The equation -4x + y = 0 relates the
number of pages in a photo album y to
the number of pictures in the album x.
Tell whether the relationship is a direct
variation. Explain your answer.

Answer:

We can use the Central Limit Theorem to solve this problem since we are dealing with a sample size greater than 30. The distribution of sample means will be approximately normal with a mean of 74 beats per minute and a standard deviation of 12.5 / sqrt(4) = 6.25 beats per minute.

To find the probability that the mean pulse rate of 4 adult females is between 70 and 78 beats per minute, we need to calculate the z-scores for both values and then use a z-table or calculator to find the area under the normal curve between those two z-scores.

The z-score for 70 beats per minute is:

z = (70 - 74) / 6.25 = -0.64

The z-score for 78 beats per minute is:

z = (78 - 74) / 6.25 = 0.64

Using a standard normal distribution table or calculator, the area between these two z-scores is approximately 0.4115.

Therefore, the probability that 4 adult females have pulse rates with a mean between 70 and 78 beats per minute is approximately 0.4115 or 41.15%.

Answer:

Step-by-step explanation:

17.5

The system of equations that has a solution of (5,-3) is y +  3 = m (x-5).

or

We have the points (5, -3).

Now, The point-slope form of a linear equation is:

(y - y₁) = m (x - x₁)

(y - (-3)) = m (x- 5)

y +  3 = m (x-5)

Now, let the slope m = -2 then

y + 3 = -2(x-5)

y + 3 = -2x + 10

y + 2x + 3 -10 = 0

y + 2x - 7 = 0

Or we can also form the equation as

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The resort should sell a number of 255 packages at a price of $2400 per person to maximize their monthly profit and the maximal profit is $613,400.

Maximal profit refers to the highest level of profit that a business or organization can achieve given certain constraints such as cost, demand, or pricing. It is the point at which a company or business generates the most revenue after accounting for all expenses associated with production and distribution of goods or services. To determine the maximal profit, a business will need to find the optimal balance between costs and revenue, while also taking into account factors such as competition and market demand. This involves analyzing a variety of financial metrics such as revenue, cost of goods sold, gross profit margin, and net profit margin, among others.

Let's begin by defining some variables:

P = price of the package

Q = number of packages sold

R = revenue

C = cost

Profit = revenue - cost

Based on the information given, we can create the following equations:

R = P * Q

C = 1600 + 2000 * Q

Profit = R - C = P * Q - (1600 + 2000 * Q)

We want to find the price that will maximize the monthly profit. To do this, we need to find an expression for profit in terms of P only. We can use the equation for C to substitute Q in the expression for profit:

C = 1600 + 2000 * Q

Q = (C - 1600) / 2000

Profit = P * Q - (1600 + 2000 * Q)

Profit =

Profit = P * ((C - 1600) / 2000) - C + 1600

Now we can find the derivative of profit with respect to P:

dProfit/dP = (C - 1600) / 2000

To find the value of P that maximizes profit, we need to set the derivative equal to 0:

dProfit/dP = 0

(C - 1600) / 2000 = 0

C = 1600

This means that profit is maximized when revenue equals cost, which makes sense. Substituting C = 1600 into the expression for profit, we get:

Profit = P * ((1600 + 2000 * Q - 1600) / 2000) - 1600

Profit = P * Q - 1600

Now we need to find the corresponding values of P and Q. We know that for every increase of $100 in price, there will be a decrease of 5 in the number of packages sold. This means that:

Q = 300 - (P - 2000) / 100 * 5

Substituting this into the expression for profit, we get:

Profit = P * (300 - (P - 2000) / 100 * 5) - 1600

To find the maximum profit, we can take the derivative of this expression with respect to P and set it equal to 0:

dProfit/dP = 300 - (P - 2000) / 20 = 0

P = 2400

This means that the price that will maximize the monthly profit is $2400 per person. To find the corresponding number of packages sold, we can substitute this into the equation for Q:

Q = 300 - (2400 - 2000) / 100 * 5 = 255

Therefore, the resort should sell 255 packages at $2400 per person to maximize their monthly profit. To find the maximal profit, we can substitute these values into the expression for profit:

Profit = 2400 * 255 - 1600 = $613,400.

