A bowl contains 14 beads, of which 4 are brown.
What is the probability that a randomly selected bead will be brown?

The height of the arch at a distance of 1.5 meters from the center is approximately D. 1.73 meters

The shape of a semi-elliptical arch can be described by the equation:

y = c * sqrt(1 - (x/a)^2)

where "a" is half the span of the arch, "c" is the central height of the arch, and (x,y) are the coordinates of a point on the arch, measured relative to the center of the arch.

In this case, we have a span of 6 meters, so a = 3 meters. The central height of the arch is 2 meters, so c = 2 meters. We want to find the height of the arch at a distance of 1.5 meters from the center, so x = 1.5 meters.

Substituting these values into the equation, we get:

y = 2 * sqrt(1 - (1.5/3)^2)

y = 2 * sqrt(1 - 0.25)

y = 2 * sqrt(0.75)

y = 2 * 0.866

y = 1.732

Therefore, the height of the arch at a distance of 1.5 meters from the center is approximately 1.73 meters. Answer D

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Your question is incomplete, but probably the complete question is :

A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.

A.   1.41 m C.   1.56 m

B.   1.63 m D.   1.73 m

The only number between 18 and 30 that is a multiple of 5 and satisfies this condition is 20, Therefore, the mystery number is 20

The GCF of 18, 36, and the mystery number is 2.

This means that the mystery number is divisible by 2.

The mystery number is also a multiple of 5, so it must end in either 0 or 5.

The mystery number is greater than 18 and less than 30, so it can only be 20 or 25.

Let's check if the GCF of 18, 36, and 20 is 2.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

The factors of 20 are 1, 2, 4, 5, 10, and 20.

The only factor that 18, 36, and 20 have in common is 2, so the mystery number is 20.

Therefore, the mystery number is 20.

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Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

The slope is the rate at which the pool is being filled.

A slope of 2 means a filling rate of 2 inches per minute.

Answer: The height of the water increases 2 inches per minute.

Answer:

a two-dimension surface formed by two number lines.

The total number of t-shirts principal ordered in $1520 for the school store is given 214.

Let us consider the number of t-shirts the principal ordered be equal to 'x'.

The cost of each t-shirt is equal to $7.

⇒ The total cost of 'x' t-shirts =  7x dollars.

Shipping cost is a flat rate for any order, regardless of the number of t-shirts =  $22

Total cost of the order (including shipping) =  $1520.

Required equation is equal to,

7x + 22 = 1520

Subtract 22 from both sides of the equation we get,

⇒ 7x = 1498

Divide both sides of the equation by 7 we get,

⇒ x = 214

Therefore, the number of t-shirts ordered by  principal for the school store is equal to  214.

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Answer:

12x - 6

Step-by-step explanation:

[tex] \rm \: 4 + 5(3x - 2) - 3x[/tex]

[tex] \rm \: = 4 + 15x - 10 - 3x \: \sf (distribute \: the \: 5)[/tex]

[tex] \rm= 12x - 6 \: \sf (combine \: like \: terms)[/tex]

[tex] \rm= 6(2x - 1) \: \sf (factor \: out \: a \: 6)[/tex]

[tex] \rm \: = 6(2x) - 6(1) \: \sf (distribute \: the \: 6)[/tex]

[tex] \rm \:= 12x - 6 \: \sf (simplify)[/tex]

Answer:

2

Step-by-step explanation:

The vertical distance between (2, 11/3) and (2, -4/3) is -5 units.

The distance formula is a mathematical equation used to find the distance between two points in a plane. It is derived from the Pythagorean theorem and is expressed as:

d = √((x₂- x₁)²+ (y₂ - y₁)²)

The distance formula can also be extended to three-dimensional space by adding an additional term to the equation.

The two points (2, 11/3) and (2, -4/3) have the same x-coordinate, which means they lie on a vertical line. To find the vertical distance between these two points, we simply subtract their y-coordinates:

Vertical distance = (y-coordinate of second point) - (y-coordinate of first point)

= (-4/3) - (11/3)

= -15/3

= -5

Therefore, the vertical distance between (2, 11/3) and (2, -4/3) is -5 units. Since this is a negative value, it means that the second point is located 5 units below the first point.

