. Two popcorn boxes are shown below. The boxes
have congruent openings and equal heights. If
the larger box of popcorn sells for $3.00, what
is a fair price for the smaller box?

Answer:

x=58.74

Step-by-step explanation:

4x+5(-42)=25

4x+-210=25

4x=25+210

4x=235

x=235/4

x=58.75

The end behavior of [tex]g(x) = -3e^x[/tex] is As x approaches positive infinity, g(x) approaches negative infinity, As x approaches negative infinity, g(x) approaches 0.

To determine the end behavior of the function g(x) = -3e^x, we need to consider what happens to the output of the function as x gets very large (approaches positive infinity) or very small (approaches negative infinity).

As x approaches positive infinity, e^x also approaches positive infinity, since e is a positive number greater than 1. Therefore, -3e^x approaches negative infinity as x approaches positive infinity. We can write this as:

lim x → ∞ (-3[tex]e^x[/tex]) = -∞

This means that the function g(x) approaches negative infinity as x approaches positive infinity.

Similarly, as x approaches negative infinity, e^x approaches 0, since e to a negative power is equal to 1 divided by e raised to the absolute value of that power. Therefore, -3e^x approaches 0 as x approaches negative infinity. We can write this as:

lim x → -∞ (-3[tex]e^x[/tex]) = 0

This means that the function g(x) approaches 0 as x approaches negative infinity.

So, in summary, the end behavior of g(x) = -3[tex]e^x[/tex] is:

As x approaches positive infinity, g(x) approaches negative infinity.

As x approaches negative infinity, g(x) approaches 0.

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Okay, let's break this down step-by-step:

In the beginning of BS 2077, Dolma deposited B? 120,000 in her account.

The interest rate is 9% per annum.

So in the first year (BS 2077), she earned 9% of 120,000 = B? 10,800 in interest.

Her principal amount increased to 120,000 + 10,800 = B? 130,800

In BS 2078, she earned 9% of 130,800 = B? 11,772 in interest.

Her principal now was 130,800 + 11,772 = B? 142,572

In BS 2079, she earned 9% of 142,572 = B? 12,781 in interest.

Her principal now was 142,572 + 12,781 = B? 155,353

In the beginning of BS 2080, her total balance was B? 155,353.

She paid 6% of her interest as income tax.

9% of 155,353 is 13,991.

6% of 13,991 is 839.

So her total interest received in BS 2080 after paying tax was 13,991 - 839 = B? 13,152.

Her total amount received in BS 2080 was:

Principal (155,353) + Interest (13,152) = B? 168,505

So the total amount Dolma received in the beginning of BS 2080 was B? 168,505

Let me know if you have any other questions!

The total length of the chord PR is 30.

Given a circle Q.

Given a chord named as PR.

We have to find the length of the chord.

Here Q is the center of the circle.

Given that ∠QSP is a right angle.

Then clearly, ∠QSR is also a right angle.

Consider the triangle QSR and QSP.

QP = QR, since they are radius of the circle.

So, QP = QR = 17

QS ia a common side.

So QS = 8

Then it is clear that,

PS = SR

Using Pythagoras theorem,

(PS)² = 17² - 8²

        = 225

PS = √225 = 15

So the length of the chord, PR = 15 + 15 = 30.

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Answer:

Step-by-step explanation:

5 minutes is the outlier. It sticks out from the rest.

The angles that we can determine their measure are ∠1, ∠5, ∠6, and ∠7.

option A is the correct answer.

The measure of the angles of the polygon is calculated as follows;

The following angles were given;

angle 3 = 60⁰

angle 8 = 135⁰

The following angles can be determined as follows;

angle 5 = 180 - 60⁰  ( sum of angles on a straight line )

angle 5 = 120⁰

angle 7 = angle 3 = 60⁰ (corresponding angles )

angle 5 = angle 1 = 120⁰  (corresponding angles )

The value of angle 6 is calculated as;

∠5 + ∠6 + ∠7 + ∠8 = 360 (sum of angles in quadrilateral)

120 + ∠6 + 60 + 135 = 360

315 + ∠6 = 360

∠6 = 360 - 315

∠6 = 45⁰

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The area of a right triangle is 70 yds².

