the naturally made bath and body store pays $550 a month for rent and utilities. the average cost for its products to be manufactured is about $3.00 an item. if the average price for a product sold in the store is $5.50, what will the break-even point be? let x represent the number of products sold. the break-even point occurs when the cost function equals the revenue function. 550 3.00x

The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z

The linear equation to represent how much Martina collects for one night of stay in her home is:

y = 25 + 10x - 5z

where:

y is the total amount collected in dollars

x is the number of additional guests (besides the first one)

z is the number of hours the guests check out late

This equation represents the flat fee of $25 per night for the first guest, the additional fee of $10 per person per night for additional guests, and the extra fee of $5 per hour for late checkouts.

Therefore, The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z

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Because the temperature is greater, the relative humidity of the atmosphere is higher.

Water vapor is also measured by relative humidity (RH), which is stated as a percentage but RELATIVE to the air's temperature. In plenty of other terms, it is a comparison between the quantity of water vapor that is really present in the air and the maximum amount water vapor that is possible for the air at the current temperature.

By deducting the temperature just on wet-bulb thermometer from of the temperature just on dry-bulb thermometers and utilizing a relative humidity chart, one may determine the relative humidity.

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Answer: [tex]y-1=\frac{1}{4}(x-5)[/tex]

Step-by-step explanation:

The median from vertex [tex]A[/tex] passes through [tex]A[/tex] and the midpoint of [tex]\overline{BC}[/tex].

Using the midpoint formula, the midpoint of [tex]\overline{BC}[/tex] has coordinates [tex]\left(\frac{3+7}{2}, \frac{5-3}{2} \right)=(5, 1)[/tex].

Therefore, we need the equation of the line passing through [tex](-3,-1)[/tex] and [tex](5,1)[/tex].

The slope of this line is [tex]\frac{-1-1}{-3-5}=\frac{1}{4}[/tex].

Using point-slope form, the equation is y[tex]y-1=\frac{1}{4}(x-5)[/tex].

On solving the provided question we can say that in this triangle 6 blocks separate the bus stop from his house.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon.

The graph of the provided data is included below. 10 blocks separate his residence from the park.

His friend's home is 15 blocks away from his home. 9 blocks separate the grocery shop from his home.

The sides are in proportions according to Side-Angle-Side Similarity. Consequently, we calculate a ratio using the corresponding triangles.

= distance from home to friend's home / distance from home to park

= distance from home to grocery / distance from to bus stop

= 15/10 = 9/x

x = 6

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Answer:

His friend's house, grocery store, and his home

Step-by-step explanation:

Had this question on a test and got it right.

Answer:

Step-by-step explanation:

The equation of line passing from point (x1,y1) and having slope m is

y- y1 =m(x- x1)

m=-3, x1=1, y1=-3

y-(-3) = -3(x-1)

y+3=-3(x-1)

y+3=-3x+3

y=-3x

3x+y=0

Answer:

y + 3x = 0

Step-by-step explanation:

The formula for equation of the line is :

y - y1 = m ( x - x1 )

NB: The m is the slope, then use substitution, solve and equate everything to 0

When a 6-sided die is rolled, P(3 or 5) is equal to B. 1/3.

A 6-sided die has six possible outcomes: 1, 2, 3, 4, 5, and 6. To find P(3 or 5) or the probability of rolling a 3 or a 5, we need to add the probabilities of rolling each of those numbers separately and then subtract the probability of rolling both numbers (3 and 5) at the same time to avoid overcounting.

The probability of rolling a specific number on a fair die is 1/6, since there are 6 possible outcomes.

So, P(rolling a 3) = 1/6 and P(rolling a 5) = 1/6

P(3 or 5) = P(rolling a 3) + P(rolling a 5) - P(rolling 3 and 5) = 1/6 + 1/6 - 0 (since rolling 3 and 5 is not possible)

= 2/6 = 1/3

Therefore, the probability of rolling 3 or 5 on a fair 6 sided die is 1/3.

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The probability of 30 random people having weight more than 6000 pounds is 0.3134 or 31.34%.

To find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds, we can use the Central Limit Theorem (CLT) which states that the sum of a large number of independent and identically distributed random variables will tend to be normally distributed, regardless of the underlying distribution of the individual variables.

Since we know the average weight of a passenger (190 pounds) and a reasonable standard deviation (35 pounds), we can use this information to calculate the mean and standard deviation of the total weight of 30 passengers.

The mean weight of 30 passengers is:

30*190 = 5700 pounds

The standard deviation of the weight of 30 passengers is:

sqrt(30)*35 = 59.8076211353316

Now we can use the standard normal distribution table, or z-score formula to find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.

z = (6000-5700)/59.8076211353316

z = 0.50251572

The probability of a z-score being greater than 0.50251572 is 0.3134, this means that there is a 31.34% chance that the total weight of 30 randomly selected passengers will exceed 6000 pounds.

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The probability for an aircraft to experience crosswinds upon takeoff or landing is generally greatest during the months of spring and fall, specifically in March, April, September and October.

During these months, the transition from winter to summer or summer to winter can lead to greater temperature and pressure differences between the air masses, which can create stronger winds. Additionally, these seasons are also associated with increased storm activity, which can also lead to stronger winds.

However, the probability of experiencing crosswinds upon takeoff or landing can also be affected by regional weather patterns and location, and it's always best to consult with local weather forecast and airport meteorological services before planning any flight.

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The smallest possible sum of the two perfect squares is 205.

Now, According to the question:

The data is given as:

The difference between two perfect squares is 133.

