what is the area of a circle with a diameter of 12in?

ANSWER

120 ways

EXPLANATION

We want to see how many ways 3 projects can be selected from 10 possible projects.

Since there is no particular order for the selection, we will use combinuation.

We have:

That is the answer.

Answer:

1). y= -4+ 4x

2). y= 3+ x/2

Step-by-step explanation:

hope this helps !

Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )

Answer:

100 seconds

i hope this helps

Monthly payment: $75

Number of months in 2 years: 24

Then, the answer is the product of the number of months (24) and the monthly payment ($75):

Answer:

A: 12.5

B: 36

C: 40

D: 88

Step-by-step explanation:

those are the answers

Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.

A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.

The area of the rectangular patio is given by multiplying its length by its width, so the area is:

A = (1 + 2x)(2 - 3x)

Now using distributive property we get,

A = 2 - 3x + 4x - 6x²

Simplifying further, we get:

A = -6x² + x + 2

Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.

To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:

P = 2(1 + 2x) + 2(2 - 3x)

Simplifying this expression, we get:

P = 2 + 4x + 4 - 6x

P = 6 - 2x

Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.

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Answer:

False. The center of a semisimple Lie algebra is usually not trivial.

Step-by-step explanation:

The center of a semisimple Lie algebra is the set of elements of the Lie algebra that commute with all other elements in the algebra. In most cases, the center of a semisimple Lie algebra is not trivial, meaning it contains at least one non-zero element. For example, the center of the simple Lie algebra sl(2,C) contains the two-dimensional Lie algebra spanned by the scalar matrices I and -I. The center of the Lie algebra so(5,C) is spanned by the five-dimensional Lie algebra spanned by the matrices diag(1,1,1,-1,-1). These examples demonstrate that the center of a semisimple Lie algebra is usually not trivial.

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A box-and-whisker plot, also known as a box plot, is a data visualization technique used to summarize and display the distribution of a set of values.

The five-number summary, which includes the minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value, is used to create the box plot. In this case, we are comparing the data for two cities, Greenville and Oaktown.

The five-number summary for each city is provided in the question: Greenville: minimum = 1 Q1 = 8 median = 12 Q3 = 16 maximum = 22 Oaktown: minimum = 2 Q1 = 6 median = 8 Q3 = 9 maximum = 15 To construct a box-and-whisker plot for each city on the same number line, we will use the following steps:

1. Draw a number line with the minimum and maximum values for both cities.

2. Draw a vertical line at the first quartile (Q1) for both cities.

3. Draw a box from Q1 to Q3 for both cities.

4. Draw a vertical line at the third quartile (Q3) for both cities.

5. Draw whiskers from the box to the minimum and maximum values for both cities.

6. Label each box-and-whisker plot with the name of the corresponding city. The resulting box-and-whisker plot for Greenville and Oaktown on the same number line is shown below:

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Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)

\(\implies B=88^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)

\(\implies a=13.0876493...\)

\(\implies a=13.1\)

Solve for b:

\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)

\(\implies b=26.9194211...\)

\(\implies b=26.9\)

\(\hrulefill\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies C=180^{\circ}-A-B\)

\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)

\(\implies C=73^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)

\(\implies a=20.8847511...\)

\(\implies a=20.9\)

Solve for b:

\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)

\(\implies b=12.5954671...\)

\(\implies b=12.6\)

In linear equation, -1.15  is the value of 21 over 4 − 32 over 5.

What in mathematics is a linear equation?

An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation. The above is sometimes called a "linear equation in two variables" where x and y are variables.

                                An equation with only one variable is called a univariate linear equation. It contains the expression Ax + B = 0. where A and B are any two real numbers and x is an ambiguous variable with only one possible value. 

(21/4) - (32/5)

=   21 * 5 - 32 * 4/ 20

=  105 -  128/20

= -1.15

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Answer:

Brand A

Step-by-step explanation:

Brand A has a box of 25 forks for 1.99

Take the price per fork

1.99 /25 = .0796

              .08 per fork

Brand B has a box of 42 totals for 3.89

3.89 / 42

.092319048

.09 per fork

The area of the trapezoid \(36^{2}\) centimeters

To use the formula A = ¹h(b₁ + b₂) to find the area of a trapezoid, you need to know the height (h) and the lengths of the two parallel bases (b₁ and b₂).
For example,

The formula for finding the area of a trapezoid is A = ¹h(b₁ + b₂),

Where A represents the area of the trapezoid, h represents the height, and b₁ and b₂ represent the lengths of the two parallel bases.

