There are 6 students in an art class, made up of 4 girls and 2 boys. Four children are chosen at random to attend an art exhibit. What is the probability that at least three girls are chosen

Solve this problem using the golden ratio. Given the golden ratio (1 + √5) : 2 and the width of the door, we will find the height of the door.

Step 1: Write the ratio as a fraction.
The golden ratio can be written as a fraction: (1 + √5) / 2.

Step 2: Set up a proportion.
Let the height of the door be h. Then we can write the proportion:

height : width = (1 + √5) / 2
h / 36 = (1 + √5) / 2

Step 3: Solve for h.
To find the height of the door, we'll cross-multiply and solve for h:

h = 36 * (1 + √5) / 2

Step 4: Simplify the expression.
First, we'll distribute the 36:

h = (36 + 36√5) / 2

Next, we'll divide each term by 2:

h = (18 + 18√5)

So, the height of the door is 18 + 18√5 inches, which is in simplest radical form.

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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Miguel will need approximately 636.76 cubic inches more air to completely fill the ball.

To help you with your question, we'll first determine the total volume of the ball using the given radius and then calculate the additional air needed to fill it completely. The ball has a radius of 7 inches.

To find its total volume, we use the formula for the volume of a sphere: V = (4/3) * π * r³.

Plugging in the radius, we get V = (4/3) * π * (7³) ≈ 1436.76 cubic inches.

Miguel has already put 800 cubic inches of air into the ball

To find out how much more air is needed, subtract the air already inside from the total volume:

1436.76 - 800 = 636.76 cubic inches.

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Answer:

a = 127° , b = 12° , c = 115°

Step-by-step explanation:

a and 53° are same- side interior angles and sum to 180° , that is

a + 53° = 180° ( subtract 53° from both sides )

a = 127°

c and 115° are alternate angles and are congruent , then

c = 115°

53° , b and c lie on a straight line and sum to 180°

53° + b + c = 180°

53° + b + 115° = 180°

b + 168° = 180° ( subtract 168° from both sides )

b = 12°

then a = 127° , b = 12° , c = 115°

Answer:

a = 127; b = 12; c = 115

Step-by-step explanation:

c =115

b = 180 - 115 - 53

b = 12

a = b + c

a = 12 + 115

a = 127

Answer:

In the first draw of the trial, the card drawn can be a king of spades, clubs, diamonds, or hearts. So, the size of the sample space is 4 in the first draw. In the second draw, the sample space size becomes 42 = 16.

Step-by-step explanation:

Plato answer !! Hope this helps !! <3

The sample space consists of 16 possible outcomes.

We have trial in which you draw one card twice from a set of 4 kings: spade, club, diamond, and heart and the card is replaced in the set before the second draw.

We have to find the sample space of the trial.

A sample space of any event is the set of total number of possible outcomes of that event.

The card is replaced in the set before the second draw.

After the card is drawn twice - the sample space set S will consist of-

4 x 4 = 16

Hence, the sample space consists of 16 possible outcomes.

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In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.

The correct answer is Option D.

The key concept here is that a plane is defined by having at least three non-collinear points.

When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.

Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.

Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.

The correct answer is Option D.

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Zero is greater than 2, so second one from the left.

Therefore, the distance along an arc on the surface of Earth that subtends a central angle of 5 minutes is approximately 32.85 miles.

The formula that will be used to find the distance along an arc on the surface of Earth that subtends a central angle of 5 minutes is the formula for the length of an arc on the surface of a sphere.

Therefore, the distance along an arc on the surface of Earth that subtends a central angle of 5 minutes is approximately 32.85 miles.

The radius of the Earth is given as 3,960 miles.

The length of an arc on the surface of a sphere is given as:

L = rθwhere L is the length of the arc,

r is the radius of the sphere, and

θ is the central angle subtended by the arc.

So, if θ = 5 minutes = 1/12 degree (since 1 degree = 60 minutes),

then we have:

L = (3,960) (1/12) π / 180= 32.85 miles.

Therefore, the distance along an arc on the surface of Earth that subtends a central angle of 5 minutes is approximately 32.85 miles.

