The table lists recommended amounts of food to order for party guests. And are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering​ purposes, they will count each of these​ "drop-in" guests as half a guest. How much of each food item should and order for a graduation party with ​drop-in guests?

The second line is 153ft long.

We are making a figure out of the given statment. Where we have the Triangle ABC and other two Triangle ADB and ADC inside Triangle ABC. Here Angle ADC = 80 degress and Angle ACD = 40 egress.

According to given statement and figure,

In triangle ABO, AD= 100 ft

Hence, BD/AD = Cos80

or, BD = (100 * Cos80)

or, BD = 17.36 ft

Now, AB/AD = Sin80

or, AB = (100* Sin 80)

or, AB = 98.48

Now, In case of triangle ABC

AB/AC = Sin40

or, AC = AB/ Sin 40

or, AC = 98.48/ Sin40

or, AC = 153.2 ft (nearly equal to 153 ft)

The second line is 153ft long.

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The Angle 2 and angle 8 in the given figure are called as the alternate interior angle and they are equal .

What are Alternate Interior Angles ?

The alternate interior angles are defined as the angles that are formed when a transversal intersects the two coplanar lines.

The alternate interior angles  lie on inner side of parallel lines but they are on the opposite sides of the transversal.

So , From the figure we can conclude that the angle 2 , angle 8 and angle 3 and angle 5 are the alternate interior angles .

Therefore , the angle 2 and 8 are alternate interior angles.

The given question is incomplete , the complete question is

What are the angles 2 and 8 called in the given figure ?

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Answer:

It appears that the solution set of the inequality 5n + 1.5 ≥ 4 is the set of all real numbers greater than or equal to -0.3. This can be determined by looking at the graph and noting that the region to the right of the vertical line x = -0.3 is shaded, which indicates that all values of x in that region are included in the solution set.

To verify this, we can substitute -0.3 into the inequality in place of n to see if the inequality is satisfied:

5(-0.3) + 1.5 ≥ 4

This simplifies to:

-1.5 + 1.5 ≥ 4

Which further simplifies to:

0 ≥ 4

Since this is not true, -0.3 is not a solution of the inequality. However, all values of x that are greater than or equal to -0.3 are solutions, as indicated by the shaded region on the graph.

Step-by-step explanation:

The value of the expression 0.7 x √300 is 12.124.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

0.7 x √300

This can be written as,

= 0.7 x √3 x √100

= 0.7 x 1.732 x 10

= 12.124

Thus,

The value is 12.124.

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Answer:

2 gallons of milk per week

0.35 weeks(3.5 days) to consume 1 gallon

Step-by-step explanation:

Jaidyn's family drinks 10 gallons of milk every 5 weeks, which is a ratio of

10:5

To find how many gallons of milk they drink per week, you'd have to divide 10/5

10 ÷ 5 = 2

Considering that 1 week is 7 days, it would take them 0.35 weeks to consume 1 gallon of milk, which is the same as 3 and a half days.

How likely something is to occur is known as its probability.Probability when die rolled 1st time is 6C1 i.e. (1,2,3,4,5,6).

How likely something is to occur is known as its probability.We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.

Probability when die rolled 1st time=6C1 i.e. (1,2,3,4,5,6) suppose 1 comes, then 2nd time it should not be .as it is given that no 2 people will roll same number.

so 2nd time probability=5C1 i.e. (2,3,4,5,6). same way 3rd and 4th time probability=4C1 and 3C1 respectively.Probability that no one rolls the same no. = 6*5*4*3and total possibility =6^4 

p(same number)= 6*5*4*3/ 6^4

= 5/18

p(no same number will roll)=1-5/18

=13/18

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Answer:

The answer to your question is C, 15

Step-by-step explanation:

Answer is 15, C

Answer:

$68

Step-by-step explanation:

Let x = original price.

The sale price is 75% of the original price, so the sale price is 75% of x.

75% as a decimal is 75/100 = 0.75

75% of is the same as 0.75x

We are told the sale price is $51, so 0.75x must equal $51.