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Answer:

Step-by-step explanation:

when h=0

0=-1125d²+d

1125d²-d=0

d(1125d-1)=0

d=0

or 1125d-1=0

d=1/1125 meters

Here, we want to get the final volume

From the general gas equation, we have it that:

[tex]\dfrac{P_1V_1}{T_1} =\dfrac{P_2V_2}{T_2}[/tex]

From the question, we have it that:

P1 is the initial pressure which is 475 torr

V1 is the initial volume which is 296 mL

T1 is the initial temperature which we have to convert to absolute value by adding 273.15 K ([tex]68 + 273.15 = 341.15 \ \text{K}[/tex])

P2 is the final pressure that is the same as the initial which is 475 torr

V2 is the final volume that we want to calculate

T2 is the final temperature which is 273.15 K (0 degrees Celsius is 273.15 K)

Substituting the values, we have:

            [tex]\dfrac{475\times296}{341.15}=\dfrac{475\times V_2}{273.15}[/tex]

[tex]V_2=\cfrac{475\times296\times273.15}{341.15\times475} =\boxed{\bold{237 \ mL}}[/tex]

We could have solved this by using Charles' law that relates temperature to volume (volume is directly proportional to temperature)

Answer:

208

Step-by-step explanation:

4*4(2)+11*4(2)+11*4(2)=208

Find the small squares.

4^2+4^2=32

4*11*4=176

176+32=208

Thus, the statement  -3 to the -3 power written without using exponents is -1/27.

A number's power or exponent, in other words, tells how many times it must be multiplied by itself. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.

Given that-

-3 to the -3 power

This can written as:

= (-3)⁻³

Now using the property of exponents,taking reciprocal of the number will remove the negative number.

= (1 /-3)³

= (1)³ / (-3)³

= 1/(-27)

= - 1/ 27

Thus, the statement  -3 to the -3 power written without using exponents is -1/27.

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The area of the shaded region = 30.903 in²

From the attached figure we can observe that the radius of the circle R is r = 6 in.

Using the forula for the area of circle, the area of circle R would be,

A₁ = πr²

A₁ = π × 6²

A₁ = 36π

A₁ = 113.097 in²

So, the diameter would be d = 6 × 2 = 12 in.

The circle R is inscribed in a square.

So, the side length of square is equal to the diameter of the circle.

This means the side length 'a' os square = 12 in.

Using the formula of the area of square,

A₂ = side²

A₂ = a²

A₂ = 12²

A₂ = 144 in²

so, the area of the shaded region would be,

A = A₂ - A₁

A = 144 -113.097

A = 30.903 in²

This is the required area.

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A line plot for the data is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 3.5 or 3 1/2 because it has the highest frequency of 5.

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Answer:sorryy if this is late but its 2

Step-by-step explanation:

You have to find what 0.2 of 132 is

132 x 0.2 = 26.40

The answer [tex]\boxed{\bold{\$26.40}}[/tex]

The general common factor (GCF) of the polynomial equation [tex]24x^9 + 21x^6 = 0[/tex] is 3x6, which, after factoring, is the common factor of the coefficients and the terms enclosed in brackets.

We must factor out the common terms from both the coefficients and the exponents in order to determine the GCF (Greatest Common Factor) for the polynomial equation 24x9 + 21x6 = 0.

The first step is to determine the coefficients' common factor, which is 3. The equation can be changed to read:

3(8x^9 + 7x^6) = 0

We now need to determine which term the parenthesized terms have in common the most. Since x is raised to a power in both terms, we may factor out x^6 to obtain:

3x^6(8x^3 + 7) = 0

The greatest common factor of the polynomial equation 24x^9 + 21x^6 = 0 is 3x^6.

