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A flying squirrel lives in a nest that is 12 feet up in a tree, but wants to
eat an acorn that is on the ground 9 feet away from the base of his tree.
If the flying squirrel glides from his nest to the acorn, then scurries back
to the base of the tree, and then climbs back up the tree to his nest,
how far will the flying squirrel travel in total?

P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of science, such as statistics, physics, and engineering, as well as in everyday life to make informed decisions based on the likelihood of various outcomes.

The probability of drawing a green block on the first draw is 4/20 (since there are 4 green blocks out of a total of 20 blocks in the bag).

Since the block is being replaced back into the bag after each draw, the probability of drawing a yellow block on the second draw is still 3/20.

Therefore, the probability of drawing a green block followed by a yellow block is:

P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%

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The probability that the song will be played on exactly 2 days out of 5 days is approximately 0.164.

To find the probability that a particular song is played exactly 2 days out of 5 days at radio station WMZH, we can use the binomial probability formula.

The binomial probability formula is given by P(x) = C(n, x) * p^x * (1-p)^(n-x), where P(x) is the probability of x successful outcomes, n is the number of trials, p is the probability of a successful outcome on a single trial, and C(n, x) represents the binomial coefficient, which is the number of ways to choose x items from a set of n items.

In this case, we want to find the probability of the song being played exactly 2 days out of 5 days, so x = 2, n = 5, and p = 3/8.

Using the formula, we have:

P(2) = \(C(5, 2) * (3/8)^2 * (1 - 3/8)^(^5^-^2^)\)

C(5, 2) = 5! / (2! * (5-2)!) = 10

P(2) = 10 * (3/8)^2 * (5/8)^3

P(2) ≈ 0.164 (rounded to three decimal places)

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The mean for the number of people with the genetic mutation in such groups of 600 is 18.

Given that,

About 3% of the population has a particular genetic mutation.

This means that for any group of people, 3% of the people has a particular genetic mutation.

This is a binomial distribution.

Probability that people having genetic mutation = 3% = 0.03

Random sample size = 600

Mean for a binomial distribution can be calculated as,

Mean = n × p

         = 600 × 0.03

         = 18

Hence the mean number of people having genetic mutation is 18.

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Place them horizontally or vertically

The asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

What is the standard position of angles?

Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive x-axis. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle.

To draw an angle in standard position with measure 8/3 π, follow these steps:

Start with the positive x-axis.

Counterclockwise, rotate the initial side of the angle until it coincides with the positive x-axis.

Starting from the initial side on the positive x-axis, rotate the terminal side of the angle in a counterclockwise direction until the angle measures 8/3 π.

The resulting angle will have a measure of 8/3 π and will look like the following:

       |

       |

--------*-----------

       |

       |

Here, the asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

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Answer:

\(y=-5x+9\)

Step-by-step explanation:

The slope of the line is \(-5\).

The given point is \((2,-1)\).

The equation of line in a point-slope form is \((y-y_1)=m(x-x_1)\)

Subsitute \(2\) for \(x_1\), \(-5\) for \(m\) and \(-1\) for \(y_1\) in \((y-y_1)=m(x-x_1)\)

\((y-(-1))=-5(x-2)\\y+1=-5x+10\\y=-5x+10-1\\y=-5x+9\)

Esta es la pendiente de la recta tangente a la curva f(x) en el punto x = a.

La tangente de una derivada no es una operación matemática bien definida. Supongo que lo que se quiere encontrar es la pendiente de la recta tangente a la curva representada por la función f(x) cuya derivada es f'(x) = 6x^2 - 6x - 12 en algún punto x = a.

La pendiente de la recta tangente a la curva f(x) en el punto x = a está dada por la derivada de f(x) evaluada en ese punto, es decir:

m = f'(a)

Entonces, para encontrar la pendiente de la recta tangente a la curva de la función f(x) en el punto x = a, tenemos que evaluar f'(x) en x = a:

m = f'(a) = 6a^2 - 6a - 12

donde f(a) es el valor de la función en el punto x = a.

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Answer:Andy runs 7 meters per second.

436.8/62.08 = x/1

436.8/62.08=7.04

7.04/1 =7.0/1

Hope that help!:)

The sοlutiοn οf the system οf equatiοn is x = 0 and y = 7/3.

If there is nο sοlutiοn tο a system οf equatiοns, it is incοnsistent system; οtherwise, there must be at least οne sοlutiοn. If a set οf equatiοns has infinitely many sοlutiοns, it is dependent.

Every οne οf the equatiοns in a system οf equatiοns must have a sοlutiοn in οrder fοr the system tο be cοnsistent. This demοnstrates that a set οf values fοr the variables may simultaneοusly satisfy all οf the system's equatiοns and shοw that they are nοt mutually exclusive.

There is nο sοlutiοn tο an equatiοn system that satisfies all οf the equatiοns in the system. This indicates that nο cοmbinatiοn οf values fοr the variables can cοncurrently satisfy all οf the system's equatiοns since they are incοmpatible.

The given equatiοns are:

y = 2/3x + 7/3

-4x+6y=14

Substituting the value of y in the second equation:

-4x + 6y = 14

-4x + 6(2/3x + 7/3) = 14

-2x + 4x + 14 = 14

2x = 0

x = 0

Substitute the value of x = 0 we have:

y = 2/3(0) + 7/3

y = 7/3

Hence, the solution of the system of equation is x = 0 and y = 7/3.

