At the Middletown Middle School fun run, teams compete in a relay race. Each person runs 1 2 of a mile, and the race is 2 miles long. How many people are on each team?

The length of ML in the line segment is 35 units.

The figure below has the following length as follows:

LN = 79 units

Let's find ML in the line segment as follows:

LM + MN = LN

Hence,

LM = 5y - 5

MN = 4y + 12

Therefore,

LN = 5y - 5 + 4y + 12

79 = 5y - 5 + 4y + 12

79 = 9y + 7

79 - 7 = 9y

72 = 9y

divide both sides by 9

y = 72 / 9

y = 8

Therefore,

ML = 5(8) -5

ML = 40 - 5

ML = 35 units

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Part A: You can decompose Figure ABCDE into two triangles and two rectangles. The two triangles are triangle ABC and triangle AED. The two rectangles are rectangle BCD and rectangle AEB.

Part B: The length of Side AB is 4 units and the length of Side AE is 5 units.

Part C: To find the area of Figure ABCDE, we can simply add the areas of the two triangles and two rectangles. The area of triangle ABC is 3 units2, the area of triangle AED is 6 units2, the area of rectangle BCD is 10 units2, and the area of rectangle AEB is 3 units2. Thus, the area of Figure ABCDE is 3 + 6 + 10 + 3 = 22 units2.

The system of inequalities of the given question is x>0, y>0 and 24x+8y=160

When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalties.

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

We are given that;

Price per hour for tutoring=$24

Price per hour for clearing tables=$8

Earning no less than $160

Work no more than in tutoring= 8hr

Maximum working for clearing table=5hr

Now,

x = number of hours tutoring y = number of hours landscaping

We cannot have negative values for either x and y, so xo and

x+y= total hours worked for both jobs combined

This total cannot exceed 11 hours

x+y≤11

Either x+y= 11 or x+y < 11

22x amount of money made from tutoring only = By amount of money made from landscaping only 22x+8y = total amount made from both jobs

24k+By 160 since he must make at least $160 Either 24x+8y = 160 or 24x+8y> 160

Therefore, the system of inequalities will be x>0,y>0,24x+8y=160

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Answer: 6x = 6x. || x is equal to any number.

Step-by-step explanation:

Step 1. 3x + 3 / 9 = 2x + 2 / 6

Step 2. We multiply all terms by the same value to eliminate fraction denominators, then cancel multiplied terms that are in the denominator. After this, distribute. 6x + 6 = 6x + 6

Step 3. Subtract 6 from both sides. 6x (6 - 6) = 6x (6 - 6)

Step 4. Simplify the expression. 6x = 6x

Step 5. x = any number.

Answer:

Third side > 13 - 8 = 5 cm. Therefore, the length of the third side is between 5 cm and 9 cm, respectively.

Step-by-step explanation:

Answer:21>c>5

Step-by-step explanation:

a+b>c>a-b

so,

13+8>c>13-8

21>c>5

The fraction of these 36 chemical elements that are named for women or places is 27/36 or by simplifying it, 3/4.

A fraction is defined as a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

Here,
To find the fraction of the 36 chemical elements that are named for women or places, we need to add the number of elements named for women (2) and the number of elements named for places (25), and then divide by the total number of elements (36),

Fraction = (2 + 25) / 36 = 27 / 36

Therefore, the fraction of these 36 chemical elements that are named for women or places is 27/36 or simplify it, 3/4.

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Answer:

Step-by-step explanation:

Let's start by defining our variables:

a = number of student tickets sold

y = number of adult tickets sold

To write the system of inequalities, we need to take into account the given conditions:

The auditorium can hold no more than 85 people, so the total number of tickets sold cannot exceed 85:

a + y ≤ 85

The drama club must make no less than $690 from ticket sales:

7a + 10y ≥ 690

They must sell a minimum of 10 student tickets and at least 55 adult tickets:

a ≥ 10

y ≥ 55

To solve this system of inequalities graphically, we can plot the lines representing each inequality on the same graph and shade the feasible region. The feasible region is the area that satisfies all the inequalities.

