A teacher pops 4 bags of popcorn
for the class party. There are 10
students in the class. What part of a
bag of popcorn will each student
receive?

The triangles in this problem are similar using the SSS theorem.

Similar triangles are triangles that share these following two features:

For this problem, we have that the two triangles share two common angle measures.

A triangle is composed by three angles, and the sum of their measures is of 180º, hence the third angle measure will be equal for both triangles.

As the angle measures are equal, the side lengths are going to be proportional, thus the triangles are similar by the SSS theorem.

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The conversion of the equation from slope-form to standard form is 3x + y = 2.

In Mathematics, the slope-intercept form of a line is generally modeled by using this linear equation:

y = mx + b

Where:

In Mathematics, the standard form of a linear function is is generally modeled by this mathematical expression:

Ax + By = C

Where:

A, B, and C represents a number, numeral or numerical value.

Next, we would convert the given linear function in slope-intercept form to standard form as follows:

3x + y = 2.

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50/3 is the minimum function value.

∇f(x,y,z)=(2x,4y,6z)

∇g(x,y.z)=(1,2,3)

set up the system of equations:

2x=λ

4y=2λ

6z=3λ

x+2y+3z=10-----(1)

solve the first three equations for λ.

2x=λ

2y=λ

2z=λ

From these three equations, we conclude that

x=y=z.

Plug this into the constant equation.

x+2y+3z=10

x+2x+3x=10

6x=10

x=3/5

Therefore, there is one point of interest and it occurs at (5/3,5/3,5/3).

f (5/3,5/3,5/3)=50/3

This is the minimum function value. Notice that the function is unbounded above and therefore has no maximum.

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Answer:

20

Step-by-step explanation:

Answer:

(7,12)

Step-by-step explanation:

We are add 1 to the x value each time and 3 to the y value

1st: (3,0)

2nd: (4,3)

3rd: (5,6)

4th: (6,9)

5th: (7,12)

Answer:

14X

Step-by-step explanation:

The new point A(-5,1) will lie in quadrant 3.

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,

Given here: The point A(-4,5) is translated over y=2

Thus after the transformation( translation), the new points are

A(-4,5)→A(-4-1,5-4)=A(-5,1)

The point was translated horizontally by 1 to the left and then translated vertically by 4 units downwards.

Hence, The new point will lie in quadrant 3.

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The constant of proportionality for this variation is 0.174cm/gallon .

Every relationship that always maintains the same ratio is referred to be proportionality. For instance, the average amount of apples per tree determines the proportionality between both the quantity of apples in a crop and the number of trees in the orchard.

Let the amount a tree grows in one month be - x  

The amount of water   given be -  y

If the amount a tree grows in one month is directly proportional to the amount of water given, then

x ∝ y

x = ky

k is defined as the constant of proportionality

k = [tex]\frac{x}{y}[/tex]

Given

x = 4cm

y = 23 gallons

k = [tex]\frac{4}{23}[/tex]  

k = 0.174cm/gallon

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The statement that answers the linear model possibility is NO

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

Initial = 100

Year 1 = 110

year 2 = 121

year 3 = 133.10

The savings account balance is increasing at an inconsistently increasing rate, which is not linear.

The savings account starts with $100, and increases by $10 in the first year, by $11 in the second year, and by $12.10 in the third year.

This is an example of exponential growth, which cannot be modeled by a single linear equation.

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The perimeter of triangle XYZ is 38.95 inches

Consider the following figure.

The area of rectangle WXYZ is 115. 5 in.²

From given figure we can observe that PQ = 4 in.

So, XW = YZ = 2 × PQ

XW = YZ = 2 × 4

XW = YZ = 8 inches

This means, the width of rectangle WXYZ is  8 inches

We know that the area of the reactngle is given by the formula,

A = length × width

here, A = 115.5 in.² and width = 8  in.

115.5 = length × 8

length = 115.5 / 8

length = 14.44 in.

So, XY = WZ =  14.44 in.

For right triangle XYZ using Pythagoras theorem,

XZ² = XY² + YZ²

XZ² = 14.44² + 8²

XZ² = XY² + YZ²

XZ² = 272.51

XZ = 16.51 in.