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Answer:

To find the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures, we first need to convert both temperatures to Celsius or Fahrenheit. Since Oklahoma's temperature is given in Fahrenheit and New Jersey's temperature is given in Celsius, we'll convert Oklahoma's temperature to Celsius.

Using the formula F = 1.8C + 32, we can solve for C:

-31°F = -35°C

(To see how we arrived at this conversion: first, we use the formula to convert Fahrenheit to Celsius: F = 1.8C + 32. Rearranging the equation, we can solve for C: (F - 32) / 1.8 = C. Plugging in -31°F for F, we get (-31 - 32) / 1.8 = -35°C)

Now we can find the difference in Celsius between the two temperatures:

|-35°C| - |-37°C| = |-2| = 2°C

So the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures is 2°C.

The value of the perimeter, p, of the smaller trapezium is 113.

The perimeter of the trapezium is the distance round the trapezium and for this given diagram it can be calculated using congruence theorem.

The Congruence Theorems are a set of geometric principles that state when two geometric figures are congruent, which means they have the same size and shape.

Applying congruence theorem, we will have the following equation;

Side length: x/42

Area: 200/288

Perimeter : p/162

x/42 = p/162 ------ (1)

200/288 = p/162 ---- (2)

from (1), p = (162x)/42 = 3.857x

Substitute the value of p into (2)

200/288 = (3.857x)/162

162(200/288) = 3.857x

112.5 = 3.857x

x = 29.17

p = 3.857 x 29.17

p = 112.5

p ≈113

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The measure of angle J, m∠J = 41.2°.

angle mwasurement:

We can use trigonometry to find the measure of ∠J. Since we know the lengths of the two sides adjacent to ∠J (GH and GJ), we can use the tangent function, which is defined as the opposite side divided by the adjacent side:

tan(J) = opposite/adjacent = GH/GJ

We can solve for J by taking the inverse tangent (or arctan) of both sides:

J = [tex]tan^{-1}[/tex](GH/GJ)

Substituting the given values, we get:

J = [tex]tan^{-1}[/tex](14/16)

Using a calculator, we find:

J ≈ 41.186

Rounded to the nearest tenth, the measure of angle J is 41.2°.

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Given:

ratio = 5:6 , Antecedent = 95

so, as we know that if a ratio is in the form of a/b, then  

a is antecedent and b is called consequent.

so,

5/6 =95/b

on doing cross multiplication we get;

5×b=95×6

b=(95×6)/5

b=19×6

b=114

Hence, consequent(b) is 114.

Hence, the correct match of probabilities with their corresponding situations is given by option 4.

To match the probabilities with their corresponding situations, we can utilize the formulas given below:

[tex]P(A ∩ B) = P(A) x P(B|A)P[/tex](2 aces) =[tex](4/52) x (3/51) = 1/221[/tex]

P(heart and club) =[tex](13/52) x (13/51) = 169/2652[/tex]P(spade and ace of hearts) = 0P(2 of the same card) = (1/52) + (3/51) + (2/50) + (1/49) + (4/48) + (3/47) + (2/46) + (1/45) = 20/663P(red card and four of spades) = (16/52) x (1/51) = 4/663

Therefore, the probabilities with their corresponding situations are:3: P(spade and ace of hearts) = 0 (Not possible as Ace of hearts is not spade)

4: P(2 aces) = 1/2211: P(heart and club) = 169/26521: P(heart and club) = 169/26522: P(red card and four of spades) = 4/663

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Answer:

4x^{3} ÷ 8 = x^{3}/2

The extreme values of the function f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27 are minimum = 0 and maximum = 18

Given that

f(x, y, z) = x^2 + y^2 + z^2, x^2 + y^2 + z^2 + xy = 27

To find the extreme values of the function f(x, y, z) subject to the given constraint, we can use the method of Lagrange multipliers.

Defining the Lagrangian function L as follows:

L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z))

where g(x, y, z) is the constraint function and λ is the Lagrange multiplier.

