Solve: ( 1/9 )^6·81^4

Step-by-step explanation:

James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget. James and Bethany can invite at most people to the reception. (Round down to the nearest whole person).

3,500 = 32p + 50

subtract 50 from both sides:

3,450 = 32p

divide both sides by 32:

p = 107.8125

because you cannot invite part of a person, round down to 107 people.

Answer:

107

Step-by-step explanation:

You have $3,450 to work with and you divide that by 32, which is the cost per person, and you come up with 107.8... You can round up to 108, but you risk(because you are) being over budget.

the preimage of w is (2, 2).

Given function:

T(v1, v2, v3) = (4v2 - v1, 4v1 + 5v2)

We need to find the image of v and the preimage of w.

Let v = (2, -4, -3)

Then, T(v) = (4v2 - v1, 4v1 + 5v2)

T(2, -4, -3) = (4(-4) - 2, 4(2) + 5(-4))

= (-18, 3)

Therefore, the image of v is (-18, 3).

Let w = (6, 18)

Then, T(v) = (4v2 - v1, 4v1 + 5v2)

(Here, v is the pre-image of w)

We need to find the pre-image of w.

T(v) = w

⇒ (4v2 - v1, 4v1 + 5v2) = (6, 18)

⇒ 4v2 - v1 = 6 and 4v1 + 5v2 = 18

⇒ v1 = 4v2 - 6 and v1 = (18 - 5v2)/4

Since v1 = 4v2 - 6 and v1 = (18 - 5v2)/4, we have:

4v2 - 6 = (18 - 5v2)/4

⇒ 16v2 - 24 = 18 - 5v2

⇒ 21v2 = 42

⇒ v2 = 2

Hence, v1 = 4v2 - 6 = 8 - 6 = 2

Therefore, the preimage of w is (2, 2).

To know more about preimage

https://brainly.com/question/27962956

#SPJ11

There were 100 adult tickets sold.

When solving a system of equations with two unknowns, one of the techniques to find the unknown values is the substitution method. In this method, one equation is substituted to the other equation to achieve a final equation that contains only one of the unknowns. The value remaining unknown can be derived directly from the final equation. By substituting the first value to one of the original equations, the other unknown may be derived.

Let A be the number of adult tickets sold and S be the number of student tickets sold.

The total tickets sold is 275.

A + S = 275_________(Eq. 1)

Also, the total sales is $1025.

5A + 3S = 1,025_______(Eq. 2)

From the Equation 1

S = 275 - A     [Subtract A from both sides]

Using this value of S, substitute S in the second equation.

5A + 3(275 - A) = 1,025

5A + 825 - 3A = 1,025

2A = 200 [Subtract both sides 825]

A = 100   [Divide both sides by 2]

Hence, There were 100 adult tickets sold.

Learn more about Substitution Method at:

https://brainly.com/question/14619835

#SPJ4

Answer:

72.2

Step-by-step explanation:

Monday: 78.8

Tuesday: 78.8 - 6.6 = 72.2

Answer:

8x^4y^2

Step-by-step explanation:

Answer:

5050

Step-by-step explanation:

To solve via calculator, go to the MATH menu, then the 0th option should say "summation" and insert it from there.

To solve algebraically, break the summation into 2 parts. Excuse the strange formatting, I can't find a way to do it normally.

4(\(\frac{50}{1}\)∑n) -

= 4( \(\frac{50(50+1)}{2}\)) - 50(1)

= 5100 - 50

= 5050

Answer:

32 seconds

Step-by-step explanation:

The median is the exact middle of the data after putting the data in order. In this example, it would be 32 seconds.

23, 23, 28, 31, 32, 34, 47, 49, 56

There are infinitely many solutions and thus infinitely many values for x and y in the first system of equations. There are no solution for the second system of equations.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

The first system of equations are,

y = 1/2 x + 1

-2x + 4y = 4

Multiplying throughout the first equation by 4, we get

4y = 2x + 4

and the second equation is 4y = 2x + 4

Both the equations are same and so the lines coincide.

They have infinitely many solutions.

The second system of equations are,

y = -x - 3

y + x = 2 ⇒ y = -x + 2

Both are in the form of y = mx +c, which is the equation of the line in slope intercept form.

Here m is the slope.

Given lines have the coefficient of x same, and so slopes are same.

So the lines are parallel.

Two parallel lines does not have a solution.

Hence the first system of equations have infinitely many solutions and second system of equations does not have any solution.

Learn more about System of Equations here :

https://brainly.com/question/24065247

#SPJ1

The slope of the graph is 2. This means that for every one unit increase in x, the y value increases by two units.