We have,

Base= 17 yards

Height = 8 yards

The area of a triangle is given by the formula:

Area = (1/2) x base x height

Substituting the given values, we get:

Area = (1/2) x 17 x 8

Area = 68 square yards

Therefore, the area of a right triangle is 70 yds².

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The probability that a randomly selected resident is in favor of the dog park is option

B. 7/18

To find the probability that a randomly selected resident is in favor of the dog park  we  have  to determine the number of residents who are in favor and divide it by the total number of residents surveyed

the number of residents in favor of the dog park

= in favor both male and female

=  19 + 16

= 35.

total number of residents surveyed is  90

the probability

P(In Favor) = Number of residents in favor / total number of residents surveyed

= 35 / 90

= 7/18

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To find the percentage of M2 that M1 represents, we can use the following formula:(M1 / M2) x 100%Substituting the given values, we get:(1050 / 3500) x 100% = 30%Therefore, M1 represents 30% of M2.

The correct answer is Add all of the numbers, then divide.

Given that we need to determine which choice demonstrates the process for calculating the mean,

We know that the mean is calculated by,

You must add up all the values in a dataset and divide the total by the overall number of values in order to determine the mean, also known as the average.

The following steps should be followed to determine the mean:

Add up all the figures.

Subtract the amount from the overall value set.

In order to determine the mean, the option "Add all of the numbers, then divide" is the proper course of action.

Hence the correct answer is Add all of the numbers, then divide.

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4.5 mm is the measurement of the given line AB.

In the given graph both lines AE and BD are parallel.

So, the ratio between the two lines will be the same,

Thus, from the above property

AC/AB= EC/ED

in the given case,

AC =36 mm

EC = 72 mm

ED = 9 mm

Substitute the value in the above equation,

36/AB = 72/9

AB = 9/2

AB = 4.5 mm

Therefore, the measurement of line AB is 4.5 mm.

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The approximate value of √329 to the nearest integer is 18.

Approximation is the process of using rounded values when presenting numerical data and making rough calculations.

To approximate √329 to the nearest integer, we can find the perfect squares that are less than or equal to 329.  

The perfect squares less than or equal to 329 are 16, 25, 36, and 49. But the nearest perfect square to 329 is 324, which is the square of 18 (i.e. 18² = 324).

Therefore, the nearest integer to √329 is 18.

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In a circle with congruent line segments DE and FG, statements A is true, B is false, C and D are false, and E may or may not be true.

In the given circle ⊙C, DE and FG are two line segments that are congruent. The following statements must be true:

A. △DCE≅△FCE: This statement is true because both triangles share the same side lengths of DE and FG and the common angle ∠DCE = ∠FCE.

B. arcDE = arcFG: This statement is false since congruent line segments do not necessarily correspond to congruent arcs in a circle.

C. △FCE≅△FCG: This statement is false since there is no given information to suggest that the line segment CG is congruent to CE.

D. ∠DCE≅∠GCF: This statement is false since there is no given information to suggest that ∠GCF is congruent to ∠DCE.

E. EF≅ED: This statement may or may not be true since we are not given any information about the length of either of these line segments.

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Answer:

Line 2

Step-by-step explanation:

In the second line, 4 is taken as 4x and added with 6x resulting in 10x.

The line 2 should be written as follows:

6x - 5 = 6x - 5

6x - 6x = 5 - 5

0 = 0

The equation of the polynomial is f ( x ) = -13.5 ( x + 2 )²( x - 3 )

Given data ,

The equation of degree 3 polynomial function with real coefficients

And ,  zeros x = - 2 with multiplicity 2 and x = 3 with multiplicity 1

where function passes through the point (1, 54)

If a polynomial function has a zero x = a with multiplicity k, then the factor (x - a)^k appears in its factored form.

