What is the lcm of 50

The proportion of those surveyed who chose basketball as their favorite sport is 34.149 (option a)

Let's denote the proportion of adults who chose basketball as their favorite sport as P(Basketball). To calculate P(Basketball), we need to divide the total number of adults who chose basketball by the total number of surveyed adults. Mathematically, it can be represented as:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

To calculate the number of adults who chose basketball, we sum up the values from the age range categories:

Number of adults who chose basketball = Number of adults (18-30) who chose basketball + Number of adults (31-50) who chose basketball + Number of adults (51 and above) who chose basketball

Looking at the table, we find that the number of adults (18-30) who chose basketball is 15, the number of adults (31-50) who chose basketball is 8, and the number of adults (51 and above) who chose basketball is 11. Adding these values together, we get:

Number of adults who chose basketball = 15 + 8 + 11 = 34

Now, let's calculate the total number of surveyed adults. We can sum up the values from the age range categories:

Total number of surveyed adults = Total number of adults (18-30) + Total number of adults (31-50) + Total number of adults (51 and above)

From the table, we find that the total number of adults (18-30) is 49, the total number of adults (31-50) is 48, and the total number of adults (51 and above) is 52. Adding these values together, we get:

Total number of surveyed adults = 49 + 48 + 52 = 149

Now, we have the values we need to calculate the proportion:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

= 34 / 149

Hence the correct option is (a).

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The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

Yes

2n+4

No

76 percent

Step-by-step explanation:

Answer:#1. No

#2. Second option

#3. No

#4. 76%

Step-by-step explanation:

None is needed.

Answer:

m=-3

Step-by-step explanation:

Answer:

y = -3x - 1

Step-by-step explanation:

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (1,-4), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=-4.

Also, let's call the second point you gave, (-2,5), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-2 and y2=5.

To find b, think about what your (x,y) points mean:

(1,-4). When x of the line is 1, y of the line must be -4.

(-2,5). When x of the line is -2, y of the line must be 5.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-3x+b. b is what we want, the -3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,-4) and (-2,5).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(1,-4). y=mx+b or -4=-3 × 1+b, or solving for b: b=-4-(-3)(1). b=-1.

(-2,5). y=mx+b or 5=-3 × -2+b, or solving for b: b=5-(-3)(-2). b=-1.

See! In both cases we got the same value for b. And this completes our problem.

Answer:

Please require a picture pls

Step-by-step explanation:

Answer:

when both sides look the same is symmetry

Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.

P(A) = f / N.

probability = 2%/100=0.0002

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

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The Power e is to which a number should be raised to get the specified number is called the logarithm of that specific number. For example, the logarithm to the base of 10 of 1000 is 3 because 10 raised to the power 3 is 1000.

The logarithmic function is the reverse of the Mathematical function of the exponential function. The logarithmic function is log ax = y is equal to x = ay.

There are mainly two types of logarithms normally used in Mathematics. They are one is common logarithms and second natural logarithms.

The log number ‘e’ is an irrational Mathematical constant and is mostly used as the base of natural logarithms. The number ‘e’ is the only unique number in mathematics whose value of natural logarithm is equal to unity.

The value of log ‘e’ was calculated in 1683 by Jacob Bernoulli.

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The linear function for this problem is defined as follows:

y = x + 50.

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

y = mx + b

In which:

The graph touches the y-axis at y = 50, hence the intercept b is given as follows:

b = 50.

When x increases by 10, y also increases by 10, hence the slope m is given as follows:

m = 10/10

m = 1.

Hence the function is given as follows:

y = x + 50.

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39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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The expressions x + x + x + x and 4x are equivalent.

We can see this by simplifying the first expression:

x + x + x + x = 4x

So we can see that both expressions represent the same quantity, which is the total of adding x four times.

To explain this using a diagram, we can draw four boxes, each labeled with an "x".

x   x   x   x

Then, we can count the total number of "x" in the diagram, which is 4x.

Alternatively, we can also think of distributing the coefficient 4 to each term in the second expression:

4x = 4 * x

= x + x + x + x

This gives us the same expression as the first one, so they are equivalent.

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The length of the arc WX is the number of units on the arc

The length of the arc WX is \(\frac{8}{9} \pi\)

The given parameters are:

Central angle, m<WVX = 20 degrees

Radius, VW = 8

The length (L) of the arc is calculated as:

\(L = \frac{\theta}{360} * 2\pi r\)

Substitute known values

\(L = \frac{20}{360} * 2\pi *8\)

Evaluate the product

\(L = \frac{320}{360} \pi\)

Simplify the fraction

\(L =\frac{8}{9} \pi\)

Hence, the length of the arc is \(\frac{8}{9} \pi\)

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Answer: BCE

Step-by-step explanation:

The angle has a vertex at N, so the correct options are B, C, and E.