In our case, we have:

f(x, y, z) = x^2 + y^2 + z^2

g(x, y, z) = x^2 + y^2 + z^2 + xy - 27

So, our Lagrangian function becomes:

L(x, y, z, λ) = x^2 + y^2 + z^2 - λ(x^2 + y^2 + z^2 + xy - 27)

To find the extreme values of f(x, y, z) subject to the constraint g(x, y, z) = 0, we need to solve the following system of equations:

∂L/∂x = 0

∂L/∂y = 0

∂L/∂z = 0

∂L/∂λ = 0

g(x, y, z) = 0

Taking the partial derivatives of L with respect to x, y, z, and λ, we get:

∂L/∂x = 2x - λ(2x + y) = 0

∂L/∂y = 2y - λ(2y + x) = 0

∂L/∂z = 2z - λz = 0

∂L/∂λ = x^2 + y^2 + z^2 + xy - 27 = 0

From the third equation, we get:

2z - λz = 0

z(2 - λ) = 0

So, either z = 0 or λ = 2.

If z = 0, then from the first two equations, we get:

2x - λy = 0

2y - λx = 0

Multiplying the first equation by y and the second equation by x, we get:

2xy - λy^2 = 0

2xy - λx^2 = 0

Subtracting the second equation from the first, we get:

λ(x^2 - y^2) = 0

Since λ cannot be zero, we have x^2 = y^2 and x = y

Similarly, if λ = 2, then from the first two equations, we get:

2x - 2y = 0

x = y

Substituting x = y into the constraint equation, we get:

2x^2 + x^2 = 27

x^2 = 9

x = ±3

So, the possible critical points are:

(3, 3, 0)

(-3, -3, 0)

(0, 0, 0)

Recall that

f(x, y, z) = x^2 + y^2 + z^2

So, we have

f(3, 3, 0) = 3^2 + 3^2 + 0^2 = 18

f(-3, -3, 0) = -3^2 + -3^2 + 0^2 = 18

f(0, 0, 0) = 0^2 + 0^2 + 0^2 = 0

Hence, the minimum is 0 and the maximum is 18

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The probability of having to wait at least 1 more hour for the next car is 0.631 or approximately 63.1%.

The given problem can be solved using the Poisson distribution. Let [tex]$\lambda$[/tex] be the average rate of cars passing through the section per hour. Then, since the probability of no cars passing in one hour is 0.4, we have:

Solving for [tex]$\lambda$[/tex], we get [tex]$\lambda= -ln(0.4) \approx 0.916$[/tex]. Therefore, the probability of no cars passing in three hours (two hours have already passed) is:

The probability of waiting at least 1 more hour for the next car is the same as the probability of having no cars pass in the next hour, given that no cars have passed in the last 2 hours. This can be calculated using the conditional Poisson distribution:

[tex]$= \frac{\frac{(0.916\cdot1)^0e^{-0.916\cdot1}}{0!}\cdot \frac{(0.916\cdot2)^0e^{-0.916\cdot2}}{0!}}{0.148} \approx 0.631$[/tex]

Therefore, the probability of having to wait at least 1 more hour for the next car is 0.631 or approximately 63.1%.

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Answer:

bar chart

Step-by-step explanation:

you are right box plot, histogram and a circle graph aren't the right ones

We may conclude after answering the presented question that rectangle Therefore, the expression for the width of the porch is x + 2 feet.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

area of a rectangle

Area = length x width

To do this, we can factor the expression for the area, which gives us:

x² + 9x + 14 = (x + 2)(x + 7)

Area = length x width

(x + 2)(x + 7) = (x + 7) x width

x + 2 = width

Therefore, the expression for the width of the porch is x + 2 feet.

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According to the exponential growth formula , there will be 38400 bacteria present after 3 days.

The given formula for the bacteria population, f(x) = 75 - 8², seems to be incorrect. Since the bacteria reproduce by dividing in half every 8 hours, we should use an exponential growth formula.

Let's denote the number of bacteria present after z days as f(z). Since there are 24 hours in a day, there are 3 reproduction cycles in a day (24 hours / 8 hours per cycle = 3 cycles). Therefore, the total number of reproduction cycles after z days is 3z.

The formula for the bacteria population after z days is: f(z) = 75 * 2^(3z)

Now, let's find the total number present after 1, 2, and 3 days.