First, let's plot the line a + y = 85. To do this, we can find the intercepts:

a + y = 85

a = 0 ⇒ y = 85

y = 0 ⇒ a = 85

Plotting these points and connecting them with a straight line, we get:

     |

   85|       /

     |       /

     |     /

     |   /  

     | /    

     |/______

          85    

Next, let's plot the line 7a + 10y = 690. To do this, we can find the intercepts:

7a + 10y = 690

a = 0 ⇒ y = 69

y = 0 ⇒ a = 99

Plotting these points and connecting them with a straight line, we get:

     |

   85|      /

     |      /

     |    /

     |  /  

     |/

     |______

          99

Finally, we need to shade the feasible region. We know that a ≥ 10 and y ≥ 55, so we can shade the region above the line a = 10 and to the right of the line y = 55.

markdown

Copy code

     |

   85|        /\

     |         /   \

     |       /       \

     |     /          \

     |    /             \

      /_________\

          99    55

This shaded region represents all the possible solutions that satisfy all three inequalities. We can now find one possible solution by picking any point within this region. For example, the point (20, 65) represents selling 20 student tickets and 65 adult tickets, which meets all the conditions and generates a total revenue of 720 + 1065 = $690.

Answer:B

Step-by-step explanation: I took the test

trust me :p

If the discriminant is negative, there are nο real sοlutiοns, but there are twο cοmplex sοlutiοns in the fοrm οf cοmplex cοnjugates.

In algebra, a quadratic equatiοn is any equatiοn that can be rearranged in standard fοrm as where x represents an unknοwn value, and a, b, and c represent knοwn numbers, where a ≠ 0.

A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable οf the fοrm:

ax² + bx + c = 0

where a, b, and c are cοnstants, and x is the variable. The quadratic equatiοn is used tο sοlve prοblems that can be represented by a secοnd-degree pοlynοmial functiοn.

The general fοrm οf the quadratic equatiοn can be sοlved using the quadratic fοrmula:

x = (-b ± √(b² - 4ac)) / 2a

where the "±" sign means that there are twο pοssible sοlutiοns, οne with the pοsitive square rοοt and the οther with the negative square rοοt.

The quadratic equatiοn can have οne, twο, οr nο real sοlutiοns depending οn the value οf the discriminant b² - 4ac. If the discriminant is pοsitive, there are twο distinct real sοlutiοns. If the discriminant is zerο, there is οne real sοlutiοn with a multiplicity οf 2.

If the discriminant is negative, there are nο real sοlutiοns, but there are twο cοmplex sοlutiοns in the fοrm οf cοmplex cοnjugates.

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The area of the ENTIRE rectangle would be: Area = Base * Height

I think you can see that the triangle is 1/2 of the rectangle. so the

    The area of the right triangle would be: Area = 1/2 * base * height

if the area of the triangle is 18 square inches, then h = 2(18)/6 = 6 inches.

If the base, b, is 6 inches, and the area, A, is 18 square inches, then the height, h, of the triangle is 6 inches.

Triangle is a three-sided geometric shape that has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

The area of a right triangle can be found by using the formula A=1/2bh, where b is the base of the triangle and h is the height. In this example, the base, b, is 6 inches. To find the height, h, we can solve the equation for h: h = 2A/b, where A is the area of the triangle.

Therefore, if we know the area of the triangle, A, we can find the height, h, of the triangle by plugging in the values and solving for h. For example, if the area of the triangle is 18 square inches, then h = 2(18)/6 = 6 inches.

The area of a right triangle can be found by using the formula A=1/2bh and plugging in the known values of b and h. In this example, if the base, b, is 6 inches, and the area, A, is 18 square inches, then the height, h, of the triangle is 6 inches.

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Answer:

6.21

Step-by-step explanation:

tha ratio 2.97/2.2 has to be the same as x/4.6.

so the new lenght, x, is 4.6×(2.97/2.2)

[tex]\stackrel{ \textit{ratio of (L)ength to (w)idth of old phone} }{\stackrel{L}{2.2}~~ : ~~\stackrel{w}{4.6}\qquad \implies \qquad \cfrac{L}{w}~~ = ~~\cfrac{2.2}{4.6}} \\\\\\ \stackrel{\textit{Length of new phone}}{2.97}\qquad \stackrel{\textit{keeping the same ratio}}{\cfrac{2.97}{w}~~ = ~~\cfrac{2.2}{4.6}} \\\\\\ (2.97)(4.6)=2.2w\implies \cfrac{(2.97)(4.6)}{2.2}=w\implies \stackrel{ new~width }{6.21=w}[/tex]

15% of a price of 116 dollars would be a price decrease of $17.40. This means that the price when on sale would be $98.60 as you have to subtract 17.40 from 116.