Therefore, a degree 3 polynomial function with zeros x = -2 with multiplicity 2 and x = 3 with multiplicity 1 can be written in factored form as:

f(x) = a(x + 2)²(x - 3)

where a is a constant factor. To find the value of a, we use the fact that the function passes through the point (1, 54):

f(1) = a(1 + 2)²(1 - 3) = 54

a(-1)²(-2) = 54

-4a = 54

Divide by -4 on both sides , we get

a = -13.5

Hence , the equation of the degree 3 polynomial function with the given zeros and passing through the point (1, 54) is f ( x ) = -13.5 ( x + 2 )²( x - 3 )

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Answer:

i think this is the correct answer

sorry if its wrong

It is a simple method for transforming 2D shapes. By separating between planar transformations and spaces, the transformation can be grouped

Step-by-step explanation:

Answer: 5, 9

Step-by-step explanation:

factors of 45:

1, 3, 5, 9, 15, 45

Sums: 46, 24, 14

the factors 5 and 9 multiply to get 45 and add to get 14

voila!

The required perimeter of the equilateral triangle is 12.72 cm.

An equilateral triangle has all three sides equal in length. Therefore, if the edge of an equilateral triangle is 4.24 cm, then all three sides are 4.24 cm.

To find the perimeter of the equilateral triangle, we need to add the length of all three sides together:

Perimeter = 4.24 cm + 4.24 cm + 4.24 cm

Perimeter = 12.72 cm

Therefore, the perimeter of the equilateral triangle is 12.72 cm.

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The quotient of x⁴ - 3x³ + 9x + 6 ÷ x + 1  using synthetic division is x³ +  2x² - 2x  + 7  and the remainder is 13

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

x⁴ - 3x³ + 9x + 6 ÷ x + 1

The synthetic set up is

-1  |   1  3  0   9   6

    |__________

Bring down the first coefficient, which is 1 and repeat the process

-1  |   1  3  0   9   6

    |__-1_-2_-2_7____

       1  2  -2  7  13

This means that the quotient is

x³ +  2x² - 2x  + 7  

And the remainder is 13

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Complete question

Find the quotient and remainder using synthetic division.

x^4-3x^3+9x+6/x+1

The quotient is

The remainder is

Answer:

Step-by-step explanation:

To use synthetic division, we need to set up the coefficients of the dividend polynomial in decreasing order of powers of x, including any missing terms with zero coefficients.

So we have:

Dividend: x^4 - 3x^3 + 9x + 6

Divisor: x + 1

We can represent the divisor as (x + 1) and set up the synthetic division table as follows:

-1 | 1 -3 9 0 6

| -1 4 -13 13

|___________________

| 1 -4 13 -13 19

The numbers on the first row of the table are the coefficients of the dividend polynomial in decreasing order of powers of x. The -1 on the left of the table is the opposite of the divisor, x + 1.

The first number in the second row is always 0, and we get it by bringing down the first coefficient, which is 1. To get the next number in the second row, we multiply the divisor, -1, by 1, and add the result to the second coefficient, which is -3. This gives us -1 x -3 = 3, which we write under -3 in the first row.

We repeat this process for the next numbers in the second row, always multiplying the divisor by the last number in the second row, and adding the result to the next coefficient in the first row. We continue until we reach the last coefficient in the first row.

The last number in the second row, 13, is the remainder of the division. The other numbers in the second row are the coefficients of the quotient polynomial in decreasing order of powers of x. So the quotient is:

x^3 - 4x^2 + 13x - 13

And the remainder is:

13

Therefore, the quotient is x^3 - 4x^2 + 13x - 13, and the remainder is 13.

Answer:

15

if you count the length and breadth with the height and multiply them it'll give you 15

Answer:

Hope this helps ^^

Step-by-step explanation:

Let's define the variables:

Let's call the cost of a burger "B" (in dollars).

Let's call the cost of a hotdog "H" (in dollars).

Now, we can set up a system of equations based on the given information:

Equation 1: 2B + H = 4.82 (Two burgers and one hotdog cost $4.82)

Equation 2: B + 2H = 3.70 (One burger and two hotdogs cost $3.70)

To solve this system of equations, we can use the method of substitution or elimination.

Using the method of elimination, we can multiply Equation 2 by 2 to eliminate the "B" term:

2(B + 2H) = 2(3.70)

2B + 4H = 7.40

Now, we can subtract Equation 1 from this new equation to eliminate the "2B" term:

(2B + 4H) - (2B + H) = 7.40 - 4.82

2H - H = 2.58

H = 2.58

Therefore, the cost of a hotdog is $2.58.