1 day: f(1) = 75 * 2^(3 * 1) = 75 * 2^3 = 75 * 8 = 600
There will be 600 bacteria present after 1 day.

2 days: f(2) = 75 * 2^(3 * 2) = 75 * 2^6 = 75 * 64 = 4800
There will be 4800 bacteria present after 2 days.

3 days: f(3) = 75 * 2^(3 * 3) = 75 * 2^9 = 75 * 512 = 38400
There will be 38400 bacteria present after 3 days.

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Answer:

The correct answer is OD.

Step-by-step explanation:

To find how many classes each instructor teaches per week, you need to set up and solve a system of equations based on the given information. In other words,

Let x be the number of classes Bo teaches per week and y be the number of classes Erica teaches per week.

The first equation is based on the total number of classes they teach

x + y = 37

The second equation is based on the relationship between their numbers of classes

y = 2x - 14

To solve this system, you can use substitution or elimination methods. For example, using substitution, you can plug in y = 2x - 14 into the first equation and get

x + (2x - 14) = 37

Simplify and solve for x

3x - 14 = 37

So, Bo teaches 17 classes per week and Erica teaches 20 classes per week.

Answer:

A. 19 Bo; 18 Erica

Step-by-step explanation:

im good like that hehe

The total area of the composite figure is 114.25 square feet.

The area of a circle of diameter D is:

A = 3.14*(D/2)²

And the area of a triangle of base B and height H is:

A = B*H/2

We can decompose the figure into two simpler ones, a triangle of base of 10ft and height of 15 ft, whose area is:

A = 10ft*15ft/2 = 75ft²

And half of a circle of diameter of 10ft, whose area is:

A = 0.5*3.14*(10ft/2)² = 39.25 ft²

Then the total area of the figure is:

area =  75ft² + 39.25 ft² = 114.25 ft²

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The probability that an ugly splice is weak is 2/3.

This can be calculated by multiplying the probability of weak splices (1/1000) with the probability of ugly splices (1/20) and the probability that a weak splice is also ugly (2/3).

In order to calculate the probability that an ugly splice is weak, we need to use the equation: P(A∩B) = P(A) * P(B|A). In this equation, A represents the probability of weak splices (1/1000), and B represents the probability of ugly splices (1/20).

The probability that a weak splice is also ugly (2/3) is then multiplied by A and B, giving us a final answer of 2/3. This means that 2 out of every 3 ugly splices are weak.

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This shows that they read less frequently than 95.7% of their classmates in the same grade level.

In statistics, a percentile is a metric that is used to express where one observation stands in relation to a larger group of data. It displays the proportion of data points that fall under a given value. For instance, if a student achieves a score in the 90th percentile on a standardised test, it signifies that they outperformed 90% of their peers who also took the test. As an alternative, if a child is taller than 25% of children their age and shorter than 75%, their height is in the 25th percentile for their age.

given

We must first compute the z-score using the following formula to determine the percentile of the child's reading proficiency.

z = (x - μ) / σ

where x represents the child's reading rate, represents the grade-level mean reading rate, and represents the standard deviation.

Inputting the values provided yields:

z = (46.2 - 85) / 22

z = -1.727

We can calculate or use a conventional normal distribution table to obtain the value of 0.0428 for the region to the left of z = -1.727. The child's reading rate is at the 4.28th percentile according to this statistic.

As a result, the child's reading proficiency is 4.3 percentile (rounded to one decimal place).

This shows that they read less frequently than 95.7% of their classmates in the same grade level.

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The length of the long diagonal of the cube is 3sqrt(3) inches.

Let's denote the length of one side of the cube as "a". Then the cube has a volume of a^3, a surface area of 6a^2 (since a cube has 6 faces with side length a), and a total edge length of 12a (since each face has 4 edges of length a).

Using the given equation, we can write

a^3 + 3(12a) = 2(6a^2)

Simplifying this equation, we get

a^3 + 36a = 12a^2

a^3 - 12a^2 + 36a = 0

a(a^2 - 12a + 36) = 0

a(a - 6)^2 = 0

The only positive solution for "a" is a = 6 (since a cannot be zero or negative). Therefore, the cube has a side length of 6 inches.

