11. At astronomy school, 30% of the students studying stars, 40% are studying black holes, 10% are studying planets, and 20% are studying comets. Use the random-number table to find the experimental probability that in a group of 4 students, at least 2 will be studying stars. Assign values from the table for each field of study: 11. A. Assign values for the number of stars. M. B. Assan values for the number of black holes. chshe 11. C Assign values for the number of planets. 11. D. Assign values for the number of comets. Use the table to simulate the probability that at least 2 will study stars. 3516 D 1388 5476 2802 11 E What is the simulated probability that at least 2 will be studying stars? 6035 5147 1264​

The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.

The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.

For the given question:

Triangle with degree angles - 45-45-90

It means two legs are of same length 5 units.

Then, hypotenuse H will be:

H² = 5² + 5²

H² = 25 + 25

H² = 50

H = 5√2

Thus, the correct third side of the triangle will be 5√2.

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Answer:

8.449 square centimeters

Step-by-step explanation:

Area of the figure = area of square + area of triangle

[tex] {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5[/tex]

[tex].142 \times 59.5 = 8.449[/tex]

So 8.449 square centimeters of this figure is green.

Answer:

Step-by-step explanation:

adjacent:   [tex]\angle BOC, \angle EOD[/tex]   (both are adjacent)

complementary:  [tex]\angle BOC[/tex]

supplementary:   [tex]\angle EOD[/tex]

vertical angles:   [tex]\angle AOE[/tex]

Answer:

-2

Step-by-step explanation:

Answer:

hope its right

Step-by-step explanation:

The tοtal price οf the game including tax is $29.96.

Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.

Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:

0.07 x $28 = $1.96 in taxes

As a result, the purchase tax is $1.96.

Tο calculate the tοtal price, add the purchase price and the tax:

Purchase price + Tax = Tοtal Price

Tοtal cοst: $28 + $1.96 = $29.96

As a result, the tοtal cοst οf the game, including tax, is $29.96.

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Answer:

Step-by-step explanation:

Given g(x) = 8x2 − x + 5, find the following.

(a). g(0) = 5

(b). g(−1) = 14

(c). g(r) = ?

(d). g(x + h) = ?

Hence, x has a value of 36 as the sum of the supplementary angles 3x and 2x must equal 180 degrees .

Angles in mathematics are used to quantify how much two intersecting surfaces or lines rotate relative to one another. Angles can be measured in degrees, radians, or various ways. Degrees, which divide a whole rotation into 360 equal parts, are the most popular unit of measurement for angles. Angles are a fundamental idea in geometry and trigonometry and have practical uses in a number of industries, including physics, engineering, and navigation.

given

The sum of the supplementary angles 3x and 2x must equal 180 degrees. Which is:

3x + 2x = 180

Putting similar phrases together on the left side, we get:

5x = 180

When we multiply both sides by 5, we get:

x = 36

Hence, x has a value of 36 as the sum of the complementary angles 3x and 2x must equal 180 degrees .

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Answer:

Step-by-step explanation:

In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph

Answer:

The answer is 96

Step-by-step explanation:

2*(26+22)

2*48

96

Answer:

1. y = 3 1/3

2. y = 6

3. y = 12

Step-by-step explanation:

A = xy => xy = 14 => y = 14/x

1. x = 4 1/5 = 21/5

y = 14/x = 14/(21/5) = (5 x 14)/21 = 10/3 = 3 1/3

2. x = 2 1/3 = 7/3

y = 14/x = 14/(7/3) = (3 x 14)/7 = 6

3. x = 7/6

y = 14/x = 14/(7/6) = (6 x 14)/7 = 12

Answer:

44 students

Step-by-step explanation:

1200 for the first year

a third of that is 400

400 for the second year

a third of that is 133.4

133.4 for the third year

a third of that is 44

The solutions for x are x= +[tex]\sqrt{12.5[/tex] and -[tex]\sqrt{12.5[/tex] which has been obtained by solving the equations given in the question.

Define Equation?

An equation can be defined in numerous ways. An equation is a claim that demonstrates the equivalence of two mathematical expressions, according to algebra.

In the initial equation, we get: by substituting y=x:

[tex]x^2[/tex] +[tex]y^2[/tex]= 25

[tex]x^2[/tex] +[tex]x^2[/tex] = 25 (since y = x)

2[tex]x^2[/tex] = 25

[tex]x^2[/tex] = 12.5

When the two sides are square, we get:

x = ±[tex]\sqrt{12.5[/tex]

Therefore, the solutions for x are x = +[tex]\sqrt{12.5[/tex] and x = -[tex]\sqrt{12.5[/tex]

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Answer:

Step-by-step explanation:

To calculate the volume of the room, we need to integrate the difference between the ceiling and floor functions over the region bounded by the circle. We can use double integrals to do this.

