Grace wants to find the probability of a family of 3 children having 2 boys and 1 girl. Use a tree diagram to list the possibilities and state the probability of 2 boys and 1 girl.
A) 3/8
B) 2/3
C) 5/8
D) 1/2

Answer: 700

Step-by-step explanation:

772

-72

____

700

The probability of getting:

a) 2 apples is 5/33

b) 1 apple and 1 orange 35/132 .

Here, we have,

given that,

A fruit basket contains 5 apples and 7 oranges.

Paul picks a fruit at random from the basket and eats it.

He then picks another fruit at random to eat.

so, we get,

total number of fruits = 12

now, we have,

a) P( pick 1 apple) = 5/12

then, P( pick another 1 apple) = 4/11

so, we get,

P( picking 2 apples) = 5/12 * 4/11 = 20/132 = 5/33

b) P( pick 1 apple) = 5/12

then, P( pick 1 orange) = 7/11

so, we get,

P( picking 1 apple and 1 orange) = 5/12 *  7/11 = 35/132

Hence, The probability of getting:

a) 2 apples is 5/33

b) 1 apple and 1 orange 35/132 .

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The total number of possible codes is 500.

According to the fundamental counting principle, if there are n ways to do one thing and m ways to do another, then there are n×m methods to accomplish both things.

Given that, the first digit of the four-digit code is 2 and the number is odd.

The first digit of the number is 2, therefore, there is only one possible number for the first digit.

Since the number is odd, the last digit of the number must be an odd number.

Therefore, there are 5 possible numbers, 1,3,5,7, and 9, for the last digit.

Now, for the second and the third digit there are 10 possible numbers, from 1 to 10.

Therefore, as per the principle of counting, the total number of possible codes is:

1 × 10 × 10 × 5

= 500

Hence, the total number of possible codes is 500.

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Answer:

The answer of this question is C

minus 6

Step-by-step explanation:

From 49 to 43 you minus 6

from 43 to 37 you minus 6

Please give me brainliest!

Answer:

d= 44.145 m (meters)

Step-by-step explanation:

distance = (g*t²)/2

t=3 sec. d=?  , g=9.81 m/s²

distance (d)=9.81*(3)²/2  

d= 44.145 m

The equations x1(t) and x2(t) govern the amount of salt in both tanks. These equations can be derived based on information about the initial salt quantities, rates of inflow, outflow, and inter-tank transfer.

The differential equations can be formulated to represent the rates of change of salt in each tank over time.

Let's denote x1(t) as the amount of salt in Tank A at time t, and x2(t) as the amount of salt in Tank B at time t. The rates of change of salt in the tanks can be described using the following equations:

For Tank A:

The rate of salt inflow from the external source is 10 g/liter * 1.5 liter/min = 15 g/min.

The rate of salt outflow to Tank B is (x1(t) / 30) * 3 liter/min = x1(t) / 10 g/min.

The rate of salt outflow from Tank A is 0 since there is no direct drainage.

Therefore, the equation governing the amount of salt in Tank A is:

dx1(t)/dt = 15 - x1(t)/10.

For Tank B:

The rate of salt inflow from the external source is 30 g/liter * 1 liter/min = 30 g/min.

The rate of salt inflow from Tank A is (x1(t) / 30) * 3 liter/min = x1(t) / 10 g/min.

The rate of salt outflow to Tank A is (x2(t) / 20) * 1.5 liter/min = x2(t) / 13.333 g/min.

The rate of salt outflow from Tank B is 2.5 liter/min.

Therefore, the equation governing the amount of salt in Tank B is:

dx2(t)/dt = 30 + x1(t)/10 - x2(t)/13.333 - 2.5.

These equations represent the rates of change of salt in Tanks A and B over time, based on the given inflow, outflow, and inter-tank transfer rates. Solving these differential equations will provide the functions x1(t) and x2(t), which describe the amount of salt in Tanks A and B, respectively, at any given time t.

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Answer:

Step-by-step explanation:

1.  x is the width and length is x+5.  