We can verify this by dividing both terms in the equation by 3x^6. Doing so gives us:

(8x^3 + 7) = 0

This equation has no common factors, and we cannot factor it further. Thus, the GCF of the original polynomial equation 24x^9 + 21x^6 = 0 is 3x^6

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If the job takes Reba 1 hours, the cost would be $ 19 with either artist

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let's assume the number of hours that Reba takes to paint the window is h. Then, the total cost of the job with Reba would be:

Total cost with Reba = $19 ( h )  + $41

The total cost with Pete is already given as a flat rate of $60.

We want to find the number of hours that Reba would have to take to charge the same amount as Pete, so we can set the two expressions for the total cost equal to each other and solve for "h":

$ 19 ( h ) + $ 41 = $ 60

Subtracting $41 from both sides, we get:

$ 19 ( h ) = $ 19

Dividing both sides by $ 19, we get:

h = 1

So Reba would have to take 1 hour to charge the same amount as Pete.

To calculate the cost of the job with either artist if it takes Reba 1 hour, we can substitute h=1 into the expression for the total cost with Reba:

Total cost with Reba = $ 19 ( 1 ) + $ 41 = $ 60

Hence , this is the same as the flat rate quoted by Pete, so the cost of the job would be $60 with either artist if it takes Reba 1 hour

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Considering the binomial random variable, the probabilities are:

a. 0.1611

b. 0.8915

c. 0.7588

d. 0.1085

e. 0.0576

The binomial distribution formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting k successes

n is the number of trials

p is the probability of success on one trial

(n choose k) is the binomial coefficient, which is equal to n! / (k! * (n - k)!)

k is the number of successes we want to find the probability for

Using this formula, we can find the probabilities for the given scenarios:

a. P(X = 4) = (10 choose 4) * 0.15^4 * (1 - 0.15)^(10 - 4) = 0.1611

b. P(X <= 1)

= P(X = 0) + P(X = 1)

= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1)

= 0.8915

c. P(X >= 1)

= 1 - P(X = 0)

= 1 - (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)

= 0.7588

d. P(X > 1)

= 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - ((10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1))

= 0.1085

e. P(X < 1)

= P(X = 0)

= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)

= 0.0576

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The required value of impulse is 88 N-s and the mass of the cart is 8.8 kg.

Newton's Second Law relates an object's acceleration as a function of both the object's mass and the applied net force on the object.

Given data:

The speed of cart is, v = 10 m/s.

We are given the Force-time graph for which the area of the force-time graph will provide the value of impulse. So from the graph, the maximum force is,

F = 22 N

And time interval is,

t = 4.5 s - 0.5 s

t = 4 s

So, the impulse is,

I = Area of graph

I = F × t

I = 22 × 4

I = 88 N-s

Now the standard expression for the impulse as per the impulse-momentum theorem is,

I = ΔP (Change in momentum)

I = m ×( v - u )

Here, u is the final velocity, and since the cart stops finally, then u = 0 m/s. And m is the mass of the cart.

Solving as,

88 = m ×( v - u )

88 = m ×( 10 - 0 )

m = 8.8 kg

Thus, we can conclude that the required value of impulse is 88 N-s and the mass of car is of 8.8 kg.

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Therefore, the lawnmower can cut grass for 2.5 hours on 5/6 of a gallon of fuel in the gas can

To find out how long the lawnmower can cut grass with 5/6 of a gallon of gas, we first need to figure out how many gallons of gas the lawnmower will use per hour:

1 hour of grass cutting = 1/3 gallon of gas

1 gallon of gas = 3 hours of grass cutting

So the lawnmower uses 1/3 gallon of gas per hour, which means that 1 gallon of gas will last for 3 hours of grass cutting.

Now we can use this conversion factor to figure out how long 5/6 of a gallon of gas will last:

5/6 gallon of gas * 3 hours of grass cutting per 1 gallon of gas = 15/18 hours of grass cutting

Simplifying this fraction by dividing the numerator and denominator by 3:

15/18=3/6

So 5/6 of a gallon of gas will last for 5/6 of 3 hours, which is equal to 2.5 hours of grass cutting.

As a result, 5/6 of a gallon of gas will last for 5/6 of 3 hours, or 2.5 hours of mowing the lawn.

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The best description of the figure would be that it is a C. a square.