First, let's rewrite the equations for the floor and ceiling in terms of x and y:

Floor: z = (x + y) / 5

Ceiling: z = 20 + xy / 100

The volume of the room can be calculated using the following double integral:

V = ∫∫(20 + xy/100 - (x + y)/5) dA

where the limits of integration are x = 0 to x = 50, and y = 0 to y = √(50^2 - x^2).

We can simplify the integrand by combining like terms:

V = ∫∫(400/100 + xy/100 - (20x + 20y)/100) dA

V = ∫∫(4 + xy/100 - 0.2x - 0.2y) dA

Now we can integrate with respect to y first:

V = ∫0^50 ∫0^√(50^2 - x^2) (4 + xy/100 - 0.2x - 0.2y) dy dx

V = ∫0^50 [(4y + xy^2/200 - 0.2xy - 0.1y^2)|y=0^√(50^2 - x^2)] dx

V = ∫0^50 [(4√(50^2 - x^2) + x(50^2 - x^2)/200 - 0.2x√(50^2 - x^2) - 0.1(50^2 - x^2)^2/200)|x=0^50]

Evaluating this integral, we get:

V ≈ 2,233.5 cubic feet

Therefore, the volume of the room is approximately 2,233.5 cubic feet, which is the amount of space that will need to be heated or cooled.

Answer:

The function g(x) = (x + 2)³ − 6 is obtained by applying three transformations to the parent function f(x) = x³.

First, g(x) is shifted 2 units to the left by subtracting 2 from x inside the parentheses:

g(x) = (x + 2 - 2)³ − 6 = (x)³ − 6

This shows that option C, "g(x) is shifted 2 units to the left and 6 units down," is not correct.

Next, g(x) is shifted 6 units down by subtracting 6 from the entire function:

g(x) = (x + 2)³ − 6 - 6 = (x + 2)³ - 12

This shows that option A, "g(x) is shifted 2 units to the right and 6 units down," is correct.

Finally, g(x) is not shifted left or right by any additional units, but it is shifted 2 units up by adding 2 to the constant term:

g(x) = (x + 2)³ − 6 + 2 = (x + 2)³ - 4

This shows that option B, "g(x) is shifted 6 units to the right and 2 units up," is not correct.

Therefore, the correct answer is option A: g(x) is shifted 2 units to the right and 6 units down.

Answer:

Yes, ∆PQR is a right triangle.

Step-by-step explanation:

A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.

Answer:

Step-by-step explanation:

34,05m my love

Answer:

The height of the tree is approximately 15.14 meters, rounded to the nearest hundredth of a meter.

Step-by-step explanation:

Let's call the height of the tree "h". We can use similar triangles to set up an equation involving Joseph's height, the length of his shadow, the height of the tree, and the length of the tree's shadow.

The two triangles we're interested in are:

Joseph's triangle: This triangle has a height of 1.75 meters (Joseph's height) and a base of x meters (the length of Joseph's shadow).

Tree's triangle: This triangle has a height of h meters (the height of the tree) and a base of 29.7 - x meters (the length of the tree's shadow).

Since the two triangles are similar, we can set up the following proportion:

h / (29.7 - x) = 1.75 / x

To solve for h, we can cross-multiply and simplify:

h * x = 1.75 * (29.7 - x)

h * x = 52.075 - 1.75x

h = (52.075 - 1.75x) / x

Now we need to find the value of x that makes the tips of the two shadows meet. From the problem statement, we know that x + 34.05 = 29.7, so:

x = 29.7 - 34.05

x = -4.35

This means that the tips of the shadows don't actually meet, but the problem is likely assuming that the tips of the shadows are very close together, so we can use the value x = -4.35 to approximate the height of the tree.

Substituting x = -4.35 into our equation for h, we get:

h = (52.075 - 1.75(-4.35)) / (-4.35)

h = 15.14

Based on the given conditions, the lock solution is 205.

To solve the lock, to calculate the total score based on the given conditions:

Crocus: + 20

Daffodil: + 25

Snowflake: - 50

Tulip: + 30

Bird-Red: + 25, else + 10

Calculating the scores for each input:

TULIP: +30

CROCUS: +20

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

CROCUS: +20

Total score = 30 + 20 + 25 + 30 + 25 + 30 + 25 + 20 = 205

Therefore, the solution for the lock is 205.

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Image transcribed:

SPRING NOW LOADING.

<IF CROCUS, THEN +20>

<IF DAFFODIL, THEN +25>

<IF SNOWFLAKE, THEN -50>

<IF TULIP, THEN +30>

<IF BIRD-RED, THEN +25, ELSE + 10>

TULIP

CROCUS

DAFFODIL

TULIP

DAFFODIL

TULIP

DAFFODIL

CROCUS

Solve Lock

Answer:The measure of Ф = 75.7° :)

Step-by-step explanation:the measure of Ф = 75.7°,We will use the rule sin to find the measure of Ф

At first we will find the angle opposite to the side of length 31

∵ 180° - 73° = 107°

hope this helps:)(:

Answer:

1/128

Step-by-step explanation:

The probability of tossing a head is 1/2.