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Yes, there are a few ways to check if you have simplified a rational expression fully or solved a rational equation correctly:

Check for common factors: Make sure that you have factored out any common factors in both the numerator and denominator. For example, if you have (x^2 - 4x)/(x^2 - 16), you can simplify it as x(x - 4)/(x - 4)(x + 4), and cancel out the (x - 4) terms.

Check for restrictions: Check if there are any values of x that would make the denominator equal to zero. If there are, these values are called restrictions, and they must be excluded from the domain of the expression. For example, if you have 1/(x + 3), x cannot be -3, since that would make the denominator equal to zero.

Check your answer: One way to check if your answer is correct is to substitute some values of x into the original expression and the simplified expression, and see if you get the same answer. You can also multiply the simplified expression by the original denominator, and see if you get the original numerator.

Use an online calculator: There are many online calculators that can simplify rational expressions and solve rational equations. You can use these to check your work, or to see step-by-step solutions to problems you are struggling with.

Remember, practice is key when it comes to simplifying and solving rational expressions and equations. Keep practicing, and don't be afraid to ask your teacher or a tutor for help if you are struggling.

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Answer:

h(-3)= 2

h(1)= -14

Step-by-step explanation:

Subsitute the number in parentheses into the equation

h(-3):

-4(-3)-10

12-10

= 2

h(1):

-4(1)-10

-4-10

= -14

By using the concept of confidence interval, it can be concluded that-

Confidence interval = (0.1954, 0.2286)

We are 95 % confident that the true proportion of working adult who

were very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years falls within this interval

Second option is correct

What is confidence interval?

Suppose there is a parameter which is unknown. Confidence interval will give the range of this unknown parameter.

Let the unknown  parameter be θ,  A confidence interval for the parameter θ is an interval (u, v)

where P(u < θ  < v) = 1 - α, where P is the probability

α is called level of significance

Total number of working adults = 2305

Number of working adults surveyed = 489

Proportion of sample surveyed = \(\frac{289}{2305}=\) 0.212

Standard error = \(\sqrt{\frac{0.212 \times ( 1- 0.212)}{2305}} = 0.0085\)

At 95% confidence interval, z value = 1.96

Margin of error = 1.96 \(\times\) 0.0085 = 0.0166

Lower bound for the confidence interval = 0.212 - 0.0166 = 0.1954

Upper bound for the confidence interval = 0.212 + 0.0166 = 0.2286

Confidence interval = (0.1954, 0.2286)

Now since this is a problem on confidence interval, so a concept of confidence will come into question.

So, we are 95 % confident that the true proportion of working adult who

were very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next 5 years falls within this interval

Second option is correct

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Complete Question

The complete question has been attached

Answer:

A teashirt

Step-by-step explanation:

hahahaahahaahahahahahahahahaa

Answer:

a Teashirt

Step-by-step explanation: :)))))))))

The value of the expression \(\frac{2+\sqrt{5} }{\sqrt{5} }\) after rationalizing the denominator is \(\frac{2\sqrt{5}+5 }{5}\).

A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Rationalizing the denominator is the process of shifting a root, such as a square root or a cube root, from the fraction's denominator to its numerator (numerator).

The numerator is the part of a fraction that comes before the vinculum.

The denominator of a fraction is the phrase that comes before the vinculum.

Consider the expression,

\(\frac{2+\sqrt{5} }{\sqrt{5} }\)

Now, let \(y=\frac{2+\sqrt{5} }{\sqrt{5} }\)

To rationalize the denominator we multiply and divide the expression by √5.

\(y=\frac{2+\sqrt{5} }{\sqrt{5} } \times \frac{\sqrt{5} }{\sqrt{5} }\)

\(y=\frac{2\sqrt{5}+(\sqrt{5} )^{2} }{(\sqrt{5} )^{2}}\)

\(y=\frac{2\sqrt{5}+5 }{5}\)

The value of the expression when rationalized \(\frac{2+\sqrt{5} }{\sqrt{5} }\) is \(\frac{2\sqrt{5}+5 }{5}\).

