The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.7. (a) What are the mean and standard deviation of the average number of moths x in 60 traps? (b) Use the central limit theorem to find the probability that the average number of moths in 60 traps is greater than 0.4

The length of the wire is given as follows:

21 ft.

Similar triangles are triangles that share these two features presented as follows:

From the similar triangles, the proportional relationship to obtain the height of the tower is given as follows:

4/5 = 13/h

4h = 13 x 5

h = 13 x 5/4

h = 16.25.

Applying the Pythagorean Theorem, the length of the wire is given as follows:

l² = 16.25² + 13²

l = sqrt(16.25² + 13²)

l = 21 ft.

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The area of the composite figure is equal to 52 square units

The composite figure can be observed to be made up of two congruent triangles, and a parallelogram, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the one congruent triangles = 1/2 × 8 units × 4 units

area of the one congruent triangles = 16 square units

area of the parallelogram = 5 units × 4 units

area of the parallelogram = 20 square units

total area of the composite figure = 16 square units+ 16 square units + 20 square units

total area of the composite figure = 52 square units

Therefore, the area of the composite figure is equal to 52 square units

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Knowing the height of a rim and the diameter of the rim, we have that the rim diameter is 27.4 in.

The tire diameter can be calculated by adding the rim diameter and two times the tire height.
Formula: Tire diameter = Rim diameter + (2 x Tire height)

Given:
Tire height = 5.2 in
Rim diameter = 17 in

Plug in the given values into the formula to find the value of the tire diameter:
Tire diameter = 17 in + (2 x 5.2 in)
Tire diameter = 17 in + 10.4 in
Tire diameter = 27.4 in

Therefore, the correct answer is 27.4 in.

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The true statement about the function y = 40x is that it is a linear function

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

y = 40x

The given function is y = 40x, which represents the total number of dollars Mark earns depending on the number of lawns he mows.

Here are some properties of the function:

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Answer:4

Step-by-step explanation:

Answer:

The distance around the window in inches is 80 inches. This is because the circumference of a semi-circle is equal to π times the diameter (C = πd). So, 40 x π = 80 inches.

The converted value of measuring mass 145 kilograms to pounds is equal to 320 pounds ( round off to near pounds )

Standard relation between kilograms and pounds are :

One kilograms is equal to 2.20462 pounds

Now substitute the required converted value 145 kilograms in the above standard relation we have ,

⇒ ( 1 × 145 ) kilograms = ( 145 ) ×  ( 2.20462 ) pounds

⇒ 145 kilograms = 319.67 pounds

⇒ 145 kilograms = 320 pounds ( round off to near pounds )

Therefore, after conversion of mass unit kilograms into pounds is given by  145 kilograms = 320 pounds ( round off to near pounds ).

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Answer:

Equation: 1,152.00 = 21.80x + 16.60y

21.80x + 16.60y = 1,152.00

x = 52 days

y = 69 days

This money will buy 121 days of food for Jasmine and Siri.

The length seen in the miscroscope is 3.3 inches

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

Scale factor = 10

Object length = 0.33 in

This means that the length of the object seen through the microscope is 10 times the actual length.

So, we have

Length = 10 * Actual length

The actual length is 0.33 inches, so the length seen through the microscope is:

Length = 10 * 0.33

Length = 3,3

Hence, it would appear to be 3.3 inches long when viewed through Sam's microscope.

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The value of T when n = 1 is 1 and the equation of n is n = T²

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

T= √n

When n = 1, we jave

T= √1

Evaluate

T = 1

Recall that

T= √n

Take the square of both sides

n = T²

Hence, the equation is n = T²

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Therefore , the solution of the given problem of equation comes out to be y can be either 3 +√(6) or 3 -√(6) for FG to be equal to HI.

In arithmetic equations, the similar symbol (=) is used to denote equivalence between two statements. It is demonstrated that utilising mathematical methods, which have acted as manifestations of reality, it is feasible to compare different numerical factors. The equal sign, for instance, splits the number 12 and even the answer y + 6 = 12 into two separate parts. One can compute how many characters are already present on either end of this symbol. Contradictory symbol meanings are common.

Here,

To find y such that FG = HI, we need to first calculate FG and HI and then set them equal to each other.

The distance formula can be used to calculate the distance between two points:

Distance between F and G:

FG = √(((-4) - (-5))² + ((-4) - (-7))²)

FG = √(1² + 3²)

FG = √(10)

Distance between H and I:

HI = √((y - 3)² + (10 - 8)²)

HI = √((y - 3)² + 4)

Now we set FG equal to HI:

√(10) = √((y - 3)² + 4)

10 = (y - 3)² + 4

6 = (y - 3)²

y - 3 = ±√(6)

y = 3 ±√(6)

Therefore, y can be either 3 +√(6) or 3 -√(6) for FG to be equal to HI.

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When rotated about the x axis, a cone will form a circle and the sphere will remain a sphere. The prism and cylinder will not form any new figures when rotated about the x axis.