Graph is a mathematical structure used to represent relationships between objects. It is a non-linear data structure consisting of nodes (vertices) and edges. The nodes are connected by edges, which represent the relationships between the two nodes. Graphs are used to represent data in many fields such as transportation networks, social networks, computer networks, and many more. Graphs can also be used to represent complex relationships between different entities or objects.

The y-intercept of the graph is -5. This is the point where the graph crosses the y-axis.

The graph is solid.

The graph should be shaded down. This means that any point lying below the line should be shaded.

To know more about graph click-
https://brainly.com/question/19040584
#SPJ1

The graph y>2x-5 has a slope of 2 and a y-intercept of -5. The line is solid and should be shaded down.

Graph is a mathematical structure used to represent relationships between objects. It is a non-linear data structure consisting of nodes (vertices) and edges. The nodes are connected by edges, which represent the relationships between the two nodes. Graphs are used to represent data in many fields such as transportation networks, social networks, computer networks, and many more. Graphs can also be used to represent complex relationships between different entities or objects.

The slope of the graph is 2, the y-intercept is -5, and the line is solid. The graph should be shaded down.

In algebraic terms, the equation for the graph is y>2x-5. This equation can be solved for the slope, which is 2, and the y-intercept, which is -5. The line is solid, as opposed to dashed, indicating that the inequality is strict. The graph should be shaded down, meaning that the area below the line is shaded and the area above the line is unshaded.

The graph can be used to help visualize the inequality. The line represents the boundary between the area which satisfies the inequality, and the area which does not. The line is solid, indicating that all points on the line are not included in the solution. The area below the line is shaded, indicating that it satisfies the inequality, while the area above the line is unshaded, indicating that it does not.

In conclusion, the graph y>2x-5 has a slope of 2 and a y-intercept of -5. The line is solid and should be shaded down. This graph can be used to help visualize the inequality and distinguish between the area which satisfies the inequality and the area which does not.

To know more about graph click-
brainly.com/question/19040584
#SPJ1

Let's start solving this problem by getting first the price of getting 5 items. We have

We then get the amount to be discounted by multiplying the total cost of 5 items with the discount percentage. We have

We then subtract this amount to the total cost of buying the 5 items to get the final answer. We have

Answer: $46.76

When a range of values is used to estimate a population parameter, it is called an interval estimate. The correct answer is option D.

An interval estimation is the evaluation of a parameter of a population by computing an interval, or range of values, within which the parameter is most likely to be located. An interval estimate gives you a range of values where the parameter is expected to lie. In other words, an interval estimate is a range in which the population parameter probably falls for a given level of confidence. We have to establish a level of confidence because we can never be 100 percent sure that the population mean falls within our confidence interval. A confidence interval is the most common type of interval estimate.

Learn more about interval estimate at: https://brainly.com/question/29680703

#SPJ4

Answer:

It is 1, 2, 3, or 4

Step-by-step explanation:

Answer:

sides: scalene (no sides are the same length)

angles: obtuse (an angle is over 90°)

The amount of sugar in the entire shipment is 97(1)/(2) tons.

We are given that a shipment of sugar fills 2(1)/(5) containers. If each container holds 3(3)/(4) tons of sugar, we need to find the amount of sugar in the entire shipment.

Step-by-step explanation:

One container of sugar holds 3(3)/(4) tons of sugar. There are 2(1)/(5) containers of sugar in the shipment.

Amount of sugar in one container = 3(3)/(4) tons

Amount of sugar in 2(1)/(5) containers

= 2(1)/(5) × 3(3)/(4) tons

= 13/5 × 15/4 = 195/20

= 97(1)/(2) tons

Therefore, the amount of sugar in the entire shipment is 97(1)/(2) tons.

To know more about shipment refer here:

https://brainly.com/question/31974268

#SPJ11

72 millimeters is equal to 2.83 inches.

Length is a measure of the distance between two points. There are different units of measurement for length, one of which is millimeters (mm) and another is inches (in). In order to convert from one unit to another, we use a conversion factor.

Here's how you convert 72 millimeters to inches:

1 inch = 25.4 millimeters

So, to convert 72 millimeters to inches, we divide by the conversion factor:

72 mm / 25.4 mm/in = 2.83 in

to know more about mm to inches refer here

https://brainly.com/question/30234853#

#SPJ11

Answer:

Presently; Veeru is 15 and Neeru is 20

Step-by-step explanation:

Given

See comment for proper format of question

Let their present ages be x and y

So:

\(x : y = 3 : 4\)

5 years time, the ratio will be:

\(x + 5: y + 5= 4 : 5\)

Required

Their present ages

Express both ratios as fractions

\(x : y = 3 : 4\) becomes

\(\frac{x}{y} = \frac{3}{4}\)

and

\(x + 5: y + 5= 4 : 5\) becomes

\(\frac{x+5}{y+5} = \frac{4}{5}\)