Answer:

x = 7.5

m∠EGB = 75°

m∠EGA = 105°

Step-by-step explanation:

According to the Alternate Exterior Angles Theorem, angles EGB and CHF are equivalent. This means we can find x by setting them equal to each other.

10x = 2x + 60 (subtract 2x from both sides)

8x = 60 (divide both sides by 8)

x = 7.5

We can now plug in x to find m∠EGB.

2(7.5) + 60 = 15 + 60 = 75

Therefore, m∠EGB = 75°

As EGB and EGA are supplementary angles, that means that together, they add up to 180°. That means:

75 + EGA = 180 (subtract 75 from both sides)

m∠EGA = 105°

Using Chebyshev's Theorem, considering a standard deviation of 40, we have that at least 75% of the students scored between 360 and 520.

When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by.

here, we have,

In this problem, considering a standard deviation of 40, we have that:

440 - 2 x 40 = 360.

440 + 2 x 30 = 520.

Within 2 standard deviations of the mean, no information about the distribution, hence, at least 75% of the students scored between 360 and 520.

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The roots of the quadratic equation 4x^2 + 21 = -20x in simplest form are    x = -1/2 and x = -7/2.

What is quadratic formula ?
The quadratic formula is a standard formula used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is derived using the method of completing the square and provides a simple way to find the roots (or solutions) of the quadratic equation.

The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

Steps to be followed:

To solve the quadratic equation 4x^2 + 21 = -20x using the quadratic formula, we first need to rearrange the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, we have:

4x^2 + 20x + 21 = 0

So, we can identify a = 4, b = 20, and c = 21. Now we can substitute these values into the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values of a, b, and c, we get:

x = (-20 ± √(20^2 - 4(4)(21))) / 2(4)

Simplifying the expression under the square root, we get:

x = (-20 ± √(400 - 336)) / 8

x = (-20 ± √64) / 8

x = (-20 ± 8) / 8

This gives us two possible solutions:

x = (-20 + 8) / 8 = -1/2

x = (-20 - 8) / 8 = -7/2

Therefore, the roots of the quadratic equation 4x^2 + 21 = -20x in simplest form are x = -1/2 and x = -7/2.

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The supplies expense to be reported on the income statement for the year can be calculated using the formula:

Supplies expense = Beginning supplies balance + Supplies purchased during the year - Ending supplies balance

Substituting the given values, we get:

Therefore, the supplies expense to be reported on the income statement for the year is $3,050.

~ Zeph

Answer:

he probability of Violeta pulling out a green marble is 0.3 or 30%.

Step-by-step explanation:

he probability of pulling out a green marble is the number of green marbles divided by the total number of marbles in the bag:

P(green marble) = number of green marbles / total number of marbles

In this case, there are 6 green marbles and 14 pink marbles, so the total number of marbles is:

total number of marbles = 6 + 14 = 20

Therefore, the probability of pulling out a green marble is:

P(green marble) = 6 / 20 = 3/10 = 0.3

So the probability of Violeta pulling out a green marble is 0.3 or 30%.

Answer:

Step-by-step explanation:

To solve the polynomial P(m) = -m + 5m² - 8m + 4m⁵ - 8m⁰, we can simplify the expression by combining like terms:

P(m) = 4m⁵ + 5m² - 9m - 8

Therefore, the simplified form of the polynomial is P(m) = 4m⁵ + 5m² - 9m - 8.

Answer:p=\frac{4m^5+5m^2-9m-8}{m};\quad \:m\ne \:0

Step-by-step explanation:

The 800 readers have a newspaper if the local newspaper has letters to the editor for 40 people if this is the number represents 5%.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

The local newspaper has letters to the editor for 40 people if this is the number represents 5% of all the newspaper readers.

Let x be the total number of newspaper readers.

The value of x can be found as follows:

5 % of x = 40

(5/100)x = 40

x = 40/0.05

x = 800

Thus, the 800 readers have a newspaper if the local newspaper has letters to the editor for 40 people if this is the number represents 5%.

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Complete question:

The local newspaper has letters to the editor for 40 people if this is the number represents 5% of all the newspaper readers how many readers does the newspaper have

The solution is, radius: 23 inches.

Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (a segment of a circle). In simple words, the distance that runs through the curved line of the circle making up the arc is known as the arc length.

here, we have,

Formula: ∅r = arc length

Here the ∅ is 2 rads and arc length is 46 inches.

using the formula:

2*r = 46

r = 23 inches

The solution is, radius: 23 inches.

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The critical value z Subscript alpha divided by 2zα/2 that corresponds to the given confidence level. 94% is 1.88.

To find the critical value zα/2 that corresponds to the given confidence level of 94%, we need to use the standard normal distribution table or a calculator with a normal distribution function.

The steps to find the critical value are:
1. Subtract the confidence level from 100% to get the level of significance α: α = 100% - 94% = 6%
2. Divide the level of significance by 2 to get α/2: α/2 = 6%/2 = 3%
3. Convert the percentage to a decimal: 3% = 0.03
4. Find the z-score that corresponds to the area to the left of the critical value, which is 0.5 + α/2 = 0.5 + 0.03 = 0.53
5. Use the standard normal distribution table or a calculator to find the z-score that corresponds to an area of 0.53. The z-score is approximately 1.88.

Therefore, the critical value zα/2 that corresponds to the given confidence level of 94% is 1.88.

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Answer:

x is (a) 125.

Step-by-step explanation:

We can solve this proportion by using the property that the ratios of two equal proportions are equal. In other words:

a : b :: c : d if and only if a/b = c/d

Using this property, we can set up the proportion:

26 : 48 :: 82 : x

where x is the unknown term we want to find.

To solve for x, we can cross-multiply the terms in the proportion:

26 * x = 48 * 82

Simplifying the right side of the equation:

26 * x = 3936

Dividing both sides of the equation by 26:

x = 3936/26

x = 152

Therefore, the value of x is 152. However, 152 is not one of the answer choices provided. To choose the closest answer choice, we can round 152 to the nearest value among the answer choices. Rounding 152 to the nearest value, we get:

125: 27 less than 152

122: 30 less than 152

115: 37 less than 152

120: 32 less than 152

The closest value to 152 is 150, which is between 122 and 125. Therefore, the answer closest to the value of x is (a) 125.

a.  The probability that they are actually lying is 0.3214. b. The polygraph test must be 98.7% in order that this probability is at least 80%.

It is simpler to construct and see every possible scenario using the tree diagram. Its two main sites are the ends and the branches of the tree. The probability is written on each branch, and the ends hold the final findings. Use tree diagrams to identify when to multiply and when to add.

The probability of lie = 0.5

The probability of truth = 1 - 0.5 = 0.95

The liars that pass polygraph = 0.10

The liars that fail the polygraph is = 0.90

The truth that pass on polygraph = 0.90

The truth that fails on polygraph = 0.10

a. The probability that they are actually lying is:

P (Lying| fair) = P (fair| Lying) P (lying) / P (fair)

= (0.90)(0.05)/ (0.70)(0.05) + (0.10)(0.95)

= 0.3214

b. P (Lying| fair) > 0. 80

= (x)(0.05)/ (x)(0.05) + (1-x)(0.95) > 0.80

x > 0.987

Hence, the polygraph test must be 98.7% in order that this probability is at least 80%.

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Therefore, 11/2 + 3/4 expressed as a fraction is 25/4.

A fraction is a number that represents a part of a whole. It is represented as a ratio of two numbers, the numerator and the denominator, separated by a horizontal line. The numerator represents the number of parts, while the denominator represents the total number of parts that make up the whole. Fractions can be expressed in different forms, including proper fractions, improper fractions, and mixed numbers. A proper fraction is a fraction where the numerator is less than the denominator. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. A mixed number is a combination of a whole number and a proper fraction.

Here,

5 1/2+3/4

5 1/2=5*2+1/2

=11/2

11/2+3/4

To add 11/2 and 3/4, we need to find a common denominator. The smallest common multiple of 2 and 4 is 4, so we can rewrite 11/2 as an equivalent fraction with a denominator of 4:

11/2 = (11/2) x (2/2) = 22/4

Now we can add the two fractions:

11/2 + 3/4 = 22/4 + 3/4

To add the two fractions, we add the numerators and keep the same denominator:

= (22 + 3)/4

= 25/4

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If A 15-foot pole is leaning against a tree and  bottom of the pole is 8 feet away from the bottom of the tree. then the top of the pole  reaches option (C) 12.7 feet