So, the perimeter of triangle XYZ would be,

P = XY + YZ + XZ

P = 14.44 + 8 + 16.51

P = 38.95 inches

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Three lots with parallel side boundaries extend from the avenue to the boulevard.

x + y + z = 140 meters

According to the proportion theorem,

Solving for x, using cross multiplication:

Similarly,

x/40 = z/35

solving for z by cross multiplication,

z = 35x/40

z = 7x/8

Now, the third proportions,

y/30 = z/35

Solving for y,

y = 30z/35

y = 6z/7

x + y + z = 140

4y/3 + 6z/7 +  7x/8 = 140

(224y + 144z + 147x)/168 = 140

224y + 144z + 147x = 23520

Substituting z = 7x/8,

224y + (144 × 7x/8) + 147x = 23520

224y + 126x + 147x = 23520

224y + 273x = 23520

Now,

Substitute y = 3x/4

(224×3x/4) + 273x = 23520

168x + 273x = 23520

441x = 23520

x = 53.33

Now,

We know that

y = 3x/4

so,

y = 40

And,

z = 7x/8

Z = 46.66

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The length of the altitude is 10. 4 yards

The formula for the perimeter of an equilateral triangle is expressed as;

P = 3a

Where;

Substitute the values

36 = 3a

Divide the value by the coefficient  of a

a = 36/3

a = 12 yards

Using the Pythagorean theorem, we get;

12² = h² + 6²

Find the square values

144 = h² + 36

collect like terms

h² = 108

Find the square root

h = 10. 4 yards

Hence, the value is  10. 4 yards

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Answer:

x= 4/3

Step-by-step explanation:

Think the negative sign outside the parentheses as -1. Then do distributive property to the numbers inside the parentheses.

-1 x 3x and -1 x -12

That equals to -3x + 12 so now your entire equation is -3x + 12 = 9x - 4. Now lets take away 9x from both sides like this,

9x - 9x and -3x - 9x.

That equation is now -12x + 12 = -4.

Now subtract 12 from both sides like this,

12 - 12 and -4 - 12.

And then you have -12x = -16.

Now you divide both numbers by -12 like this,

-12x/-12 which equals to just x and then do -16/-12 which would equal as 1.3333 and repeating but, it can be put as 4/3 for a clearer answer.

So your answer is

The number of basketballs and soccer balls that there are in the bag are;

Soccer balls = 10

Basketballs = 53

We are told that Joseph has a bag of balls for the students to play with. The bag  has 5 times as many basketballs as soccer balls in the bag.

Let basketballs be b

Let soccer balls be s.

Thus;

b = 5s

Total number of balls is 63 balls. Thus;

5s + s = 63

6s = 63

s = 63/6

s = 10.5

b = 5(10.5)

b = 52.5

We can estimate an approximate value of s = 10 and b = 53

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The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.

The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.14.5v ≥ 235

To figure out how many visits Brianna needs to earn her first free movie ticket, we can set up an inequality. We'll set the left side of the equation equal to the total points needed for a free movie ticket (235 points). We'll set the right side of the equation equal to the points earned per visit (14.5 points) multiplied by the number of visits (v).

14.5v ≥ 235

The inequality 14.5v ≥ 235 can be used to determine the minimum number of visits Brianna needs to earn her first free movie ticket.

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The expected value of the sample mean of the values obtained in these 300 tosses is 3.5

300 fair throws of a six-sided die are made.

The expected value of the sample mean of the results acquired from these 300 tosses must be determined.

Six sides make up a dice:

Every side of a fair dice has an equal chance of happening.

Now, each side's likelihood of being present is 1/6.

Now, the sample mean of the values collected in these 300 tosses is predicted to be equal to:

E(x) = Σx P(x =x)

= 1*1/6 + 2*1/6 + 3*1/6 + 4*1/6 + 5*1/6 + 6*1/6

= 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6

= 1/6 (1+2+3+4+5+6)

= 1/6 (21)

= 21/6

E(x) = 3.5

Hence, the expected value of the sample mean of the values obtained in these 300 tosses is 3.5

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Answer:

Step-by-step explanation:

5y/5=y+y+y+y+y

Answer:

Step-by-step explanation:

m= -1/2

The values of ∠T is 18.78 degree.

In ΔSTU ,

We have:

T = 390 cm,

S = 900 cm

and ∠S=48°.

Using the sine rule which works law of sin with the formula:

[tex]\frac{SinT}{T} = \frac{SinS}{S}[/tex]

Plug all the values in above formula:

sinT/ 390 = sin48°/900

sin T = 0.743 × 390 / 900

sin T = 0.3220

T = [tex]sin^-^1[/tex](0.3220)

T = 18.78 degree.

Hence, The values of ∠T is 18.78 degree.

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A closed quadrilateral is a kind of polygon having 4 sides, 4 vertices, and 4 angles. A triangle doesn't have four sides because if it did, it wouldn't be a triangle. It would be a quadrilateral, the term used to describe geometric objects with four sides.

