temperature from above ,

we get ,

Change in temperature = 10.2 -(-8.5)

= 10.2 + 8.5

= 18.7

the temperature change is 18.7°F .

Therefore , the temperature change is 18.7°F .

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Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 , then

sin²x = 1 - cos²x and cos²x = 1 - sin²x

Consider the left side

\(\frac{(1-sinA)(1 + sinA)}{(1+cosA)(1-cosA)}\) ← expand numerator/denominator using FOIL

= \(\frac{1-sin^2A}{1-cos^2A}\)

= \(\frac{1-(1-cos^2A)}{1-(1-sin^2A)}\)

= \(\frac{1-1+cos^2A}{1-1+sin^2A}\)

= \(\frac{cos^2A}{sin^2A}\)

= cot²A = right side , thus proven

Answer:

To find the total distance, we need to add up the distance the student ran in the first 5 days and the distance the student ran in the next 5 days.

Distance for the first 5 days = 3 1/2 miles/day × 5 days = 17.5 miles

Distance for the next 5 days = 4 1/4 miles/day × 5 days = 21.25 miles

Total distance = Distance for the first 5 days + Distance for the next 5 days

Total distance = 17.5 miles + 21.25 miles

Total distance = 38.75 miles

Therefore, the student ran a total of 38.75 miles during these 10 days.

Answer:

The measure of the angles are 61° and 119°

Step-by-step explanation:

Let the first angle = x°

let the second angle = y°

The sum of two supplementary angles = 180°

x° + y° = 180° ----- equation (1)

based on the given question; "the difference of two supplementary angles is 58 degrees."

x° - y° = 58° ------- equation (2)

from equation (2), x° = 58° + y°

Substitute the value of x into equation (1)

(58° + y°) + y° = 180°

58 + 2y = 180

2y = 180 -58

2y = 122

y = 122 / 2

y = 61°

The second angle is given by;

x° = 58° + y°

x = 58° + 61°

x = 119°

Thus, the measure of the angles are 61° and 119°

The correct trigonometric substitution for evaluating integral ∫√(x² + 64) dx is option B. x = 8 tan θ.

To evaluate the integral ∫√(x² + 64) dx using trigonometric substitution, use the substitution x = 8 tan θ.

Let's go through the steps to see how this substitution leads us to the solution:

1. Substitute x = 8 tan θ.

This implies dx = 8 sec² θ dθ.

2. Substitute the expression for x and dx in the integral:

∫√(x² + 64) dx becomes ∫√((8 tan θ)² + 64) * 8 sec² θ dθ.

3. Simplify the expression:

∫√(64 tan² θ + 64) * 8 sec² θ dθ = ∫√(64(sec² θ - 1)) * 8 sec² θ dθ.

4. Further simplify:

∫√(64sec² θ - 64) * 8 sec² θ dθ = ∫√(64sec² θ) * 8 sec² θ dθ.

5. Simplify the expression inside the square root:

∫8sec θ * 8 sec² θ dθ = ∫64sec³ θ dθ.

6. Integrate with respect to θ:

∫64sec³ θ dθ = 64∫sec³ θ dθ.

Now, this integral can be evaluated using standard trigonometric integral identities or integration techniques. However, it's worth noting that the original integral did not involve the variable θ, so we would eventually need to convert the result back to x by substituting x = 8 tan θ.

The correct answer is B. x = 8 tan θ.

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Answer:

///////////////////

Step-by-step explanation:

Answer:

x=4.44

Step-by-step explanation:

1st step:  multipy both sides by -4

x(-4) divided by -4 = (-1.11)(-4)

x(-4) divided by -4 = 1.11*4

11.4*4=4.44

Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

\(y = -x^2 - 4x + 2\)

Step-by-step explanation:

The equation of a parabola in vertex form is:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

\(-3 = a(1 - (-2))^2 + 6\)

\(-3 = a(3)^2 + 6\)

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

\(y = -1(x + 2)^2 + 6\)

This equation can also be written as:

\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)

Answer:

B.     \( 9^{\frac{1}{8}x} \)

Step-by-step explanation:

\( \sqrt[4]{9}^{\frac{1}{2}x} = \)

\( = ({9}^{\frac{1}{4}})^{\frac{1}{2}x} \)

\( = 9^{\frac{1}{4} \times \frac{1}{2}x} \)

\( = 9^{\frac{1}{8}x} \)

Answer:

The empirical rule, also known as the 68-95-99.7 rule, states that:

- About 68% of data falls within one standard deviation of the mean.

- About 95% of data falls within two standard deviations of the mean.

- About 99.7% of data falls within three standard deviations of the mean.

Using this rule, we can answer the questions as follows:

(a) An IQ score between 40 and 160 is within two standard deviations of the mean, since it is between 100 - 2(20) = 60 and 100 + 2(20) = 140. Therefore, about 95% of people have an IQ score between 40 and 160.

(b) An IQ score less than 60 is more than two standard deviations below the mean, while an IQ score greater than 140 is more than two standard deviations above the mean. From the empirical rule, we know that about 2.5% of people have an IQ score less than 60, and about 2.5% have an IQ score greater than 140. Therefore, the percentage of people who have an IQ score less than 60 or greater than 140 is 2.5% + 2.5% = 5%.