To find out the type of figure that we have, it would be best to find the lengths of the sides of the figure. We should find AB, BC, CD, and AD.

We can use the distance formula which is:

D=√ ( x 2 - x1 ) ² + ( y2 - y1) ²

Using this formula, we find that AB, BC, CD, and AD are all a distance of 6 units. This therefore means that this figure is a square because all the sides are equal.

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Full question is:

Which best describes the figure that is represented by the following coordinates?

A(-3, 4), B(3, 4), C(3,-2) and D(-3,-2)

a rectangle

a trapezoid

a square

The options that are not seen as retirement plan(s) are: II, IV

II. Pension Plan

IV. Traditional IRA

A defined contribution plan is a retirement plan in which the contributions made by or on behalf of the employee are defined, but the ultimate benefit depends on the performance of the investments made with those contributions.

Based on this definition, the retirement plans that are not considered defined contribution plans are:

II. Pension Plan - Pension plans are typically defined benefit plans, where the ultimate benefit is based on a formula that takes into account the employee's salary and years of service, rather than the contributions and investment returns.

IV. Traditional IRA - Traditional Individual Retirement Arrangements (IRAs) are also not defined contribution plans. While they do involve individual contributions, the ultimate benefit is not solely based on the contributions and investment returns, but rather on various factors, such as the individual's age, income, and tax deductions.

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The expression simplified can be written as:

6x³y  -7xy²

The correct option is the first one.

Here we have the following expression:

(4x³y - 2xy² + 3xy) + (2x³y - 5xy² - 3xy)

To simplify it, we need to group the like terms (this is terms with the same variables and correspondent exponents).

Then we can rewrite the expression as:

(4 + 2)x³y + (-2 - 5)xy² + (3 - 3)xy

6x³y  -7xy²

That is the expression simplified.

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Answer:

A:6x3y − 7xy2

Step-by-step explanation:

i took the test and got it right

The area of the composite figure is equal to 278 square inches

The composite figure can be observed to be made up of two triangles, a rectangle and a parallelogram, so we shall calculate for the area and sum the results to get the total area of the composite figure as follows:

area of top triangle = 1/2 × 8 in × 11 in = 44 in²

area of the side triangle = 1/2 × 9 in × 4 in = 36 in²

area of the rectangle = 11 in × 9 in = 99 in²

area of the parallelogram = 11 in × 9 in = 99 in²

total area of the composite figure = 44 in² + 36 in² + 99 in² + 99 in²

total area of the composite figure = 278 in²

Therefore, the area of the composite figure is equal to 278 square inches

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Plan A lasts for 2/7 hours or approximately 17.14 minutes, and Plan B lasts for 9/7 hours or approximately 1 hour and 17.14 minutes.

In algebra, the definition of an equation in its simplest form is a mathematical statement that shows that two mathematical expressions are equal. For example, 3x 5 = 14 is an equation where 3x 5 and 14 are two expressions separated by an equal sign.

Let's say plan A takes x hours and plan B takes y hours.

Based on the given data, we can create two equations:

Monday: 6x + 5y = 7

Tuesday: 2x + 3y = 3

We can solve this system of equations by elimination or substitution.

Eliminating, we can multiply the second equation by two and subtract it from the first equation:

(6x + 5 y) - 2 (2x + 3y) = 7 - 2 (3)

Simplifying this, we get:

2x - y = 1

Using substitution, we can solve an equation in one variable and replace it with another equation:

From the first equation we can solve for x:  

6x + 5y = 7

6x = 7-5 years

x = (7-5 ​​years) / 6

Substituting this into the second equation, we get:

2 ((7-5 years) / 6) + 3 y = 3

Simplifying this, we get:

7 y = 9

y = 9/7

Now that we know y, we can substitute it back into both equations to solve for x:

6 x + 5 (9/7) = 7

Simplifying this, we get:

x = 2/7

Therefore, Plan A takes 2/7 hours, or approximately 17.14 minutes, and Plan B takes 9/7 hours, or approximately 1 hour and 17.14 minutes.