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(a) Is this an observational study or an experiment?

ans=Observational study – no treatment was imposed

(b) What are the explanatory and response variables?

ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior

d) Does this study show that child care causes children to be more aggressive? Explain.

No. Observational studies cannot show cause-and-effect

Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.

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Answer:

\(Cost \ total= \$ 1755\)

Step-by-step explanation:

Find the total cost of a rectangular shaped carpet, given the carpets length,  width, and the cost of carpet per square foot. Using the formula for the area of a rectangle.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Area of a Rectangle:}}\\\\A=l \times w\end{array}\right}\)

Where...

Given:

\(l=15 \ ft\\w=9 \ ft\\ 1 \ ft^2= \$ 13\)

Find:

\(Cost \ total = \ ?? \\)

(1) - Calculating the total area of the carpet, which is a rectangle

\(A=l \times w\\\\\Longrightarrow A=15 \ ft \times 9 \ ft\\\\\therefore \boxed{A=135 \ ft^2}\)

(2) Calculate the total cost of the carpet by multiplying the total area of the carpet by the cost of one square foot of carpet

\(Cost \ total=135 \ ft^2 \times \$ 13\\\\\therefore \boxed{\boxed{Cost \ total= \$ 1755}}\)

Thus, the total cost of the carpet is found.

Answer:

The maximum height of the sign is 3.6 inches.

Step-by-step explanation:

To obtain the maximum height of the sign, we need to understand the relationship between the eccentricity and the dimensions of an ellipse.

The eccentricity of an ellipse measures how elongated or stretched the ellipse is. It is defined as the ratio of the distance between the foci of the ellipse to the length of the major axis.In this case, the eccentricity is given as 0.60, which means the distance between the foci is 0.60 times the length of the major axis.

The length of the major axis is 36 inches, we can calculate the distance between the foci:

Distance between foci = eccentricity * length of major axis

Distance between foci = 0.60 * 36 inches

Distance between foci = 21.6 inches

Now, to obtain the maximum height of the sign, we need to consider that the distance from the center of the ellipse to the highest point (vertex) is equal to the distance from the center to one focus.

The maximum height of the sign is half the length of the minor axis, and it can be calculated using the formula:

Height = 0.5 * (length of major axis - 2 * distance between foci)

Height = 0.5 * (36 inches - 2 * 21.6 inches)

Height = 0.5 * (36 inches - 43.2 inches)

Height = 0.5 * (-7.2 inches)

Height = -3.6 inches

However, negative height does not make sense in this context, so we take the absolute value of the height:

Absolute Height = |-3.6 inches

Absolute Height = 3.6 inches

Therefore, the maximum height of the sign is 3.6 inches.

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Answer:

-2

Step-by-step explanation:

Answer:

Start at 10 and do rise over run. Rise over how many numbers (spaces) and run over how many plots.

The cost of  the two clubs will be the same after 4 sessions

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Let x represent the number of session

Since One tennis club charges $ 34 per session to play tennis. We can write the cost as:

cost = 34x

And another tennis club charges an annual fee of $ plus $ 22 per session. We can write the cost as:

cost = 48 + 22x

At the same cost, we have:

34x = 48 + 22x

34x - 22x = 48

12x = 48

x = 48/12

x = 4

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Complete Question

One tennis club charges $30 per session to play tennis. Another tennis club charges an annual fee of $48 plus $22 per session. After how many sessions is the cost at the two clubs the same?

In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.

The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.

We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).

This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.

Therefore, the correct probabilities are:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.

The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3

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Answer:

11.5 gotchu 100% correct

Step-by-step explanation:

Answer:

\(\frac{23}{2}\) or 11.5

Step-by-step explanation:

I hope this helps!

Answer:

A ≈ 199.1 cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \(\frac{135}{360}\) ( r is the radius )

   = π × 13² × \(\frac{3}{8}\)

   = \(\frac{\pi (169)(3)}{8}\)

   ≈ 199.1 cm² ( to the nearest tenth )

The area of the sector with a central angle of 135 degrees and a radius of 13 cm is 507π/8 cm².