Each toss is an independent event.

We toss 7 times and get a head each time.

1/2 * 1/2* 1/2* 1/2* 1/2* 1/2* 1/2

1/128

It takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.

calculating the elevation the hiker climbs in stage one:

2% of 2,150 feet = 0.02 × 2,150 feet = 43 feet

Therefore, the hiker climbs 43 feet in stage one. To find the time it takes for the hiker to climb the remaining elevation of the mountain in stage two, we need to know the total elevation he needs to climb in this stage. This can be calculated by subtracting the elevation climbed in stage one from the total elevation of the mountain: Total elevation - Elevation climbed in stage one = 2,150 - 43 = 2,107 feet

Now, we can use the rate of climb in stage two to find the time it takes to climb 2,107 feet:

Time = Distance / Rate

Time = 2,107 feet / 12 feet per minute

Time ≈  175.58 minutes

Therefore, it takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.

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The two statements that are both true are as follows: line

AC is perpendicular to line HB and line AC is parallel to FG. That is option A.

A perpendicular line is defined as the line that forms angle 90° where it meets with another line in a plane.

A line is said to be parallel to each other when they do not intercept as they are both on the same plane.

From the given diagram, line AC is perpendicular to line HB because they form angle 90° at the point of intersection.

Also, line AC is parallel to FG, because they can never intersect till infinity.

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Answer:

The percent decrease in population can be calculated by dividing the difference between the two populations by the original population and then multiplying by 100. In this case, the percent decrease is ((137000-117820)/137000)*100 = 14%.

Step-by-step explanation:

Answer:

it is not likey bc inless the class have over 2 mil ppl in it itis doouptfull

Step-by-step explanation:

The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac

The distributive property is a mathematical property that applies to multiplication and addition or subtraction.

It states that when you multiply a number (or variable) by a  sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.

This is represented by the following formula:

a(b + c) = ab + ac

This is represented by Option (B)

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Answer:

To determine which statements are true, we can use the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Using this form, we can rewrite the given equation as:

(x - 1)^2 + y^2 = 3^2 + 1^2 = 10

Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.

To find the radius, we can rearrange the equation as follows:

x^2 - 2x + y^2 = 8

Completing the square for x, we get:

(x - 1)^2 + y^2 = 9

This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Therefore, the three true statements are:

1.The radius of the circle is 3 units.

2.The center of the circle lies on the x-axis.

3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Step-by-step explanation:

hope its help <:

Answer:

Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:

Step-by-step explanation:

Answer: When there are n teams in a league and each team plays every other team twice, then each team will play a total of n-1 games (since they don't play against themselves). Therefore, the total number of games played in the league is the sum of all the games played by each team, which is:

Total number of games = (number of teams) × (number of games played by each team) / 2

The division by 2 is necessary since each game involves two teams, so counting each game twice would result in double counting.

For the given basketball league with 11 teams, the total number of games played would be:

Total number of games = 11 × (11-1) / 2

= 11 × 10 / 2

= 55 × 2

= 110

Therefore, 110 games would be played in the league.

Step-by-step explanation:

Using the supplementary angle theorem, the value for x so that points A, B, and C are collinear is 8.

What is a supplementary angle?

The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.

A line segment AC is drawn.

Point B is in between A and C.

A transversal DE is drawn passing through point B.

Points D, B, and E are collinear.

The measure of angle CBE is 148° and the measure of angle EBA is 4x°.

The angles ∠CBE and ∠EBA forms a pair of supplementary angles.

Their sum result in value of 180°.

Mathematically, this can be represented as -

∠CBE + ∠EBA = 180°

Substituting the values into the equation -

148° + 4x° = 180°

Solving for x, we get -

4x° = 180° - 148°

4x° = 32°

x = 32 / 4

x = 8

Therefore, the value for x is obtained as 8.

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Answer:

Step-by-step explanation:

f Trevor used 2 lb 6 oz of a 5-lb bag of potatoes, then the weight of the remaining potatoes is:

5 lb = 80 oz (since 1 lb = 16 oz)

Remaining potatoes = Total potatoes - Used potatoes

Remaining potatoes = 80 oz - 2 lb 6 oz

Remaining potatoes = 80 oz - (2 × 16 oz + 6 oz)

Remaining potatoes = 80 oz - 38 oz

Remaining potatoes = 42 oz

Therefore, the remaining potatoes weighed 2 lb 10 oz (or 42 oz).