2. x(x+5) = 126

3. x^2 + 5x = 126

4. subtract 126 from each side to set to zero

5. x^2 + 5x - 126 = 0

6. factor

7. (x+14)(x-9)=0

8.  x can equal -14 or 9 but -14 doesn't make sense in this problem because a length can't be negative

9. so width is 9 and length is 14

Answer:

Starting from

2(-x) = 3x - 5

Distribute

-2x = 3x - 5

add 2x to both sides

0 = 5x - 5

Add 5 to both side

5 = 5x

Flip

5x = 5

Answer:

A= 0.625% that is your answer

Answer:

C. 62.5%

Step-by-step explanation:

6.25 × 100 = 62.5%

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Have an excellent day!

Answer:

232 grams

Step-by-step explanation:

To calculate the mass of the object, we need to use the formula:

Mass = Density × Volume.

First, let's calculate the volume of the rectangular prism. The volume of a rectangular prism is given by:

Volume = Length × Width × Height.

Given that the length is 5 centimeters, the width is 4 centimeters, and the height is 2 centimeters, we can substitute these values into the formula:

Volume = 5 cm × 4 cm × 2 cm = 40 cubic centimeters.

Now, we can calculate the mass using the density and volume:

Mass = 5.8 g/cm³ × 40 cm³ = 232 grams.

Therefore, the mass of the object is approximately 232 grams when rounded to the nearest gram.

Answer:

A because of inflation............

The probability that a pupil selected uses the tennis courts only is the fraction 11/50 or 0.22

The probability of an event occurring is the ratio of the number of required outcome divided by the total number of possible outcomes.

From the question,

The pupils that uses only tennis courts = 92 - (30+19+10) { where 30 is the number of pupils that uses all three, 19 is the number of pupils that uses only swimming pool and 10 is the number of pupils that uses only gym and tennis court}

The pupils that uses only Tennis courts = 92 - 59

The pupils that uses only Tennis courts = 33

The probability of selecting a pupil who uses only the tennis court = 33/150

Therefore by simplification, the probability that only a pupil selected uses only the tennis court is the fraction 11/50

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Answer:

410

Step-by-step explanation:

Revenue is given by the relation :

x . (4,920 - 6x)

F(x) = 4920x - 6x²

To obtain the price, x which maximizes revenue, we take the first derivative of the revenue function and equate to 0

F'(x) = 0

F'(x) = 4920 - 12x

4920 - 12x = 0

-12x = - 4920

x = 4920 / 12

x = 410

Price will be 410

Answer:

b

Step-by-step explanation:

Because if it has to be random then you wouldn't know what 25 numbers you were going to pull out.

By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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The quiz scores of Rich Borne's Chemistry 101 students are as follows: 24, 31, 47, 29, 31, 16, 48, 41, 50, 54, 37, 22, 54, 38, 7, and 16.the performance of Rich Borne's Chemistry 101 students on the quiz

To analyze this data, we can calculate various descriptive statistics such as the mean, median, mode, range, and standard deviation. The mean (average) score can be obtained by summing up all the scores and dividing by the total number of scores. The median represents the middle value when the scores are arranged in ascending order. The mode refers to the most frequently occurring score. The range is the difference between the highest and lowest scores, indicating the spread of the data. The standard deviation measures the variability or dispersion of the scores around the mean.

By calculating these descriptive statistics, we can gain insights into the performance of Rich Borne's Chemistry 101 students on the quiz and understand the central tendency and variability of their scores.

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Answer:

To convert binary into decimal, multiply each binary digit with a power of 2 corresponding to its position.

So for example 1010 would be 1·2³ + 0·2² + 1·2¹ + 0·2⁰ = 8+2 = 10 in decimal.

now you can calculate the answers yourself!

To convert decimal into binary, you can use the following approach:

Write down the answer from right to left

A. if your number is odd, write down a 1, if it is even, write a 0

B. divide the number by 2 and round down, ie. discard any decimals (e.g., 7 / 2 = 3)

C. repeat step A until your number is 0.

example:

18 -> write down 0

18/2 = 9 -> write down 1

9/2 = 4 -> write down 0

4/2 = 2 -> write down 0

2/2 = 1 -> write down 1

1/2 = 0 finished

The result is 10010.