By plugging in the given values for the height and bases and performing the necessary arithmetic operations, you can find the area of the trapezoid.

It's important to remember to use the correct units and follow the order of operations to obtain the correct result.

If the height of the trapezoid is 9 cm, the lengths of the two bases are 3 cm and 5 cm, you can plug these values into the formula to find the area :
A = ¹h(b₁ + b₂)

= ¹(9)(3 + 5)

= ¹(9)(8)

= 36 square centimeters
So, the area of this trapezoid is 36 square centimeters.
If you have different values for the height and bases, you can use the same formula to find the area.

Just make sure to use the correct units and follow the order of operations (parentheses first, then multiplication and division, then addition and subtraction).

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why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

Answer:

Who picks up that many pecans?

Step-by-step explanation:

i get bored after like 30. jeez.

By solving a system of equations, we will see that the equation is:

-4*x - 3*y = -18

We know that the linear equation:

A*x + B*y = -18

We know that this linear equation passes through the points (-3, 10) and (6, -2), then replacing these values in the equation we will get two equations:

A*-3 + B*10 = -18

A*6 + B*-2 = -18

So we have a system of equations:

-3A + 10B = -18

6A - 2B = -18

if we add the two times the first equation and the second one we get:

2*(-3A + 10B) + 6A - 2B = 2*(-18) - 18

18B = -3*18

B = -3

by replacing that value of B in one of the equations we will be able to solve it for A.

6*A - 2*(-3) = -18

6*A + 6 = -18

6*A = -18 - 6 = -24

A = -24/6 = -4

The equation is:

-4*x - 3*y = -18

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Answer:

C.) 2^10

Step-by-step explanation:

You would add the exponents which in this case are 3 and 7 getting 10 as your exponent.

Answer: C)

Step-by-step explanation: If you do 2^3 x 2^7 = 1024 also 2^10 = 1024

Answer:

47523.84

Step-by-step explanation:

Let's draw the scenario to understand it better:

From the figure, the information given are:

Question:

Step 1: We write a function that relates the quantities in the diagram using Pythagorean

Theorem.

Step 2: Differentiate with respect to t.

Now we wish to plug in specific numbers for every quantity in the above equation except for dD/dt. However, we notice that we don’t have a specific value for D at y = 400 ft. So first we need to find D at y = 400 ft. using the Pythagorean Theorem.

Step 3: Finish the problem by plugging in numbers for every quantity in the equation

containing dD/dt.

Conclusion: When the rocket is 300 ft. feet from the ground, the distance between the observer and the rocket is increasing at a rate of 180 ft./sec.

Answer:

the absolute value of -3.75 is 3.75

Answer:

1.24

Step-by-step explanation:

oahsofhasdf0as0dfadera

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

We know that,

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

a_n = a_1 + (n-1)d

where d is the difference and a₁ is the first term of the sequence.

The major distinction between recursive and explicit formulas is that a recursive formula returns the value of a particular term depending on the preceding term, whereas an explicit formula returns the value of a given term based on its location.

When the value of the first term and the common difference is known then an explicit formula is used, while the recursive formula will be used when the value of the previous value is known and the value of the common difference is known.

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complete question:

what is the difference between the explicit formula and recursive formula for sequences when would you use one over the other​

Answer: The probability that both events A and B will occur is 5/18 or 0.28.

Step-by-step explanation:

To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.

Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.

Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.

To find the probability that both events A and B occur, we multiply the probabilities:

Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.

Answer:

After 3 min

Step-by-step explanation:

So becuase Tim is walking and Tim gave Alex a 50 meter head start so after 3 min they will tie each other.

Answer:

A) 0.23

B) 0.14

Step-by-step explanation:

Part A)
To solve this question, we'll have to use the Bernoulli formula.
The formula claims that the probability to get \(k\) successes out of \(n\) attempts is given by \(\binom{n}{k}p^k(1 - p)^{n - k}\).

In our case, \(n = 5\), \(k = 3\), and \(p = 0.78\).

Therefore, the probability that 3 out of the 5 drivers use their turn signal is

\(\binom53 \times 0.78^3 \times 0.22^2 \to 0.23\)

Part B)

We are told that the police officer pulled over 5 drivers, 3 of them using turn signals. In this part, we are asked "what is the probability that the 5th driver uses the turn signal and only 2 of the previous four drivers use turn signals?".