0.75x = 51

Divide both sides by 0.75 to find the value of x.

x = 51/0.75

x = 68

Answer: $68

Answer:

Step-by-step explanation:

$51 is 75% of 100%

75% = 3/4

51 / 3 = 17

17 = 1/4

51 + 17 = 68

$68 is the original price of the shoes

Answer: So Jamie ran 3 1/2 miles on Monday and half that distance on Tuesday. We need to know how far she ran "in all" which are key words for "addition".

We need to add 3 1/2 + (1/2)(3 1/2)

It's probably easiest to do this by converting to an improper fraction.

So let's convert:

3 1/2 is the same as 7/2. now we can rewrite the problem:

7/2 + (1/2)(7/2)

= 7/2 + 7/4 . Now we need a common denominator:

7/2 = 14/4

Now we have 14/4 + 7/4 = 21/4.  Now we should convert to a mixed number.

21/4 = 5 1/4

So Jamie ran 5 1/4 miles in all.

Step-by-step explanation:

Answer:

5.25 or 5 1/4 (Whichever you prefer)

Step-by-step explanation:

To make it simpler, we will convert 3 1/2 to decimal format.

First, take 3 and multiply it by the denominator 2 of 1/2, then add that number to the numerator of 1/2

3 x 2=6 -> 6+1=7

now add the denominator 2 under 7 and we now have 7/2, the equivalent to the mixed number 3 1/2

Afterward, to get the decimal, divide the numerator by the denominator:

7 divided by 2=  3.5

Now halve 3.5 to get the number Jaimie ran on Tuesday -> 1.75

Then add both 3.5 (3 1/2) and 1.75 (1 3/4), to get 5.25 or 5 1/4, which is your answer.

Write 30% as 30100Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

30100 of 84 = 30100 × 84Therefore, the answer is 25.2

If you are using a calculator, simply enter 30÷100×84 which will give you 25.2 as the answer.

The inequality is solved as x < 5 and it is plotted on the number line.

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The given inequality is −8 + x < −3.

It can be solved as follows,

⇒ −8 + x < −3

Add 8 both sides as,

⇒ 8 + −8 + x < −3 + 8

⇒ x < 5

It can be plotted on the number line as follows,

Hence, the solution is given as x < 5 and it is represented on the number line with clarity.

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We have inequality. So, we have to take a test point (0,0) and as the statement is true therefore Graph will shade towards the test point (0,0).

2(0)+3(0) ≤ 30 => 0≤ 30

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

A family of 3 children and 2 adults visited a health club. The club charges $y an hour for each child and $x an hour for each adult.

First we make inequality according to question.

In a family number of children 3

Charge for 1 child = $y per hour

Charge for 3 children = 3y

Charge for 1 Adult = $x per hour

Charge for 2 adults = 2x

If the family does not want to spend more than $30 an hour at health club.

2x+3y≤30

Where, x and y should be greater than 0.

x≥0 and y ≥0

Now we make the graph of this inequality.

First we take equality of equation and then find x and y table.

2x+3y=30

x        y

0        10

6        6

15      0

Here we have inequality. So, we have to take a test point (0,0)

2(0)+3(0) ≤ 30 => 0≤ 30

This statement is true. So, Graph will shade towards the test point (0,0)

Please see the attachment for graph:

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The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]

To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.

When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:

[tex]$x = ky^3$[/tex]

where k is the constant of proportionality.

Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:

[tex]$y = \frac{m}{\sqrt{z}}$[/tex]

where m is the constant of proportionality.

Substituting the second equation into the first equation gives:

[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]

Since the value of x is 3 when z is 12, the equation can be written as:

[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]

Rearranging gives:

[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]

Substituting this value of k into the original equation gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]

Substituting z as 75 gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]

Simplifying gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]

Therefore, the value of x  when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].

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Answer:

60 degrees and an equilateral triangle

Step-by-step explanation:

every triangle adds to 180 degrees

add 60+60=120

180-120=60 to find remaining angle

all angles are the same which makes all sides the same: equilateral

Answer:

1 =60

Step-by-step explanation:

a+b+c=180

60+60+c=180

120+c=180

-120. -120

c=60

The volume of the prism is 103.32 cubic inches (optionD)

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.

The base area of the prism = 4.1×7.2 = 29.52 inches squared.