Answer:

The lines never intersect because the lines are parallel.

Step-by-step explanation:

Given system of linear equations is:

y = -x +5

y=-x-3

The slope-intercept form of a line is:

\(y = mx+b\)

Here b is the y-intercept and the co-efficient of x is the slope of the line

Comparing the given equations with slope intercept form we get that the slope of both lines is -1

Both lines have the equal slope which means that the lines are parallel.

Parallel lines NEVER intersect each other.

Hence,

The lines never intersect because the lines are parallel.

Answer:

Factored -> (x+7)(x-2)

Step-by-step explanation:

If you are solving for x then its x= -7, x=2

Answer:

  (x, y) ∈ { (4, 0) }

Step-by-step explanation:

When the equations are in standard form (or close to it), it is often convenient to graph them using their x- and y-intercepts. The x-intercept is found by setting y=0 and solving for x. The y-intercept is found by setting x=0 and solving for y.

2x -4y = 8

  x-intercept = 8/2 = 4

  y-intercept = 8/-4 = -2

3x +4y = 12

  x-intercept = 12/3 = 4

  y-intercept = 12/4 = 3

__

The two x-intercepts are the same, so that is the solution to the system of equations: (x, y) = (4, 0). There are various ways to write this in set notation. Simply listing the set of solutions is one of them: { (4, 0) }.

_____

Additional comment

Standard form is ax+by=c, where 'a' is positive and a, b, c are mutually prime integers (have no common factors). In the first equation, all of the coefficients are even, so 2 is a common factor. In standard form, that equation would be ...

  x -2y = 4

The greatest common factor (GCF) of 18, 30, and 54 is 6.

The greatest number that divides two or more numbers without leaving a residue is known as the GCF.

The prime factorization approach is the most effective way to resolve this issue.

Using this technique, you will first determine the largest common factor amongst each number's prime factors.

The prime factorization of 18 is 2 x 3 x 3.

The prime factorization of 30 is 2 x 3 x 5. The prime factorization of 54 is 2 x 3 x 3 x 3.

The largest common factor amongst all of them is 6, which is the GCF.

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For an exponential function  \(f(x) = 3^{-x}2\) as x goes to infinity, f(x) goes to zero.

We have been given an exponential function \(f(x) = 3^{-x}2\)

We need to check the end behavior of f(x) as x goes to infinity.

Consider,

\(\lim_{x \to \infty} f(x)\\\\= \lim_{x \to \infty} 3^{-x}2\\\\=2\times \lim_{x \to \infty} 3^{-x}\\\\=2\times 3^{-\infty}\\\\=2\times 0\\\\=0\)

This means, x \(\rightarrow\) infinity, f(x) goes to 0

As x goes to infinity, f(x) goes to zero.

Therefore, for an exponential function  \(f(x) = 3^{-x}2\) as x goes to infinity, f(x) goes to zero.

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Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

An angular resolution of 0.56 arcseconds is required to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

Angular resolution is defined as the minimum angle between two objects that enables a viewer to see them as distinct objects rather than as a single one. A better angular resolution corresponds to a smaller minimum angle. The angular resolution formula is θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. Thus, the angular resolution formula can be expressed as the smallest angle between two objects that allows a viewer to distinguish between them. In arcseconds, the answer should be given to two significant figures.

To see the Sun and Jupiter as distinct points of light, we need to have a good angular resolution. The angular resolution is calculated as follows:

θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the telescope.

Using this formula, we can find the minimum angular resolution required to see the Sun and Jupiter as separate objects. The Sun and Jupiter are at an average distance of 5.2 astronomical units (AU) from each other. An AU is the distance from the Earth to the Sun, which is about 150 million kilometers. This means that the distance between Jupiter and the Sun is 780 million kilometers.

To determine the angular resolution, we need to know the wavelength of the light and the diameter of the telescope. Let's use visible light (λ = 550 nm) and assume that we are using a telescope with a diameter of 2.5 meters.

θ = 1.22 λ / D = 1.22 × 550 × 10^-9 / 2.5 = 2.7 × 10^-6 rad

To convert radians to arcseconds, multiply by 206,265.θ = 2.7 × 10^-6 × 206,265 = 0.56 arcseconds

The angular resolution required to see the Sun and Jupiter as distinct points of light is 0.56 arcseconds.

This is very small and would require a large telescope to achieve.

In conclusion, we require an angular resolution of 0.56 arcseconds to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Answer:12 m is longer

Step-by-step explanation:

Answer:  The long division method is a way to solve division problems by hand. Here are the steps to do long division:

Write the dividend (the number being divided) inside a long division bracket, and write the divisor (the number doing the dividing) outside of the bracket.