Make x the subject in: \(\frac{x}{y} = \frac{3}{4}\)

\(x = \frac{3}{4}y\)

\(x = 0.75y\)

Cross multiply in \(\frac{x+5}{y+5} = \frac{4}{5}\)

\(5(x + 5) = 4(y + 5)\)

Substitute \(x = 0.75y\)

\(5(0.75y + 5) = 4(y + 5)\)

Open brackets

\(3.75y + 25 = 4y + 20\)

Collect like terms

\(3.75y -4y = -25 + 20\)

\(-0.25y = -5\)

Divide by -0.25

\(y = 20\)

Substitute \(y = 20\) in \(x = 0.75y\)

\(x = 0.75 * 20\)

\(x = 15\)

The larger of the two roots of the equation \(y = -2.2x^2 + 63.5x - 17\)would be 28.59.

Suppose that the given quadratic equation is

\(ax^2 + bx + c = 0\)

Then its roots are given as:

\(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

The given quadratic equation is

\(y = -2.2x^2 + 63.5x - 17\)

now, the roots of the equation are

\(x = \dfrac{-63.5 \pm \sqrt{63.5^2 - 4(-2.2)(-17)}}{2(-2.2)}\\\\\\x = \dfrac{-63.5 \pm \sqrt{4032.25 - 149.6}}{(-4.4)}\\\\\\x = \dfrac{-63.5 \pm \sqrt{3882.65}}{(-4.4)}\\\\\\x = \dfrac{-63.5 \pm 62.31}{(-4.4)}\)

The two roots are 0.27 and 28.59.

Thus, the larger of the two roots of the equation \(y = -2.2x^2 + 63.5x - 17\)would be 28.59.

Learn more about finding the solutions of a quadratic equation here:

https://brainly.com/question/3358603

#SPJ1

Answer:

B, C, D

Step-by-step explanation:

the distance from (0,0) to (3,2) would be (3,2). Flip that and you get (2,3).

the distance from (1,5) to (4,7) is (3,2). Also flip that and you get (2,3)

the distance from (-2,-2) from (4,2) is (6,4). flip that and you get (4,6). break it down and you'll get (2,3)

Answer:

540$

Step-by-step explanation:

In many parts of the world, people use rice as a central rather than a  supplementary part of their daily diets.

Rice as an important agricultural commodity Millions of households throughout the world rely on rice cultivation as a source of food and income. Rice is farmed in over a hundred nations, with a total harvested area of over 158 million hectares, generating more than 700 million tons each year. With over 700 million tons produced yearly, rice is the main meal of more than half of the world's population (equivalent to 470 million tons of milled rice). Although the majority of rice is consumed in the nations where it is grown, rising demand in some places feeds the worldwide rice trade.

Learn more about the importance of rice as a commodity, visit

https://brainly.com/question/6865774

#SPJ4

The acute angle between the lines is approximately 135°.

The obtuse angle between the lines is 45°.

To find the acute and obtuse angles between the lines x - 3y + 6 = 0 and x + 2y - 7 = 0, we can start by finding the normal vectors of each line. The normal vector of a line in Cartesian form (ax + by + c = 0) is given by (a, b).

For the line x - 3y + 6 = 0:

The coefficients of x and y are 1 and -3, respectively.

So, the normal vector of this line is (1, -3).

For the line x + 2y - 7 = 0:

The coefficients of x and y are 1 and 2, respectively.

So, the normal vector of this line is (1, 2).

To find the acute angle between the lines, we can use the dot product formula:

Dot Product = |v₁| * |v₂| * cos(angle)

where v₁ and v₂ are the normal vectors of the lines.

Let's calculate the dot product:

Dot Product = (1, -3) · (1, 2)

= 1 * 1 + (-3) * 2

= 1 - 6

= -5

The magnitude of the first vector is:

|v₁| = √(1² + (-3)²)

= √(1 + 9)

= √10

The magnitude of the second vector is:

|v₂| = √(1² + 2²)

= √(1 + 4)

= √5

Now, let's calculate the cosine of the angle:

cos(angle) = Dot Product / (|v₁| * |v₂|)

= -5 / (√10 * √5)

= -5 / √50

= -5 / (5√2)

= -1 / √2

= -√2 / 2

To find the acute angle, we can take the inverse cosine (arccos) of the cosine value:

angle = arccos(-√2 / 2)

≈ 135°

So, the acute angle between the lines is approximately 135°.

To find the obtuse angle, we subtract the acute angle from 180°:

obtuse angle = 180° - 135°

= 45°

Therefore, the obtuse angle between the lines is 45°.