To find the length of the long diagonal of the cube, we can use the Pythagorean theorem. The long diagonal passes through the center of the cube and connects two opposite corners. The distance from the center to a corner is half the length of the long diagonal. Let's call this distance "d".

Using the Pythagorean theorem, we can write

d^2 = (6/2)^2 + (6/2)^2 + (6/2)^2

d^2 = 3(6^2)/4

d = (sqrt(3)×6)/2

d = 3sqrt(3) inches

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Johnny has 1258 more pineapples than Bobby.

Bobby has 37 pineapples, Johnny has 35 times more pineapples than Bobby. To find how many more pineapples does Johnny have than Bobby, we can use the below formula,

More pineapples = Johnny's pineapples - Bobby's pineapples

Let x be the number of pineapples that Bobby has. Therefore, the number of pineapples owned by Johnny is 35x.

It is given that Bobby originally has 37 pineapples, thus x = 37. The number of pineapples Johnny has = 35*37 = 1295

Thus, difference in number of pineapples between Johnny and Bobby:

=1295-37 = 1258

Therefore, Johnny has 1258 more pineapples than Bobby.

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The garden would require 84 plants, which is the same number of plants as the garden's surface area.

The area of the garden can be determined using the formulas below if it is shaped like a right triangle and has sides that are 7 and 24 yards long.

Area of the garden = (1/2) x Base x Height

Area of the garden = (1/2) x 7 x 24

Area of the garden = 84 square yards

Since there is one square yard of area for each plant, the number of plants needed for the garden would be equal to the area of the garden, which is 84 plants.

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The probability that an even number or a number greater than 3 is rolled on a 12-sided die is 0.833.

A 12-sided die has 12 equally likely outcomes, numbered from 1 to 12. To find the probability of rolling an even number or a number greater than 3, we need to count the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.

There are 6 even numbers on a 12-sided die, namely 2, 4, 6, 8, 10, and 12, and there are 9 numbers greater than 3, namely 4, 5, 6, 7, 8, 9, 10, 11, and 12. However, we need to be careful not to count the numbers that satisfy both conditions twice, namely 4, 6, 8, 10, and 12.

Therefore, the number of outcomes that satisfy the condition is 6 + 9 - 5 = 10. The probability of rolling an even number or a number greater than 3 is therefore 10/12, which simplifies to 5/6 or approximately 0.833.

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A future interest in real property typically exists in conjunction with a present interest in that same property at the time the future interest is granted.

What is a future interest?

Future interests are created when a property owner grants an interest in their property that will take effect at a later time, such as after their death or the expiration of a lease.

These interests are typically created in the form of a trust or a will, and they can be used to ensure that property is distributed according to the owner's wishes, to provide for the future needs of family members, or to protect property from creditors or other claims.

Examples of future interests include remainders, reversions, and executory interests.

Complete questin:

A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?

1) future interest

2) protect property

3) both a and b

4) None of these

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The sample size required is 182 families should be interviewed.

To calculate the number of families that should be interviewed to obtain the desired precision and degree of confidence, one must first determine the minimum sample size required to achieve the desired degree of confidence. As the standard deviation of the sample was computed to be $400 with the mean of $60,000.

Sample size formula: n = (Z² * s²) / E²

The formula for the degree of confidence: Z = 2.576

Sample size formula: n = (Z² * s²) / E²

Substituting the values, we get n = (2.576² * $400²) / $90²= 181.49 = 182 families. The sample size required is 182 should be interviewed families.

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Theoretical probability of drawing the letter "o" is 1/4, or 0.25 as a decimal.

The probability of drawing the letter "o" from the bag of tiles depends on the number of tiles with the letter "o" and the total number of tiles in the bag.

Since the word "Colorado" has two "o's", there are two "o" tiles in the bag. The total number of tiles in the bag is the number of letters in the word "Colorado", which is 8.

Therefore, the theoretical probability of drawing the letter "o" is:

P("o") = number of "o" tiles / total number of tiles

= 2/8

= 1/4

So the theoretical probability of drawing the letter "o" is 1/4, or 0.25 as a decimal.

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