The height of the prism is 3.5 inches

Therefore volume = base area × height

volume = 29.52× 3.5 = 103.32 cubic inches.

Therefore the volume of the shape is 103.32 cubic inches.

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The cost of a carpet of the same quality, measuring 5m by 3m is $129.

We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.

In this question, it is given that a carpet measuring 4m × 2.5m costs $86. That means the 10m² area of carpet costs $86 if we divide 10 by both the cost and area of the carpet we will find that, 1 m² area of carpet will cost $8.6. So the cost of a carpet of 5m × 3m will be the area of the carpet multiplied by the cost of the carpet per 1 m² i.e, 15m² of carpet will cost $8.6 × 15 which is equal to $129.

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Difference between coldest and hottest temperature was greater in march than July.

The range is the difference between the highest and lowest values within a set of numbers. To calculate range, subtract the smallest number from the largest number in the set.

Given,

Range of temperature in march = 32°

⇒ difference in temperature in march ΔT = 32°

Range of temperature in July = 8°

⇒ difference in temperature in July Δt  = 8°

By the above observation

ΔT > Δt .

difference in temperature in march > difference in temperature in July.

Hence, In month of march, there was greater difference between the hottest and coldest temperature than in month of July.

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The steps of finding mean and standard deviation of a simple random sample are given below.

What is standard deviation and mean?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.

The steps of finding mean and standard deviation of a simple random sample are:

Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX):  = σ/n.

How to determine sample means

Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...

Sum divided by the quantity of samples.

The outcome is the mean.

To determine the variance, use the mean.

To determine the standard deviation, use the variance.

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The solution of the given function cosx - √(3 - 3cos³x) = 0 is C. 30° + 360° n, 330° + 360°n

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are given the function as;

cosx - √(3 - 3cos³x) = 0

cosx = √(3 - 3cos³x)

Taking square root on both sides.

cos ²x = √(3 - 3cos³x) ²

cos ²x = (3 - 3cos³x)

For solving for x in

cos ²x = (3 - 3cos³x)

cos ²x = 3 (1 - cos³x)

(1 - cos³x) = cos ²x/3

x= π/6 + 2πn

or

x=11π/6 + 2πn

where n is an integer.

30° + 360° n, 330° + 360°n

The correct answer is C.

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Function Notation: another way of representing the relation between two variables, y is denoted as f(x) and x remains.

x is the input and f(x) is the output

This question is essentially asking what is the output of the function when the input is equal to 5.

[tex]f(5) = (5)^2-2(5)[/tex]

[tex]f(5) = 25-10[/tex]

[tex]f(5) = 15[/tex]

yes, (-2,4) is the solution of the system of equation 4x² - 4y = 0.

To check whether the given points are the solution of the given system of equation 4x² - 4y = 0. We have to put the values of x = -2 and y = 4 in the given equation. If we get the result equals zero then (-2, 4) is the solution of 4x² - 4y = 0 and if the result is a non-zero number then (-2, 4) is not the solution of 4x² - 4y = 0.

⇒4x² - 4y = 0

⇒4(-2)² - 4 × 4 = 0

⇒4 × 4 - 4 × 4 = 0

⇒0 = 0

Here we get the result equal to zero, hence (-2,4) is the solution of the system of equation 4x² - 4y = 0.

--This question is incomplete, the complete question is

''Is (-2,4) a solution of the system of equation 4x² - 4y = 0?''--

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Constant or Zero polynomial, Linear polynomial, Quadratic polynomial, Cubic polynomial, and Quartic polynomial are the five kinds of polynomials.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

Constant Polynomial Function: P(x) = a = ax.

Zero Polynomial Function: P(x) = 0; where all ai's are zero, i = 0, 1, 2, 3, …, n.

Linear Polynomial Function: P(x) = ax + b.

Quadratic Polynomial Function: P(x) = ax2+bx+c.

Cubic Polynomial Function: ax3+bx2+cx+d.

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Since X is an odd number, x+2 is the following odd number. If x is an even number, the subsequent odd number is x + 1.

The vehicles that will travel on the highways on particular days are decided by the Odd-Even rule, a space rationing system. According to the plan, vehicles with odd and even numbers will travel the roads on alternate days.