Divide the first digit of the dividend by the divisor. Write the answer (the quotient) above the dividend, and write any remainder (what’s left over) below the first digit of the dividend.

Bring down the next digit of the dividend next to the remainder.

Repeat step 2 until you’ve brought down all of the digits of the dividend.

The final answer is your quotient with any remainder written as a fraction.

Answer:

1/3(n)+11

Step-by-step explanation:

n represents a number

Step-by-step explanation:

THREE SOLUTION TO PROVE ITS FALSE

1:2

Multiply by 3 on each side

1*3 : 2*3 = 3:6

This is not the same as 6:3

3 apple:6 bananas is not the same as 6 apples: 3 bananas

1:2 is equivalent to 6:12 not 6:3

because 1x6=6 2×6=12 =6:12

3)

however when we solve mathematically

1/2=6/3

1/2=2

The sides are not equa so its false

Answer:

3500

Step-by-step explanation:

13% - 100% = 87

(3045 x 100) divided by 87 = 3500 people

The total number of people attending the game will be 3500.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

At a basketball game, 13% were supporting the opposing group. On the off chance that 3045 individuals going to uphold the host group.

The percentage of supporting the home team will be given as,

⇒ 100% - 13%

⇒ 87%

The total number of people attending the game will be given as,

⇒ 3045 / 87%

⇒ 3045 / 0.87

⇒ 3500

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The internal energy of the system is given by U = -2ε/kT exp(-ε/kT) + (1/kT) exp(-2ε/kT), where ε is the energy difference between the first and second energy levels, T is the temperature, and k is Boltzmann's constant.

The internal energy U of the system can be calculated using the canonical ensemble partition function:

Z = Σi \(g_i\) exp(-\(E_i\)/kT)

where \(g_i\) is the degeneracy of the \(i_{th}\) energy level and Ei is the energy of the \(i_{th}\) level. The internal energy is then given by:

U = - (∂lnZ/∂β)|V,N

where β = 1/(kT) is the inverse temperature.

Substituting the energy levels and degeneracies, we have:

Z = 1 + 2 exp(-ε/kT) + exp(-2ε/kT)

Taking the natural logarithm of both sides, we get:

lnZ = ln[1 + 2 exp(-ε/kT) + exp(-2ε/kT)]

Using the Taylor series expansion of ln(1+x), we can approximate lnZ as:

lnZ ≈ 2 exp(-ε/kT) - (1/2) exp(-2ε/kT)

Differentiating lnZ with respect to β, we obtain:

(∂lnZ/∂β)|V,N = -kT^(-2) (∂lnZ/∂T)|V,N

= kT^(-2) [2ε/kT^2 exp(-ε/kT) - ε/kT^2 exp(-2ε/kT)]

Substituting this expression into the formula for the internal energy, we get:

U = -kT^(-2) [2ε/kT^2 exp(-ε/kT) - ε/kT^2 exp(-2ε/kT)]

Simplifying, we get:

U = -2ε/kT exp(-ε/kT) + (1/kT) exp(-2ε/kT)

Therefore, the internal energy of the system is given by U = -2ε/kT exp(-ε/kT) + (1/kT) exp(-2ε/kT), where ε is the energy difference between the first and second energy levels, T is the temperature, and k is Boltzmann's constant.

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Answer:

$1,170

Step-by-step explanation:

Area around the pool = 20 x 30

Pool = 12 x 24

Carpet is sold $1.95 by square foot

Use formula A = bh

Plug it in: A = 20 x 30

So they need 600 sq ft of carpet.

Multiply 600 by 1.95 to get 1170

The total cost = $1,170

Answer:

$608.40

Step-by-step explanation:

Dimensions of pool: 12 ft by 24 ft

Dimensions of pool & cement walkways: 20 ft by 30 ft

The pool is a rectangle that sits inside the walkways. The area of the walkways (AW) is the area of the pool & walkways (the 20 ft by 30 ft rectangle) minus the area of the the pool (the 12 ft by 24 ft rectangle). Once we know the area of the just the walkways (AW), we multiply it by the price of the carpet too find the cost of the carpet.

area of walkways = area of pool & walkways - area of pool

AW = 20 ft * 30 ft - 12 ft * 24 ft

AW = 600 ft^2 - 288 ft^2

AW = 312 ft^2

The area of the walkways alone is 312 ft^2. Now we multiply it by the unit cost of carpet to find the cost of the carpet needed for the walkways.

cost = AW * unit rate

cost = 312 ft^2 * $1.95/ft^2

cost = $608.40

Answer:

Step-by-step explanation:

Let the number is xyz.

There are 9 options for x, 8 options for y and 7 options for z since no repetition is allowed.

a)

Total number of options:

b) Since number is divisible by 5, we must have z = 5. Then we have 8 options for x and 7 options for y.

Total number of options: