Solve and check
please please help i will mark u as a brill it is easy please

The surface area of the sphere, to the nearest whole number, is 1318 cm².

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume =  (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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Answer:

The wind speed is 21 miles per hour, and the speed of the plane in still air is 63 miles per hour.

Step-by-step explanation:

Since a plane traveled 588 miles each way to Athens and back, and the trip there was with the wind and took 7 hours, while the trip back was into the wind and took 14 hours, to find the speed of the plane in still air and the speed of the wind, the following calculations must be performed:

Downwind travel = 588/7 = 84 miles per hour

Headwind travel = 588/14 = 42 miles per hour

84 - 42 = 42/2 = 21

84 - 21 = 63

Therefore, the wind speed is 21 miles per hour, and the speed of the plane in still air is 63 miles per hour.

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Answer: 24.2° SouthWest

Step-by-step explanation:

First step: DRAW A PICTURE of the vectors from head to tail (see image)

I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.

Perpendicular (x):

 cos 35° = adjacent/hypotenuse

  cos 35° = x/160

→ x = 160 cos 35°

Angle (θ):

sin θ = opposite/hypotenuse

sin θ = x/320

sin θ = 160 cos 35°/320

    θ = arcsin (160 cos 35°/320)

    θ = 24.2°

Direction is down (south) and left (west)

The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.

Weekly salary = Hourly pay rate * Number of hours worked

Weekly salary = $12/hour * 20 hours

Weekly salary = $240

So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

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Answer:

1.5555556

1 5/9

14/9

Step-by-step explanation:

Answer:

18 cm

Step-by-step:

The formula for the volume of a triangular prism is given by:

V_triangular_prism = (1/2) * base * height * length

where the base is the area of the base triangle, height is the perpendicular distance between the two parallel base planes, and length is the distance between the two triangular faces.

We are given that the base area of the triangular prism is 36 cm² and the volume is 432 cm³. Using these values, we can solve for the height:

432 = (1/2) * 36 * height * length

height * length = 24

Since we want to find the base side length of a rectangular prism that has the same volume, we can use the formula for the volume of a rectangular prism:

V_rectangular_prism = length * width * height

We know that the volume of the rectangular prism is also 432 cm³, so we can substitute this value and the value we found for the height * length product:

432 = length * width * height

432 = length * width * (24/length)

432 = 24 * width

width = 18

Therefore, the base side length of the rectangular prism needs to be 18 cm.

Hope this helps!

Answer:

the extra big numbers can be written easily by the scientific notation

Answer:

Scientific Notation was developed in order to easily represent numbers that are either very large or very small.

Step-by-step explanation:

Answer: 138.557

Step-by-step explanation:

Answer:

hey :( so just wondering hru ummm and u were right and umm ig i am just gonna f my life up always umm hru ?

Step-by-step explanation:

Answer:

1.   300 degrees

2.  greater than

Step-by-step explanation:

1) θ = 300°

2) For angles between 0° and  60°, the cosine value is greater than \(\frac{1}{2}\).​

"The position of an angle with its vertex at the origin and its initial side coinciding with the positive x-axis."

For given question,

We have been given an angle  θ = 60°

We need to find  other value of θ is for which cos(θ) = \(\frac{1}{2}\)

We know that, cos(θ) is positive in the first and fourth quadrant.

Also,  cos(2π - θ) =  cos(θ)

So, cos(60) = cos(360 - 60)

                   = cos(300)

                   = \(\frac{1}{2}\)

This means, the other value of θ is for which cos(θ) = \(\frac{1}{2}\) is , θ = 300°

Also, we know that,

i) cos(0) = 1

ii) cos(30) = \(\frac{\sqrt{3} }{2}\)

                = 0.866

iii) cos(45) = \(\frac{1}{\sqrt{2} }\)

                 = 0.7071

iv) cos(60) = \(\frac{1}{2}\)

                 = 0.5

This means, for angles between 0° and  60°, the cosine value is greater than \(\frac{1}{2}\).​

Therefore, 1) θ = 300°

2) For angles between 0° and  60°, the cosine value is greater than \(\frac{1}{2}\).​

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Answer:it is b

Step-by-step explanation:

Because I know

Answer:

Correct choice: B

Step-by-step explanation:

Equation Solving

The area of a trapezoid with height h and bases b1 and b2 is given by:

We must solve this formula for h.