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Answer:160

formula:y=kx

16=(16)(10)

=160

Step-by-step explanation:

The population of Westville increased by approximately 99.95 people from 2015 to 2016.

To find the increase in population from 2015 to 2016 in Westville, we need to use the formula:

Increase in population = (Population density in 2016 - Population density in 2015) x Land area

First, we need to find the population density in 2016. To do that, we can divide the population of 2,000 people by the land area of 84.4 square miles:

Population density in 2016 = 2,000/84.4 ≈ 23.69 people per square mile

Next, we can plug in the values into the formula:

Increase in population = (23.69 - 22.5) x 84.4 ≈ 99.95 people

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Thus, the area of the given trapezium is found toe be 37.8 sq. cm.

A trapezium is a quadrilateral in two dimensions with one pair of parallel sides. The non-parallel sides of a trapezium are referred to as the trapezium's "legs," while the parallel sides are referred to as its "bases." The length of the legs or the measuring of their angles are used to categorise trapeziums.

Given data:

area of trapezium = 1/2(sum of parallel side) * height

area  of trapezium = 1/2(PQ + CR)*PA

area  of trapezium = 1/2*(3.15 + 6.3)*8

area  of trapezium = 1/2*(9.45)*8

area  of trapezium = 37.8 sq. cm

Thus, the area of the given trapezium is found toe be 37.8 sq. cm.

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The vector (3, 8, 1) provides the system's solution.

As a result, the system's vector solution is (3, 8, 1).

A sort of data structure used in computer programming is the vector. It is a collection of data objects that can be any type, such as strings, numbers, or even other vectors. The storage and manipulation of collections of data elements, such as a list of numbers, words, or other data elements, is done using vector data structures. Sorting, searching, and data manipulation can all be done with vector data structures.

The matrix equation Axequalsb's augmented matrix for the linear system is as follows:

[tex]\left[\begin{array}{ccc}1&-2&4\\7&-4&3\\-6&2&5\\-3&16&-29\end{array}\right][/tex]

Part - 2:

Step 1: Write the system's solution as a vector after solving it.

We must first reduce the augmented matrix to its reduced row-echelon form in order to solve this system.

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\-5&2&0\\-3&8&1\end{array}\right][/tex]

Step 2: We can now quickly find solutions for the unknowns.

[tex]x_1[/tex] equals

3

[tex]x_2[/tex] equals

8

[tex]x_3[/tex] equals

1

Step 3:

The vector (3, 8, 1) provides the system's solution.

As a result, the system's vector solution is (3, 8, 1).

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The property of equality that the statement m(n-p) = mn - mp illustrates is (d) the distributive property

Given that

m(n-p) = mn - mp

The above property is the distributive property

The distributive property states that

a(b - c) = ab - ac

This case

a = m

b = n

p = c

Substitute the known values in the above equation, so, we have the following representation

m(n-p) = mn - mp

Hence, the property of equality that the statement illustrates is the distributive property

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To graph the two lines, we can plot two points on each line and connect them with a straight line. For y = 3x + 2, we can choose x = 0 and x = 1 to get the points (0, 2) and (1, 5), respectively. For y = x - 2, we can choose x = 0 and x = 1 to get the points (0, -2) and (1, -1), respectively.

In the graph: The red line represents y=3x+2 and the blue line represents y=x-2

Explain the term straight line

A straight line is a geometric figure that extends infinitely in both directions and has no curvature or bends. It is the shortest distance between two points and can be described using various mathematical equations, such as y = mx + b, where m is the slope and b is the y-intercept. Straight lines are used in various fields, including geometry, physics, and engineering, to represent and analyze the relationships between objects or points.

According to the given information

To graph the system of equations y = 3x + 2 and y = x - 2, we can plot the two lines on the same coordinate plane and find the point where they intersect.

First, we can find the point of intersection by setting the two equations equal to each other:

3x + 2 = x - 2

Simplifying, we get:

2x = -4

x = -2

Substituting this value of x back into one of the equations, we get:

y = (-2) - 2 = -4

So the solution to the system of equations is the point (-2, -4).

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