After solving the equation the value of ∠A is 0.64.

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

Given: AB = 6

BC = 4

We have to find angle A.

Adjacent is adjacent to the angle,

The opposite is opposite the angle,

and the longest side is the Hypotenuse.

Sinx = Opposite / Hypotenuse

Sinx = 4/6

Sinx = 0.6

Now solve that equation!

sinx = 0.6

x = sin⁻¹(0.6)

x = 0.64

Hence, the value of ∠A is 0.64.

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To solve the question

First, we will represent the unknown number by y

then we can represent the question mathematically as follow:

Solving the above

Next, to get y, we will cross multiply

Dividing both sides by 90

Therefore, the number is 30

Answer:

(-2,-6) is your answer..

hope this helped you

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\(\huge \bf༆ Answer ༄\)

The given triangles are similar by ~

To evaluate the limit lim [cos (2x)]¹/(x-π) as x approaches T, we can use L'Hospital's Rule. The result of applying L'Hospital's Rule is that the limit is equal to -2 sin(2T) / (x-π)^2.

To apply L'Hospital's Rule, we differentiate the numerator and the denominator separately. The derivative of cos(2x) is -2 sin(2x), and the derivative of (x-π) is 1.

After differentiating, we obtain the limit lim -2 sin(2x) / 1 as x approaches T. Now, we can substitute T into the expression, resulting in -2 sin(2T) / 1.

Therefore, the limit of [cos (2x)]¹/(x-π) as x approaches T using L'Hospital's Rule is -2 sin(2T) / (x-π)^2. This result indicates the behavior of the original function as x approaches T.

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Answer:

false

Step-by-step explanation:

The difference between Pre-Image and Image is given as follows:

Usually, the difference between image and pre-image is the way or method of transformation.

A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure.

The Pre-Image is the original shape of the item, and the Image during the transformation is the final shape and location of the object.

The types of transformation in math are;

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To show that j(x) and k(x) are inverse functions, we show that the following condition holds.

Similarly:

Therefore, they are inverses.

\(\dfrac{3^{15}}{3^3} = 3^{15 -3} = 3^{12}\)

Pairwise comparison voting, also known as Condorcet voting, satisfies both majority rule and pairwise victory (the Condorcet criterion).

1. Pairwise comparison: In pairwise comparison voting, each candidate is compared to every other candidate in a head-to-head contest. Voters rank the candidates in order of preference, and the outcomes of these individual contests are used to determine the overall winner.

2. Majority rule: Majority rule is satisfied in pairwise comparison voting because, in each head-to-head contest, the candidate who receives more than 50% of the votes is considered the winner. This ensures that the candidate with the majority of votes in each comparison is acknowledged as the preferred choice.

3. Pairwise victory (Condorcet criterion): The Condorcet criterion states that if there is a candidate who can beat every other candidate in a one-on-one contest, that candidate should be the overall winner. Pairwise comparison voting satisfies the Condorcet criterion because it directly compares each candidate against all others, ensuring that any candidate who consistently wins these head-to-head contests is recognized as the overall winner.

In conclusion, pairwise comparison voting (Condorcet voting) satisfies both majority rule and pairwise victory (the Condorcet criterion) by comparing candidates in head-to-head contests, ensuring that the candidate with the majority of votes in each contest is acknowledged as the preferred choice, and recognizing any candidate who consistently wins these head-to-head contests as the overall winner.

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To answer this question we will set and solve an equation.

Since the height of the ball above the ground after t seconds is:

then its velocity after t seconds is:

Setting H'(t)=48.5ft/s we get:

Therefore:

Subtracting 97 from the above equation we get:

Dividing the above equation by -32 we get:

Answer:

Answer: 25 ounces of yogurt

Step-by-step explanation:

Blueberries to Yogurt

                2 to 5

               10 to ?

The original ratio is 2 ounces of blueberries and its now 10 ounces. We got ten ounces by multiplying 2 by 5. To get the ounces of yogurt, you have to also multiply by 5.

5 x 5 = 25

So the ratio of blueberries to yogurt is now, 10 to 25.

Hope this helped!