Three line segments combine to form a triangle, which is a straightforward closed curve or polygon. In Euclidean geometry, any three points, notably non-collinear ones, independently create a singular triangle and a singular plane.

In Euclidean geometry, any three points, notably non-collinear ones, independently create a singular triangle and a singular plane.  polygon with 4 sides that is a quadrilateral.

One fascinating feature of a quadrilateral is that its opposite parallel sides are possible.  Four non-collinear points are joined to create it. Since a triangle would not have four sides

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Answer:

68.1 grams

Step-by-step explanation:

454 × .15 = 68.1

Answer:1.25(400)

Step-by-step explanation:

The third angle of the triangle must have a measure of 180° minus the sum of the other two angles, which is 180° - (46° + 73°) = 61°. Therefore, the measure of the missing angle is 61°.

The internal angles of a triangle are measured in degrees and are known as triangle angles. The sum of a triangle's angles is always 180°.

Triangle angles are classified into three types: acute angles, right angles, and obtuse angles.

An acute angle is one that is smaller than 90 degrees. This is the most common form of angle in a triangle and is regarded the most desirable.

A right angle is one that is exactly 90 degrees. This sort of angle is the most stable and sturdy in a triangle, therefore it is usually employed to make a triangle.

An obtuse angle is one that is larger than 90 degrees but less than 180 degrees. This form of angle is common in triangles, however it is less desirable than an acute angle.

The sum of the three angles of a triangle is always 180°. Acute angles are the most desirable and stable, whereas obtuse angles are present in certain triangles but are not as ideal.

In the given question,

The measure of the missing angle is 180° - (46° + 73°).

180° - (46° + 73°) = 180° - 119° = 61°

Therefore, the measure of the missing angle is 61°.

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The inequality for the goal that Miles set for the number of steps to be taken each day is x > 10, 000.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Miles is to take over 10, 000 steps every day which means that if the number of steps is denoted as x, the inequality would be:

x > 10, 000

This shows that the steps are greater than 10, 000 steps.

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The total number of clients with a BMI of 25.9 or higher is therefore equal to 1 * 2.6 + 3 * 2

The total amount of money she would need to give in discounts next month can be found by calculating the total number of clients with a BMI of 25.9 or higher. To calculate this, the frequencies of each BMI range need to be multiplied by the width of the corresponding bar. The total amount of money she would need to give in discounts is then equal to the total number of clients with a BMI of 25.9 or higher multiplied by $50.

Using the histogram, the number of clients in each BMI range are: 18.1-20.7 (1), 20.7-23.3 (3), 23.3-25.9 (5), 25.9-28.5 (2), 28.5-31.1 (1).

The width of each bar is: 18.1-20.7 (2.6), 20.7-23.3 (2.6), 23.3-25.9 (2.6), 25.9-28.5 (2.6), 28.5-31.1 (2.6).

The total number of clients with a BMI of 25.9 or higher is therefore equal to 1 * 2.6 + 3 * 2

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If Netflix is raising it's prices from $15.99 a month to $17.99 a month , then Mr. Leone will not cancel his subscription because the percent increase is 12.507%    .

The old subscription price of the Netflix is = $15.99  ;

the new subscription price of Netflix is = $17.99  ;

the percent increase of Netflix can be calculated by using formula :

⇒ (new price - old price)/old price × 100 ;

substituting the values of Netflix prices ,

we get ;

⇒ (17.99 - 15.99)/15.99  × 100  ;

⇒ 2/15.99 × 100

⇒ 0.12507 × 100 ;

⇒ 12.507 % .

Therefore , the percent increase is less than 20% , so he will not cancel the Netflix Subscription .

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Answer:

Harrison has the greater rate

If Ty can make 7 signs in 2 hours that means in 4 hours he could double that output to make 14 signs. Harrison, on the other hand, makes 15 signs every 4 hours.

Step-by-step explanation:

Answer:

512 points altogether.

Step-by-step explanation:

This is a guess hope it helps :D

Answer:

512

Step-by-step explanation:

&:(::6)6/$/):&;!4):$:$:$:&):=512

Answer:

3√x^5/=15√x

   5√x^2=10√x  

Step-by-step explanation:

multiply 5 by 3.

multiply 2 by 5.

Answer:

If there are 3,461 teachers and 28 students per teacher, to find the total number of students, you can multiply the number of teachers by the number of students per teacher:

3,461 teachers * 28 students/teacher = 97,268 students

So there are 97,268 students in the district.