Cone generally refers to a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. It is a surface formed by the straight line segments joining a circle or other closed curve at different levels. Cone shapes are commonly seen in nature, such as in pine cones, ice cream cones, and volcanoes. In mathematics, a cone is a solid figure with a circular base and a curved surface that comes to a point at the top.

A sphere is a three-dimensional object consisting of a perfectly round shape. It is the surface of a perfectly round ball and is mathematically defined as the set of points that are all the same distance from a single point, which is the center. It is one of the most common shapes in geometry and is found in many everyday objects, such as balls and marbles.

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The correct answer is d. column headers.

A formal proof is a logical argument that uses deductive reasoning to show that a statement is true. It typically includes an introduction, a conclusion, and a series of steps that connect the two. Each step is supported by a reason, which can be a definition, an axiom, or a previously proven theorem.

A table may be used in a formal proof to organize information, but column headers are not typically included. Column headers are often used in spreadsheets or data tables to label the columns, but they are not necessary in a formal proof. Therefore, the correct answer is d. column headers.

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After 10 minutes, the first pool will contain a volume of 2267.5 liters of water and the second pool will contain 2702.5 liters of water.

It is important to first identify the information given in the question. We have the starting amounts of water in both pools, as well as the rates at which water is being added to each pool. Using this information, we can set up an equation to determine how much water will be in each pool after a certain amount of time.

Let t represent the amount of time in minutes that the pools are being filled. The equation for the first pool will be 1920 + 34.75t and the equation for the second pool will be 2500 + 20.25t.

To find out how much water is in each pool after a certain amount of time, we can simply plug in the value of t and solve for the amount of water. For example, if we want to know how much water is in each pool after 10 minutes, we can plug in t = 10 and solve:

First pool: 1920 + 34.75(10) = 1920 + 347.5 = 2267.5 liters
Second pool: 2500 + 20.25(10) = 2500 + 202.5 = 2702.5 liters

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Answer:

$9.25

Step-by-step explanation:

Let x be the original price of each ticket before the discount was taken. The discount is $1.50 off each ticket, so the price they actually paid for each ticket is x - 1.50. Since there are 6 tickets, the total price they paid for all 6 tickets is:

6(x - 1.50)

We know from the problem that the total price they paid for all 6 tickets was $46.50, so we can set up the following equation:

6(x - 1.50) = 46.50

Simplifying this equation, we get:

6x - 9 = 46.50

Adding 9 to both sides, we get:

6x = 55.50

Dividing both sides by 6, we get:

x = 9.25

Therefore, the original price of each ticket was $9.25.

Answer:

9.25$

Step-by-step explanation:

Let x be the original price of each ticket before the discount was taken. The discount is $1.50 off each ticket, so the price they actually paid for each ticket is x - 1.50. Since there are 6 tickets, the total price they paid for all 6 tickets is:

6(x - 1.50)

We know from the problem that the total price they paid for all 6 tickets was $46.50, so we can set up the following equation:

6(x - 1.50) = 46.50

Simplifying this equation, we get:

6x - 9 = 46.50

Adding 9 to both sides, we get:

6x = 55.50

Dividing both sides by 6, we get:

x = 9.25

Therefore, the original price of each ticket was $9.25.

Please Brainliest

Answer:

1. No

2. Yes

3. No

Step-by-step explanation:

1.

We know that c = 7, so we plug it in to prove if the equation is true.

[tex]7+8=15[/tex]

The variable is not a solution.

2.

We know a = 30, so we plug it in to prove if the equation is true.

[tex]30-4=26[/tex]

The variable is a solution.

3.

We know y = 4.1, so we plug it in to prove if the equation is true.

[tex]12.6-4.1=8.5[/tex]

The variable is not a solution.

The different ways that the people from can randomly sit down in adjacent seats is 138240 ways

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by nCr

There are 2 people from California, so they can be arranged in 2! = 2 ways.

There are 4 people from Mexico, so they can be arranged in 4! = 24 ways.

Now we can treat the group of Californians and the group of Mexicans as a single block of 6 people (2 Californians and 4 Mexicans), which we can arrange with the 3 people from England. There are 3 + 1 = 4 blocks of 6 people that we can form (one for each possible position of the block), and within each block, there are 6! ways to arrange the people.

Therefore, the total number of arrangements that satisfy the given conditions is:

= 2! * 4! * 4 * 6! = 2 * 24 * 4 * 720

= 138,240 ways

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The solution is, The value of x is 21.4.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

here, we have,

The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x.

The measure of the angle opposite to height is 31°.

The sine of an angle is the ratio of height to the hypotenuse.

Therefore,

sin 31° = height/hypotenuse

sin 31° = 11/x

Multiply x with both sides:

x sin 31° = 11

Divide sin 31° with both sides:

x = 11/ sin 31°

x = 21.35

x ≈ 21.4 units

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The conversion of 3/2 as a decimal is 1.5.