In jQuery, the odd() method is used to pick elements with odd index numbers (such as 1, 3, 5, etc.). The index begins at zero. It picks odd numbers, unlike the even() function, which is comparable. From the set of chosen items, the odd() method returns the odd indexed elements.

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The solution to the system of linear equations (x, y) lies along 4 and 7 and the graph is attached below.

A graph of a system of linear equations is a set of points in a coordinate plane that represent all the solutions to the system of equations. The graph can be visualized as a collection of lines that intersect at the points that are solutions to the system.

In the given problem, we have two linear equations which are

y = 3x - 6 ...eq(i)

y = 2/5x + 5 ...eq(ii)

Plotting the two equations on a graph using a graphing tool, the point of intersection is the solution to the system of linear equation.

The coordinates to the nearest integer are (x, y) 4 and 7

The value of x is 4 and y is 7

Kindly find attached graph below.

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Answer:

16

Step-by-step explanation:

16 is a positive multiple of 8, in which 16²=256>100 and 16<20 are true statements.

Answer:

[tex]$x=\boxed{16}$[/tex]

Step-by-step explanation:

Since $x$ is a positive multiple of 8, it must be at least 8. Since $x^2>100$ and $x$ is at least 8, the only solution is $x=16$.

To verify this, note that $x=8$ does not satisfy the inequality $x^2>100$, but $x=16$ does, so $x=16$ is the only solution that works.

Therefore, $x=\boxed{16}$.

Answer:

gfifhdrtjttt9668ztjt*

Answer:

Step-by-step explanation:

You want to find the measure of the angle designated as ∠1, given the other two have measures of 40° and 30°. You also want the classification of the triangle based on its angles.

The sum of angles in a triangle is 180°.

  40° +∠1 +30° = 180°

  ∠1 = 110° . . . . . . . . . . . . subtract 70°

The classification of a triangle as acute, right, or obtuse is based on the measure of its largest angle. If that angle is 90°, the triangle is a right triangle. If it is less, the triangle is acute; if it is more, the triangle is obtuse.

The angle measure 110° is more than 90°, so this triangle is an obtuse triangle.

An angle that measures 90 degrees is called a right angle, an angle that measures 180 degrees is called a straight angle and an angle that measures 270 degrees is called a reflex angle.

A right angle is an angle that measures exactly 90 degrees. It is formed by the intersection of two lines that are perpendicular to each other. A right angle is symbolized by a small square at the vertex of the angle.

A straight angle is an angle that measures exactly 180 degrees. It is formed by the intersection of two lines that are collinear, that is, they lie on the same line. A straight angle is represented by a straight line, usually with an arrow on one end pointing in the direction of the other end.

A reflex angle is an angle that measures greater than 180 degrees but less than 360 degrees. It is formed by the intersection of two lines that are not collinear, that is, they don't lie on the same line and the angle is greater than a straight angle. A reflex angle is represented by an arc with a curved arrow on one end, pointing in the direction of the other end.

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The given expression , 4x2 – 3xy is having two terms which are 4x2 and –3xy.

The term 4x2 is a product of 4 and x, whereas the other  term (–3xy) is a product of (–3), x and y.

When we will join these two terms using the addition operation we will get the result as  4x2 – 3xy .

The given equation is an example of an algebraic expression and they are made up of combination of constants and variables. They are joined to each other by various operations such as addition , multiplication , division and subtraction.

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In the given equation x = 9 is the value that satisfies the equation.

The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3, because [tex]3*3 = 9[/tex]. The symbol for square root is "√" and it can also be represented as "sqrt".

In the given equation [tex]x = 9[/tex] is the value that satisfies the equation.

To find the value of x in the equation [tex]3 \sqrt{x} = 9[/tex], we first need to square both sides of the equation to eliminate the square root.

[tex]3 \sqrt{x} = 9[/tex]

Squaring both sides:

[tex](3 \sqrt{x} )^2 = 9^2[/tex]

[tex]x = 9^2 / 3^2 = 9^2 / 9 = 9[/tex]

Therefore, x = 9 is the value that satisfies the equation.

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