To find the area of the sector with a central angle of 135 degrees and a radius of 13 cm, follow these steps:
Determine the ratio of the central angle to the total angle of the circle (360 degrees): 135/360 = 3/8.
Calculate the area of the entire circle using the formula:

Area = πr²,

where r is the radius.

In this case, Area = π(13 cm)² = 169π cm².
3. Multiply the area of the entire circle by the ratio found in step 1 to find the area of the sector:

(3/8) * (169π cm²) = 507π/8 cm².

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Answer:

x = - 4 and y= 45

Step-by-step explanation:

Multiple the first equation with 10

Then, u will get - 5x + 2y = 110

Multiple the second equation with 8

Then, u will get 24x + 2y = - 6

Now, solve those two equations!

you will get the value of x = - 4

Then substitute tgat value in any one of the equation aboved. You will get y = 45

0.0138 is the exact value of x.

The equation to solve -

log₂ (9x) + 2log₂ (8) = 3

First we will find the value of 2log₂ (8) with the help of log calculator -

log₂ (8) = 3

So, 2 log₂ (8) = 2 × 3 = 6

Putting the value of 2log₂ (8) in the above equation we get ,

⇒ log₂ (9x) + 2log₂ (8) = 3

⇒ log₂ (9x) + 6 = 3

⇒ log₂ (9x) = -3

Now we need to find

⇒ 9X = log₂ (-3) = 2⁻³ = 1/2³ = 1/8 = 0.125 [ x = log [base b] (y) = b to the        

                                                                                            power of y  ]

⇒9X = 0.125

⇒X = 0.125/9

⇒X = 0.0138

Hence, 0.0138 is exact value of x.

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The expression in spherical coordinates is r² · sin² α - 6 · r · cos α + 4 = 0.

In this question we must transform an expression in rectangular coordinates, whose equivalent expression in spherical coordinates by using the following transformation:

f(x, y, z) → f(r, α, γ)

x = r · sin α · cos γ, y = r · sin α · sin γ, z = r · cos α

If we know that x² + y² + 2² - 6 · z = 0, then the equation in spherical coordinates is:

(r · sin α · cos γ)² + (r · sin α · sin γ)² + 4 - 6 · (r · cos α) = 0

r² · sin² α · cos² γ + r² · sin² α · sin² γ - 6 · r · cos α + 4 = 0

r² · sin² α - 6 · r · cos α + 4 = 0

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Answer:

8.55 × 10^7

Step-by-step explanation:

7.9 × 10^7 + 6.5 + 10^6 =

= 7.9 × 10^7 + 0.65 × 10^7

= 8.55 × 10^7

Answer: Distributivo

Step-by-step explanation:

2*3 = 6

2 * x = 2x

Therefore:

2(3+x) = 6 + 2x

Answer:

y=3x

The turtle walks away from the rock at a constant rate.

Step-by-step explanation:

A proportional relationship is one in which the two variables vary directly with each other and can be represented by the equation:

y = kx, where k is the constant of proportionality.

Also, a proportional relationship has a constant rate which is the ratio of the two variables.

A) The equation y = 3x is a proportional relationship because it is in the form y = kx, k =3

B) After 4 minutes, the turtle has walked 12 feet away from the rock.

We cant say that this is a proportional relationship because it may or may not be proportional.

C) The turtle walks for a bit, then stops for a minute before walking again.

It is not proportional

D) The turtle walks away from the rock at a constant rate

This is a proportional relationship because it has a constant rate

Answer:

A ~ A

Step-by-step explanation:

A and another A to make a upside down face with a squiggly.

The domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].

All functions are relations in which there is no value of the domain related to more than one value of the range, functions in explicit form related the variable of the range in terms of the variable of the domain.

Based on the information shown in the graph, the domain is represented by the set of values of the time, that is, the horizontal axis, and the range is represented by the set of values of the height, that is, the vertical axis.

Hence, the domain is represented by the set of values of the time, that is, the horizontal axis, and the domain of the given function is represented by t ∈ [0, 4.5].

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