First, multiply by 2 to eliminate denominators:

Now, divide by b1+b2:

Swapping sides:

Correct choice: B

Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

The correct option is (B).

Now, According to the question:

Stratified sampling design divides the given population into small sub-groups called strata. The members of each strata share some common features and at any particular time, a sample is randomly selected from each stratum which is then compared to the entire population. During random sampling, a number proportional to the stratum size is selected from all strata. The randomly selected samples from each strata are then combined to form a common random sample.

Considering that the editor wants to adopt stratified sampling, option B fits (Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.)

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The complete question is this:

A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design?

(A) Send a survey to all city residents and use the first 500 returned surveys for the sample.

(B) Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.

(C) Select one voting district at random, and then select a random sample of 500 from the selected voting district.

(D) Alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district.

(E) Select the first 500 city residents who attend the next high school football game.

The standard deviation of the scores of all the students in the class to be:

σ = √[(Σ(x - 80)2) / 50] = 11.18

The standard deviation of the scores of all the students in the class is calculated using the formula

σ = √[(Σ(x - μ)2) / N]

where μ is the mean of the scores and N is the total number of students in the class.

In this case, the total number of students in the class is 50 (30 from section 1 and 20 from section 2). Let's assume that the mean of the scores for all students is 80.

Therefore, the standard deviation of the scores of all the students in the class is calculated as follows:

σ = √[(Σ(x - 80)2) / 50]

In this equation, Σ(x - 80)2 is the sum of the squared differences between each student's score and the mean. We can calculate this sum by first finding the squared difference for each student and then adding them up.

For example, if the scores of the 30 students in section 1 are 86, 95, 78, etc., the squared differences will be (86 - 80)2 = 36, (95 - 80)2 = 225, (78 - 80)2 = 4, and so on. Adding all these squared differences will give us the sum of the squared differences for all the students in the class.

Finally, substituting this sum and the value of N (50) in the formula, we get the standard deviation of the scores of all the students in the class to be:

σ = √[(Σ(x - 80)2) / 50] = 11.18

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Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

There are 6,435 different selections of 7 bonsais that William Smith can choose.

If we have a set of N elements, the number of different combinations of K elements (such that K is equal to or smaller than N) of those N elements is given by:

C(N, K) = N!/( (N - K)!*K!)

In this case, we know that she has 15 different variants of bonsai and she wants to use 7, then:

N = 15

K = 7

Replacing these values in the above formula we will get the possible combinations of bonsais.

C(15, 7) = 15!/( (15 - 7)!*7!) = 15!/( 8!*7!) = (15*14*13*12*11*10*9)/(7*6*5*4*3*2*1) =  6,435

There are 6,435 different selections of 7 bonsais.

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The confidence level for the true average strain is (24.69,27.31) and the prediction level is (20.01,31.99) and also it is estimated that prediction level is much wider than the confidence level

Given that sample size is 20, mean is 26%, standard deviation is 3.4, confidence level is 95%.

a)

We must calculate the true average strain in a way that conveys precision and reliability.

We have to use t-test in our problem because sample size is less than 30.

We Know that,

True average value is determined by formula,

\(\mu\pm t*\frac{S}{\sqrt{n}}\)

where μ is sample mean,

s is sample standard deviation.

Degree of freedom=n-1

=20-1

=19

t-value at 95% confidence interval=1.7281

\(26\pm 1.728*\frac{3.4}{\sqrt{20}}\\\\=26\pm1.728*0.7606\\\\=26\pm1.31\\\\=24.69,\ 27.31\)

b)

predicted value can be calculated by formula,

\(\mu \pm t*S\sqrt{1+\frac{1}{n}}\\\\=26\pm 1.728*3.4\sqrt{1+\frac{1}{20}}\\\\=26\pm 1.728*3.4*1.02\\\\=26\pm5.99\\\\=20.01,\ 31.99\)

As a result, we conclude that the prediction interval is greater than the confidence interval.

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Answer:

f= 3.5

Step-by-step explanation:

Look at attachment for further explanation

Hope this helps (:

Answer:

You need to add 150 mL of 65% alcohol solution.

Step-by-step explanation:

You have 300 mL of 20% solution.

300 mL of 20% alcohol solution has 20% * 300 mL of alcohol.

You have 65% solution.

Let the volume of 65% solution you add be x.

In 65% solution, 65% of the volume is alcohol, so the amount of alcohol in x amount of 65% solution is 65% * x.

You want 35% solution.

The total amount of 35% solution you will make is 300 mL + x. The amount of alcohol in that amount of solution is 35% * (x + 300).

Equation of alcohol content:

20% * 300 + 65% * x = 35% * (x + 300)

60 + 0.65x = 0.35x + 105

0.3x = 45

x = 150

Answer: You need to add 150 mL of 65% alcohol solution.

Answer:

y = 5000x

Step-by-step explanation:

Let x = number of days

Let y = number of widgets

Given, factory produces 5000 widget per day:

⇒ y = 5000x

The farm raises some rabbits and native chickens. The number of native chickens is six times the number of rabbits, with a total of 560 feet. farm

Raised ? rabbit.​

Answer: 25(11)=275 which is the price of the 11 bought at the door

Answer:

Jess could run 50 yards in 20 seconds.

Step-by-step explanation:

I divided 40 by 16, then multiplied that by 20, and there's the awnser!

Answer:

f(x)=(x-8)^2 -6

Step-by-step explanation:

Answer:

x=4 and y=2

Step-by-step explanation:

I'm not 100% sure but I substituted different numbers into the equation:

If x=4 and y=2 then 4+2=6 and 3x2=6 so it would be 6=6

Another option is x=7 and y=3 then 7+2=9 and 3x3=9 so it would be 9=9

I'm more confident with x=4 and y=2 because of the small size of the triangle.

I hope this helps! Good luck! :)

The cuboid in question has a surface area of 202 square units.

We must sum together the areas of all six faces to determine a cuboid's surface area.

The dimensions of the given cuboid are:

length (l) = 9 units

width (w) = 5 units

height (h) = 4 units

The area of each face is given by:

Top and bottom faces:\(lw = 9 * 5 = 45\) square units each

Front and back faces: \(lh = 9 *4 = 36\) square units each

Left and right faces: \(wh = 5 * 4 = 20\) square units each

Therefore, the total surface area of the cuboid is:

\(2(lw + lh + wh) = 2(45 + 36 + 20)\\ = 2(101) \\= 202 \ square \ units\)

Hence, the surface area of the given cuboid is 202 square units.

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Answer:

a.

The growth rate (k) can be calculated using the exponential growth formula: P = P0 * e^(kt), where P0 is the initial population, t is the time in years, and e is the natural logarithm base.

From the information provided, the initial population of elves in 2000 was 23, and in 2003, the population was 34. By substituting the values into the formula and solving for k, we get:

34 = 23 * e^(k * 3)

Taking the natural logarithm of both sides:

ln(34) = ln(23 * e^(k * 3))

Using the logarithmic identity:

ln(34) = ln(23) + ln(e^(k * 3))

Solving for k:

k = (ln(34) - ln(23)) / (3) = 0.175

Therefore, the growth rate (k) for the population of elves is 0.175.

b.

To find the population of elves in 2020, we can use the exponential growth formula:

P = P0 * e^(kt)

Substituting the initial population of elves in 2000, which was 23, and the growth rate (k), which we found to be 0.175, we get:

P = 23 * e^(0.175 * 20)

Calculating the exponential function:

P = 23 * e^3.5

Therefore, there will be approximately 51 elves in 2020.

c.

To find the year when there will be 543 elves, we can use the exponential growth formula and solve for t:

543 = 23 * e^(0.175 * t)

Dividing both sides by 23 and taking the natural logarithm of both sides:

ln(543/23) = 0.175 * t

Solving for t:

t = (ln(543/23)) / 0.175

Therefore, there will be 543 elves in the year 2027.

i am not sure

Answer:

91

Step-by-step explanation:

Answer:

m= -5/9

Step-by-step explanation:

m= y2-y1/ x2-x1

m= -3-2/ 5-(-4)

m= -3-2/ 5+4

m= -5/9

y= mx + b

(-4,2)

2= -5/9(-4) + b

2= 2.2+ b

-2.2 +2= b

-0.2= b