We can use the Pythagorean theorem to solve this problem. Let's call the height we're trying to find "x". Then, we have a right triangle where the pole is the hypotenuse, the distance from the bottom of the pole to the tree is one leg, and the height we're trying to find is the other leg. Using the Pythagorean theorem, we have:

15^2 = 8^2 + x^2

225 = 64 + x^2

Group the like terms

161 = x^2

x ≈ 12.7 feet

Therefore, the correct option is (c) 12.7 feet

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The required, we need to pay $0.132 in tax on the item that cost $3.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To calculate the amount of tax, we need to multiply the cost of the item by the tax rate. The tax rate is 4.4% or 0.044 as a decimal.

So, the amount of tax on the item is:

0.044 × $3 = $0.132

Therefore, we need to pay $0.132 in tax on the item.

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The mean and the variance of the poisson distribution are;

Mean = 2.66

Variance = 1.277

The formula for the PMF of a Poisson distribution is;

p(x:λ) = [e^(-λ) * λ^(x)]/x! for x = 0, 1, 2......

Thus;

p(x = 0) =  [e^(-λ) * λ^(0)]/0!

e^(-λ) = 0.07

λ = - In 0.07

λ = 2.66

That is the mean

Variance is square root of standard deviation;

Variance = √√(2.66)

Variance = 1.277

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Answer:

2.65926003693 for mean and variance.

Step-by-step explanation:

First of all, when it comes to Poisson distributions, the mean and variance equal the same thing. Here we can find the mean using e^-(lambda)=0.07 therefore lambda= -ln(0.07) which equals 2.65926003693 for both.

0.1728 is the correct answer. This represents the proportion of suburban park users who bike on the trail,

Proportion is a mathematical term that describes the relationship between two values. It is used to compare two parts of a whole, two ratios, or two fractions. It is expressed as a ratio, fraction, or percentage.

For example, if a person has 3 apples and 2 oranges, the proportion is 3:2 or 3/2. This means that for every 3 apples, there are 2 oranges.

Proportion can also be used to compare the size of two objects. For example, if one object is twice as long as the other, the proportion is 2:1. Proportion can also be used to compare two fractions, such as 1/4 and 1/2. In this example, the proportion is 1:2, as 1/4 is half of 1/2.

Proportion is also used to compare two percentages, such as 30% and 60%. In this example, the proportion is 3:6, as 30% is half of 60%.

Step 1: Calculate the total number of users on the suburban park trail by adding the numbers in the 'Suburban' column in the table: 125 + 76 + 42 = 243.

Step 2: Calculate the proportion of suburban park users who bike on the park trail by dividing the number of bike users (42) by the total number of users (243): 42/243 = 0.1728.

Step 3: Round the answer to the nearest thousandth: 0.1728 ≈ 0.1730.

Answer: The proportion of suburban park users who bike on the park trail is 0.1730.

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The first node in set 1 should represent the element.

For each potential value in set 2, create a branch.

Create a new node to represent the following set 1 element at the end of each branch.

Steps 2-4 must be repeated for each additional Set 1 component.

All potential outcomes are represented by the final nodes.

The appropriate line of best fit for the scatter plot is y hat equals 67 hundredths times x plus 4 and 5 hundredths.

The number is a mathematical entity used to represent a computer's magnitude it can be a symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three, or eight numbers are used to verify the context including counting measuring and computing.

This line of best fit indicates that the number of households with cable television will increase by 67 hundredths (or 0.67) each year. This line of best fit is based on the data points on the scatter plot, which suggest that the number of households with cable television has been steadily increasing over the years.

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The solution is,

the function is increasing at (-5,-2)

the function is decreasing at (6,2)

the function is constant at (-8,5)

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

from the given graph we get,

the function is increasing at (-5,-2)

the function is decreasing at (6,2)

the function is constant at (-8,5)

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The marginal revenue is 909  dollars per unit.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

R(q) = -2q² + 1000q _____(1)

Where q is the unit sold.

Now,

Substitute q = 91 in (1).

R(q) = -2q² + 1000q

R(q) = -2 x 91² + 1000 x 91

R(q) = -8281 + 91000

R(q) = $82719

Now,

91 units = $82719

1 unit = 82719/91

1 unit = $909

Thus,

909 dollars per unit is the marginal revenue.

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