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Complete question:

Given system of equations y = 2/3x + 7/3 and -4x + 6y = 14

Find the value of x and y.

According to the information, we can infer that the area of this polygon is 34 units².

To find the area of the figure we must graph it and divide it into different segments. Then we find the area of all the segments and add them to get the total area.

Rectangle 1

6 * 3 = 18

Rectangle 2

2*4=8

Triangle 1

2 * 4 / 2 = 4

Triangle 2

2 * 4 / 2 = 4

Total Area

18 + 8 + 4 + 4 = 34

Based on the above, we can infer that the total area of the polygon is 34 ² units.

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Answer:

x = -7/5  + 1/5  √22

Step-by-step explanation:

Hope this Helps!!

Answer:

10.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions to calculate the hypotenuse.

We know the opposite side from the angle labeled 59 degrees.

sin 59 = opp side / hypotenuse

sin 59 = 9.2/x

x = 9.2/ sin 59

x = 10.733

The expression that represents "3 more than twice a number" is 2n + 3.

The expression "3 more than twice a number" can be translated into an algebraic expression as 2n + 3, where "n" represents the number in question. To understand this expression, we first need to know the order of operations. In this case, "twice a number" means "2n", and "3 more than" means adding 3 to that result. Therefore, the entire expression becomes "2n + 3". It's important to remember that expressions like this are not equations, but rather just a way to represent a mathematical relationship. This type of expression is commonly used in algebraic problem-solving and can be manipulated to solve for different variables.

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Complete question:

Which expression represents "3 more than twice a number"? Choices:

2n−3

3−2n

2n+3

2+n+3

3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer: He could be 47 or 46

Step-by-step explanation: I need the exact date of the time he was born (just the month and the day) to tell you how old he really is, but with the information given, he could be 47 or 46.

He would be 47 years                       \(1945\\-\\1898\\=\\47\\\)

The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.

Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.

Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.

Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.

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Answer:

Step-by-step explanation:

Answer:

  1260 inches

Step-by-step explanation:

1 yard = 36 inches

35 * 36 = 1260 inches

The required area of the sector of the circle with radius 5 yards and central angle 3.8 radians is approximately equals to  47.500 square yards (rounded to three decimal places).

Radius of the circle is equal to 5 yards

Central angle of the sector of the circle is equal to 3.8 radians.

Let us consider θ be the central angle in radians,

And r be the radius of the circle.

Let 'A' be the area of the sector of a circle.

The formula for the area of a sector of a circle is equal to,

A = (θ/2) r^2

Substitute the values in the formula of the area of the sector we have,

⇒ A = (3.8/2) × 5^2

⇒ A = 1.9 × 25

⇒A = 47.500 square yards (rounded to three decimal places)

Therefore,  the area of the sector of the circle is approximately equals to  47.500 square yards (rounded to three decimal places).

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Answer:

160 ounces

Step-by-step explanation:

A pound = 16 ounces

16x10=160 ounces

The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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Answer:

X=27

Step-by-step explanation:

< BAC = x

< ABC = 90° KL PERPENDICULAR TO FG

<ACB= 63

X+90+63=180

X=27

Answer:

x = 27 degree      Due to complimentary = 90 as 180-90 = 90 degree and emits our right angle 90 degree then GCJ + IAK= 63 +27 = 90 due to Complementary angles where 2 angles add up to 90 degree

Step-by-step explanation:

GCJ = 63    IAK = x   Where;  DE = FG to parallel lines KAE =90 degrees and is congruent to ABG Therefore x = 180-90- 63 = 27 degree as supplementary angles up to 180 degree    or 90-63= 27 and angles GCJ + IAK= 63 +27 = 90 due to Complementary angles where 2 angles add up to 90 degree

Answer:

Step-by-step explanation:

14545

Make a basic proportion

16,000/x=110/100

Cross multiply

1,600,000=110x

Divide

x=14545

Answer:

see explanation

Step-by-step explanation:

2

4x² + 64 ← factor out the common factor of 4 from each term

= 4(x² + 16)

3

(a - 10)² = 121 ( take square root of both sides )

a - 10 = ± \(\sqrt{121}\) = ± 11 ( add 10 to both sides )

a = 10 ± 11

then

a = 10 - 11 = - 1

a = 10 + 11 = 21

Answer:

a. 3

b. 5

c. 4

d. 4

e. 10

Step-by-step explanation:

Answer:

read below

Step-by-step explanation:

a.3

b.5

c.2

d.2

6. 8p

The number of children in the school who speak a language other than English at home is 144.

The fraction of children who speak Polish is 1/6.

Percentage is the ratio of a quantity expressed as a number out of 100. Percentage is a measure of frequency. The sign that is used to represent percentage is %.

Number of children in the school who speak a language other than English at home = Percentage of the students who speak a language other than English x number of children

Number of children in the school who speak a language other than English at home = 45% x 320

Number of children in the school who speak a language other than English at home = 0.45 x 320 = 144

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.

Fraction of the students who speak Polish = number of students that speak Polish / total number of students who speak a language other than English.

Fraction of the students who speak Polish = 24 / 144 = 1/6.

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Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Given:

Graph of positions of Bear A and Bear B.

To find:

The average speed of Bear B in m/min.

Solution:

From the graph it is clear that initial point of graph of Bear B is (0,100) and the end point is (60,2800).

The average speed of Bear B is

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(m=\dfrac{2800-100}{60-0}\)

\(m=\dfrac{2700}{60}\)

\(m=45\)

Therefore, the average speed of Bear B is 45 m/min.