To convert a fraction to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number) using long division, a calculator, or by using a decimal equivalent chart. It's important to note that some fractions have repeating decimals or do not terminate, such as 1/3 or 7/11. In those cases, the decimal representation is either an infinite non-repeating decimal or a repeating decimal.

To convert a fraction to a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number).

So, to convert 3/2 to a decimal, we can perform the following division:

3 ÷ 2 = 1.5

Therefore, 3/2 as a decimal is equal to 1.5.

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In the simplest form, we can write the expression as -

y = [tex]$\frac{2}{15}[/tex].

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

4x + 5z

Given is the mathematical statement as -

"one over six one over 2/3"

We can write the given mathematical statement in the simplest form as follows. We can write the expression as -

y = [tex]$\frac{1}{6\frac{1}{(\frac{2}{3}) } }[/tex]

y = [tex]$\frac{1}{6\frac{3}{2} }[/tex]

y = [tex]$\frac{1}{\frac{15}{2} }[/tex]

y = [tex]$\frac{2}{15}[/tex]

Therefore, in the simplest form, we can write the expression as -

y = [tex]$\frac{2}{15}[/tex].

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The amount owed at the end of that period is given as follows:

$334.

An exponential function is modeled as follows:

y = ab^x.

In which:

For a decreasing exponential function, the rate of change b is given as follows:

b = 1 - r.

In which r is the decay rate.

The parameters for this problem are given as follows:

a = 390, r = 0.05, b = 0.95.

Hence the function giving the amount owed after x months is given as follows:

y = 390(0.95)^x.

After three months, the amount owed is given as follows:

y = 390(0.95)^3

y = $334.

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Answer:

$334.37

Step-by-step explanation:

At the start, Sai owes his mum $390. After the first month, his mum reduces his debt by 5% of $390, which is 0.05 x $390 = $19.50. So at the end of the first month, he owes his mum $390 - $19.50 = $370.50.

After the second month, his mum reduces his debt by 5% of $370.50, which is 0.05 x $370.50 = $18.53. So at the end of the second month, he owes his mum $370.50 - $18.53 = $351.97.

After the third month, his mum reduces his debt by 5% of $351.97, which is 0.05 x $351.97 = $17.60 (rounded to the nearest cent). So at the end of the third month, he owes his mum $351.97 - $17.60 = $334.37.

Therefore, Sai owes his mum $334.37 at the end of three months.

Answer:5 feet 4.567 in hes

Step-by-step explanation:

The conversion of one unit i.e., 164 centimetres to other feet is equals to the 5.37 feet.

Unit conversion, is the conversion between different units and measurements of the same quantity done in the process of multiplication or division. In mathematics, conversion is the process of changing a value from one form to another, such as converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units.

How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. So, 164 meters = 164 × 3.28 feet

= 537.92 feet --(1)

But we need to convert 164 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 164 meters = 16400 centimeters --(2). Now from equations (1) and (2),

16400 centimeters = 537.92 feet,

Divide both parts by 100,

=> 164 centimetres = (537.92/100 ) feet

= 5.37 feet

Hence required value is 5.37 feet.

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The equations are defined as follows:

The two trees will have the same height after four years.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The parameters for this problem are defined as follows:

Hence the equations are given as follows:

The trees will have the same height when:

A(t) = B(t)

Hence:

4t + 38 = 8t + 22

4t = 16

t = 16/4

t = 4 years.

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Answer: 25

Step-by-step explanation:

5^2 is the same as 5x5 which is 25

Answer:

F = 1.8C + 32

F= 1.8(15)+32

F= 59

Step-by-step explanation:

Fahrenheit and Celcius are unit that can be used to measure temperature. In this question, you are given the equation to calculate Fahrenheit from Celcius so you just need to put the Celcius into C variable.

                                 ^^^ P.S Kinda copied but yknow it helps

Step-by-step explanation:

We can divide both of these ratios. If they both come out to be the same number, they are proportional. If different, they are not proportional.

[tex] \frac{0.2}{2.6} = \frac{1}{13} [/tex]

[tex] \frac{0.3}{3.6} = \frac{1}{12} [/tex]

[tex] \frac{1}{13} \: does \: not \: equal \: \frac{1}{12} \: so \: not \: proportional[/tex]

A polynomial is an equation made up of coefficients and in determinates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

Multiplying Polynomials Find each product. 1) [tex]6v(2v + 3) 2) 7(-5v - 8)3) 2x(-2x -3)6v(2v + 3)[/tex]

To distribute the 6v over the binomial 2v + 3, we multiply 6v by each term inside the parenthesis:

[tex]6v(2v) + 6v(3)[/tex]

[tex]= 12v^2 + 18v7(-5v - 8)[/tex]

To distribute the 7 over the binomial -5v - 8, we multiply 7 by each term inside the parenthesis:

[tex]7(-5v) + 7(-8)= -35v - 562x(-2x - 3)[/tex]

To distribute the 2x over the binomial -2x - 3, we multiply 2x by each term inside the parenthesis:

[tex]2x(-2x) + 2x(-3)= -4x^2 - 6x[/tex]

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