\(0.78 \times \binom42 \times 0.78^2 \times 0.22^{4-2}\\\to 0.14\)

The exponential function that passes through the points (-1,-y) and (1,20) is f(x) = -20eˣ.

We need to use the given points to form two equations and solve for the constants in the exponential function.

For the first problem:

Let (0,4) and (2,16) be the given points.

Since the function is of the form f(x) = Ca², we have:

f(0) = C(0)² = 4

f(2) = C(2)² = 16

Simplifying each equation:

C = 4

4a² = 16

a² = 4

a = ±2

Therefore, the exponential function that passes through the points (0,4) and (2,16) is f(x) = 4(2)² = 16 or f(x) = 4(-2)² = 16.

For the second problem:

Let (-1,y₁) and (1,y₂) be the given points.

Since the function is of the form f(x) = Ca, we have:

f(-1) = Ca = y₁

f(1) = Ca = y₂

Simplifying each equation:

C =y₁/a

C =y₂/a

Equating both expressions for C, we have:

y₁/a = y₂/a

y₁=y₂

Therefore, the exponential function that passes through the points (-1,-y) and (1,20) is f(x) = -20eˣ.

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The derivative of the function \(f(x) = \frac{1}{\sqrt{2x^2 + 5x + 3}}\) is \(f'(x) = -\frac{4x + 5}{2((x + 1)(2x + 3))^\frac{3}{2}}\)

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \frac{1}{\sqrt{2x^2 + 5x + 3}}\)

Factor the expression

So, we ave

\(f(x) = \frac{1}{\sqrt{(x + 1)(2x + 3)}}\)

The derivative of the function can be calculated using as follows:

\(f'(x) = (-\frac{1}{2})((x + 1)(2x + 3))^{-\frac{1}{2} - 1} \cdot \frac{d}{dx}[(x + 1)(2x + 3)]\)

Next, we have

\(f'(x) = -\frac{\frac{d}{dx}(x + 1) \cdot (2x + 3) + (x + 1) \cdot \frac{d}{dx}(2x + 3)}{2((x + 1)(2x + 3))^\frac{3}{2}}\)

Differentiate

\(f'(x) = -\frac{1 \cdot (2x + 3) + (x + 1) \cdot 2}{2((x + 1)(2x + 3))^\frac{3}{2}}\)

This gives

\(f'(x) = -\frac{2x + 3 + 2x + 2}{2((x + 1)(2x + 3))^\frac{3}{2}}\)

Evaluate the like terms

\(f'(x) = -\frac{4x + 5}{2((x + 1)(2x + 3))^\frac{3}{2}}\)

Hence, the derivative of the function is \(f'(x) = -\frac{4x + 5}{2((x + 1)(2x + 3))^\frac{3}{2}}\)

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Answer:

Table B

Step-by-step explanation:

The table B shows possible outcomes of flipping 3 coins.

A probability experiment is a test in which we execute a series of trials to determine the likelihood of an event occurring in the future. A probability experiment's results may reveal a previously unknown truth or lead us to learn anything about the likelihood (or chance) of an occurrence occurring in the future.

Given:

If three coins are flipped then the possible outcomes are:

{ HHH,

HHT,

HTH

THH,

TTT,

TTH,

THT,

HTT}

So, there total 8 number of outcomes.

But in table 1 the number of outcomes is 5.

Thus, table B shows possible outcomes of flipping 3 coins.

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Answer:

Step-by-step explanation:

Given:

Arrival rate λ = 1.25 min

Mean μ = 2

Computation:

(a) Probability [No customers in system]

Probability [No customers in system] = 1-[λ/μ]

Probability [No customers in system] = 1-[1.25/2]

Probability [No customers in system] = 0.375

(b) Customers waiting for service

Customers waiting for service = λ²/ [μ(μ-λ)]

Customers waiting for service = 1.25²/ [2(2-1.25)]

Customers waiting for service = 25/24

(c) Average time customer wait

Average time customer wait = λ / [μ(μ-λ)]

Average time customer wait = 1.25/ [2(2-1.25)]

Average time customer wait = 1.25/1.5

(d) May be wait because Customers waiting for service = 25/24

(e) Per customer average time

Per customer average time = 1/(μ-λ)

Per customer average time = 1/(2-1.25)

Per customer average time = 1.33 (Approx)