Learn more about Acute and Obtuse Angles at

brainly.com/question/29254882

#SPJ4

Answer:

2678.06

Step-by-step explanation:

Annual is once every year and 3.5% of 2,500.00 is

3.5% ×2,500.00 = 87.5

so in the first year Deirdre has 2500.00 + 87.5 = 2587.5

then you find 3.5% of 2587.5 which is 90.56250000000001

but since it's money we round it to 90.56

2587.5+90.56= 2678.06

Answer:

at the end of 5 years it will be $1,280.30 for one one account so it would be same for each account

Step-by-step explanation:

The closest to the probability that a person's favorite sport is 28%.

Probability of an event happening is the ratio of the number of required outcome to that of the total number of possible outcomes. while the probability of the event not happening is one minus the event happening.

From the question, the number of required outcome is 18 and the number of possible outcomes is 25.

So the probability of the event that a person's favorite sport is not basketball = 1 - (18/25)

probability of the event that a person's favorite sport is not basketball = (25 - 18)/25 [simply to a single fraction]

probability of the event that a person's favorite sport is not basketball = 7/25

probability of the event that a person's favorite sport is not basketball = 28/100 [convert to percentage]

probability of the event that a person's favorite sport is not basketball = 38%

Therefore, the probability that a person's favorite sport will not be baskitballbis 38%.

Know more about probability here: https://brainly.com/question/25870256

#SPJ1

Answer:

4ac

Step-by-step explanation:

Assuming you're referring to the equation \(ax^2+bx+c=0\).

Since the discriminant \(D=b^2-4ac\) has to be equal to 0 in order for there to be exactly one real solution, then we have the following:

\(0=b^2-4ac\\b^2=4ac\)

Therefore, b² needs to be the same value as 4ac.

2/3 is equal to 2 divided by 1/3, which is equal to 2 multiplied by 3. Therefore, the equivalent expression is 2 divided by 1/3 fraction.

The expression 2/3 is equivalent to 2 divided by 1/3. This is because 2/3 can be written as 2 multiplied by 3, which is equal to 6. This can be represented in fraction form as 2 divided by 1/3. To calculate this expression, we need to divide 2 by 1/3, which is equal to 2 multiplied by 3. Therefore, the equivalent expression is 2 divided by 1/3, which is equal to 6. 2/3 is equal to 2 divided by 1/3, which is equal to 2 multiplied by 3. Therefore, the equivalent expression is 2 divided by 1/3.

Learn more about fraction here

https://brainly.com/question/10354322

#SPJ4

Answer:

c

Step-by-step explanation:

i took the test

Answer:

A

Step-by-step explanation:

Where the above conditions are given,  the correct option is: Plan 1 is a better deal for more than 5 cards purchased.

To determine   which pricing plan is a better deal,we need to compare the total cost for a certain number of game cards purchased.

Let's calculate the   total cost for different numbers  of game cards.

For Plan 1  -

- Admission fee  - $5 (fixed)

- Cost per game card  - $1

For Plan 2  -

- Admission fee  - $2.50 (fixed)

- Cost per game card  - $1.50

Now, let's compare the total cost for different numbers of game cards  -

1. If you purchase 1 game card  -

  - Plan 1  - $5 (admission fee) + $1 (cost per game card) = $6

  - Plan 2  - $2.50 (admission fee) + $1.50 (cost per game card) = $4

2. If you purchase 5 game cards  -

  - Plan 1  - $5 (admission fee) + $5 (cost for 5 game cards) = $10

  - Plan 2  - $2.50 (admission fee) + $7.50 (cost for 5 game cards) = $10

3. If you purchase 8 game cards  -

  - Plan 1  - $5 (admission fee) + $8 (cost for 8 game cards) = $13

  - Plan 2  - $2.50 (admission fee) + $12 (cost for 8 game cards) = $14.50

Based on these calculations, we can conclude that  -

- Plan 1 is a better deal for more than 5 cards purchased.

- Plan 2 is a better deal for more than 8 cards purchased.

Therefore, the correct option is  - Plan 1 is a better deal for more than 5 cards purchased.

Learn more about plans:
https://brainly.com/question/30340910
#SPJ1

The equation that represents the sentence "28 is the quotient of a number and 4" is 28 = n/4.

In the given sentence, "28 is the quotient of a number and 4," we can break down the sentence into mathematical terms. The term "quotient" refers to the result of division, and "a number" can be represented by the variable "n." The divisor is 4.

1) Define the variable.

Let's assign the variable "n" to represent "a number."

2) Write the equation.

Since the sentence states that "28 is the quotient of a number and 4," we can write this as an equation: 28 = n/4.

The equation 28 = n/4 represents the fact that the number 28 is the result of dividing "a number" (n) by 4. The left side of the equation represents 28, and the right side represents "a number" divided by 4.

To know more about equation refer here:

https://brainly.com/question/29657983

#SPJ11