(c) An IQ score greater than 120 is within one standard deviation above the mean, since it is between 100 and 100 + 20 = 120. From the empirical rule, we know that about 68% of people have an IQ score within one standard deviation above the mean. Therefore, the percentage of people who have an IQ score greater than 120 is approximately 68%.

a) Amy's monthly budget for Rent based on the total budget for housing and food is $853.

b) Amy's monthly budget for Utilities based on the total budget for housing and food is $142.

c) Amy's monthly budget for Food based on the total budget for housing and food is $427.

The total budget for Housing, Utilities, and Food for nine months = $12,798

Rent = 60%

Utilities = 10%

Food = 30%

Budget period = 9 months

Budget for rent = $7,679 ($12,798 x 60%)

Monthly budget for Rent = $853 ($7,679/9)

Budget for utilities = $1,280 ($12,798 x 10%)

Monthly budget for Utilities =  $142 ($1,280/9)

Budget for food = $3,839 ($12,798 x 30%)

Monthly budget for Food =  $427 ($3,839/9)

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Answer:

Amount won : $3,000,000

Step-by-step explanation:

Let the amount won be =100 x

Amount spent on house :

                                     \(\frac{4}{5} \ of \ 100 x = 80 x\)

Remaining amount = 100x - 80x = 20x

Amount spent on yacht :

                                    \(\frac{3}{4} \ of \ 20x = 15x\)

Remaining amount = 20x - 15x = 5x

Amount spent on a trip :

                                   \(\frac{2}{3} \ of \ 5x = \frac{10}{3}x\)

Remaining amount =

                         \(5x - \frac{10}{3}x = \frac{15x -10x}{3} = \frac{5x}{3}\)

This amount is given for charity :

                                                     \(\frac{5}{3}x\)

But given :

           Amount given to charity is  50000

Therefore ,

                 \(\frac{5}{3}x = 50000\)

                \(5x = 3 \times 50000\\\\5x = 150000\\\\x = 30000\)

Therefore , the amount won on lottery is = 100x = 100 ( 30000) = 3,000,000

The amount of money he won

Answer:

3.88

Step-by-step explanation:

$57 multiplied by 7%

Answer:

Cn,Cr+Cn,Cr,-C

C(n+1,r)

The spinner is divided into 10 equal sections.

Which event has theoretical probability of exactly 1/5? Select three options.

A) spinning a number less than 3

B) spinning a 4 or 5

C) spinning an odd number

D) spinning a number greater than 8

E) spinning a number less than 8

Answer:

Options A, B & D are correct

Step-by-step explanation:

From the image attached, we can see that the total number on the spinner is 10.

Now, we want to find which event has theoretical probability of exactly 1/5

Option A: spinning a number less than 3 means we get 1 or 2 which is 2 numbers.

Thus; probability = 2/10 = 1/5.

This option is true

Option B: spinning a 4 or 5 means 2 numbers.

Thus; probability = 2/10 = 1/5.

This option is true

Option C: Odd numbers in the spin are 1,3,5,7,9. This is a total of 5 numbers.

Thus, probability = 5/10 = 1/2

This option is wrong.

Option D: Numbers greater that 8 are 9 & 10. That's 2 numbers.

Thus, probability = 2/10 = 1/5

This option is correct

Option E: numbers less than 8 are;

1,2,3,4,5,6,7. That's a total of 7 numbers.

Probability = 7/10

Thus, this option is wrong.

Answer: A, B, D

Step-by-step explanation:

Considering the Set A and B given, Applying inclusion - exclusion principle the number of elements common to both Sets is 10

This is a counting techniques that ensures that elements are not counted twice

It is achieved by the formula:

(A ∪ B) = n(A) + n(B) - n(A ∩ B)  

The information from the question include the following

Set A contains 48 elements

Set B contains 16 elements

The total number elements in either Set A or Set B is 54

Applying inclusion - exclusion principle gives the formula

Set A + Set B - ( Set A ∩ Set B ) = Set A ∪ Set B

substituting the values gives

48 + 16 - ( Set A ∩ Set B ) = 54

48 + 16 - 54 = ( Set A ∩ Set B )

10 = ( Set A ∩ Set B )

( Set A ∩ Set B ) = elements Sets A and B have in common

Therefore the number of the elements common to Sets A and B  is 10

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Answer:

Hi! The answer to your question is \(1/3\)

Step-by-step explanation:

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☆Brainliest is greatly appreciated!☆

Stay Safe!!!

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- Brooklynn Deka

Answer: 25%

Step-by-step explanation:

First week of July = 1040 people

Fourth week of July = 1040- 100 + 130 - 290 = 780

The number of people that went to the swimming pool in 1st week was 1040 while the 4th week had 780. The percentage decrease will be:

= (1040 - 780) / 1040 × 100

= (260 / 1040) × 100

= 0.25 × 100

= 25%

Combining similar terms:

Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.

To determine which package is the better buy, we need to compare the cost per hook for each package.

For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:

Cost per hook = $9.95 / 25 = $0.398

Rounding to the nearest cent, the cost per hook is $0.40.

For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:

Cost per hook = $13.99 / 40 = $0.3498

Rounding to the nearest cent, the cost per hook is $0.35.

Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.

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1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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