Labeling the answer: The cost of a hotdog is $2.58.

The graph of the translations are attached

The red is the preimage while the blue is the image

The absolute value graph has equation f(x) = |2x| and the translation we want to obtain is y = f(x) + 4 and this is a translation 4 units up

This results to a graph of equation  y = f(x) + 4 = |2x| + 4

For the parabolic graph, the equation is written as

y = a(x - 2)² - 3

solving for a using (0, -5)

-5 = a(0 - 2)² - 3

-2 = 4a

a = -1/2, then the equation is g(x) = -1/2 (x - 2)² - 3

Applying the translation, the equation will be

y = g(x + 2) =  -1/2 (x - 2 + 2)² - 3 = -1/2 (x)² - 3

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The height of the tree is 60 ft

Proportion is defined as as an equation that is made equal to another

From the information given, we have that;

The shadow casted by the tree = 30 ft

The height of the pole = 6ft

The shadow casted by the pole = 3ft

Then, we have that;

If 6ft = 3ft

xft = 30ft

cross multiply the values, we have;

3x = 30(6)

Multiply the values

3x = 180

Divide both sides by the coefficient of the variable

x = 60ft

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Answer:

Hexagon

Step-by-step explanation: Count the sides, hex means 6, sept means 7, oct means 8

The solutions to the original equation are:

x = π - 3π/2 = -π/2

x = 3π/2 - 3π/2 = 0

So the values of x that satisfy the equation are -π/2 and 0.

To solve the given equation, we can use the following             trigonometric identity:

sin(A) + sin(B) = 2*sin((A+B)/2)*cos((A-B)/2)

Applying this identity to sin(3π/2+x) + sin(3π/2+x), we get:

sin(3π/2+x) + sin(3π/2+x) = 2*sin((3π/2+x + 3π/2+x)/2)cos((3π/2+x - 3π/2+x)/2)

= 2sin(3π/2+x)cos(0)

= 2(-cos(x))

Therefore, the equation can be simplified to:

-2*cos(x) = 2

Dividing both sides by -2, we get:

cos(x) = -1

This means that x is either π or 3π/2, since those are the values where cos(x) = -1.

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Answer:

972 square feet

Step-by-step explanation:

length, a, of rectangle with  width, b, will have area a X b (simplified to just ab).

so area = 36 (feet) X 27 (feet) = 972 (square feet)  

I'm also getting 22.9875, but the instructions say to round to 2 decimal places.

22.9875 rounds to 22.99 because 0.9875 is closer to 0.99 than it is to 0.98

In other words, 9875 is closer to 9900 than it is to 9800.

The volume of the shapes are;

6. 11259.47 in³

7. 14476.46 mm³

8.  3744 ft³

9. 473.6mm³

10.  18816.57cm³

To determine the values, we need to know the following;

In a right-angled triangle, a ² + b ² = c ²

Now. for each of the shapes, substitute the values, we have;

6) π (16) ² X 14

Multiply the values

= 11259.47 in³

7) Diameter² = 40² - 32²

Diameter = √(40² - 32²) = 24, Radius = 12.

Substitute the values

Volume = π (12)² X 32 = 14476.46 mm³

8) volume = 8 X 12 X 39

Multiply the values

= 3744 ft³

9) cross-section (triangle) = 1/2 X 5.4 X 11 = 29.7

Volume = 29.7 X 16 = 473.6mm³

10) radius = 33/2 = 16.5

volume = (4/3) π (16.5)³

Multiply the values

= 18816.57cm³

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The value of the missing side length x in the right triangle is 15 inches.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

( hypotenuse )² = ( leg 1 )² + ( leg 2 )²

The image in the diagram is a right triangle:

Hypotenuse = 17 inches

Leg 1 = 8 inches

Leg 2 = x

To solve for x, we use the pythagorean theorem.

( hypotenuse )² = ( leg 1 )² + ( leg 2 )²

( leg 2 )² = ( hypotenuse )² - ( leg 1 )²

( leg 2 )² = ( 17 )² - ( 8 )²

( leg 2 )² = 289 - 64

( leg 2 )² = 225

Take the square roots

Leg 2 = √225

Leg 2 = 15 inches.

Therefore, the value of x is 15 inches.

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