Let the 'x' and 'y' be the difference between two perfect squares.

Now,

The difference between two perfect squares is 133.

[tex]x^{2} -y^2=133[/tex]

[tex]-y^2=-x^2+133[/tex]

[tex]y^2=x^{2} -133[/tex]

[tex]y = \sqrt{x^2-133}[/tex]

First integer solution to this equation

x=13, y=6

Sum = [tex]13^2 + 6^2 = 205[/tex]

Hence, The smallest possible sum of the two perfect squares is 205

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Part A:Coefficients in  are 85 and 15.

X represents theatrical shifts, Y represents dog-walking gigs.

Part B: Two phrases, the first of which indicates the amount of money he makes from his work in the theater and the second, from dog-walking. A sum or a deduct sign is used to demarcate each phrase.

Part A: The information we don't know is contained in an expression's variable. In this instance, we don't know how many dog-walking jobs he has in addition to his theater duties. We have 2 variables—x and y—because of this. The variable is multiplied by the coefficient, which is a number. Since there are two variables in this situation, there are two coefficients: 85 and 15.

Part B: A sum or a subtract sign is used to denote the separation of each term in an equation. The terms are the numbers and variables that occur before and after the sum sign because there is only one sum in this situation. 85x and 15y are involved. He initially discloses how much money he makes for each shift at his total annual salary at the theater is determined by multiplying his hourly wage by the number of shifts he works. The second one is the sum of the money he makes from each dog-walking work multiplied by the number of jobs he completes; this is the total amount he makes from the dog-walking jobs.

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Ratio grade 7 is a mathematical concept that involves comparing two or more quantities using a ratio. It is a common part of mathematics curriculums for middle and high school students.

1. A ratio is a comparison of two or more numbers.

2. Ratios can be expressed as a fraction, a decimal, or a percentage.

3. Ratios are used to compare quantities of different kinds and are used to find relationships between them.

4. In grade 7, students will learn about ratios and how to use them to solve various problems. They will also learn about proportionality, rates, and unit rates.

5. Ratios can also be used to compare measurements, such as lengths, weights, and areas.

6. Students will also use ratios to calculate proportions, which can be used to solve problems involving proportional relationships.

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The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides. Since the perimeter is a linear measure, therefore, the unit of the perimeter of rectangle will be in meters, centimeters, inches, feet, etc.

Perimeter of rectangle = 42 cm.

2 × (l + b) = 42

l + b = 21

So l + b = 2 + 19 ; 3+ 18; 4+17; 5+16; 6+ 15 ; 7+14 ; 8+13 ; 9+12; 10 +11:

Area for l × b =  2× 19= 38 sq.cm

Area for second case = 3* 18=54sq.cm

Area for third case = 4* 17=68sq.cm

Area for fourth case = 5* 16=80sq.cm

Area for fifth case = 6* 15=90sq.cm

Area for sixth case =7* 14=98sq.cm

Area for seventh case =8* 13=104sq.cm

Area for eighth case =9* 12=108sq.cm

Area for ninth case =10* 11=110sq.cm

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The value of x is x = 25 and the measure of angle ∠2 = 60°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the transversal line be represented as t

Now , the measure of angles on a straight line = 180°

So , the measure of angle 1 + angle 2 = 180°

The measure of angle 1 = 5x - 5

The measure of angle 2 = 2x + 10

Substituting the values in the equation , we get

5x - 5 + 2x + 10 = 180°

7x + 5 = 180

Subtracting 5 on both sides of the equation , we get

7x = 175

Divide by 7 on both sides of the equation , we get

x = 25

Substitute the value of x in measure of angle 2 , we get

The measure of angle 2 = 2x + 10

The measure of angle 2 = 2 ( 25 ) + 10

The measure of angle 2 = 50 + 10

The measure of angle 2 = 60°

Hence , the measure of angle 2 is 60°

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Answer:

23.8

Step-by-step explanation:

Solve for the missing side, x, by using the pythagorean theorem:

5² + 3² = x²        **(8-5=3)

x² = 25+9 = 34

x = √34 = 5.831

P = sum of all sides = 5 + 5 + 8 + 5.831 = 23.8

On solving the provided question, we can say that the range of the function f(x) = 2(3)x is best described by y > 0.

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.

The range of the function f(x) = 2(3)x is best described by y > 0.

Especially when the constant is e, a function whose value is a constant increased to the power of the argument.

An exponential function is a function with the form, where b is referred to as the base and x can be any real number, if b is any number such that and.

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The amount the  family spend on items other than food and housing is PhP25000 over the time.

You should understand that budget involves the summary of income and expenditure of a person or individual over a period of time

If total expense is $50,000 and the spend 20% on food 30% on housing

Which make is 50% on both hosing and food leaving 50% on other expenses

Which makes half of the total budget

You have to work out 50% of 50000 to get

50/100* $50000 =PhP25000

This therefore means that the family spends PhP25,000 on items other than food and housing

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Complete question

The circle graph represents a family's monthly budget. If the total monthly budget is $50,000,

how much does the family spend on items other than food and housing?

By applying the first derivative of distance with respect to time, it can be concluded that the person is walking 4/3 meters per second.

Instantaneous velocity or rate is the first derivative of distance with respect to time. Mathematically it is written v = ds/dt, where v is the velocity, s is the distance and t is the time.

First, we make a simple drawing using the given information:

The walking person = 2 meters tall

The street light = 8 meters above the ground

The walking rate is constant

The person's shadow lengthening rate = 4/9 meter per second = dy/dt

We want to know the walking rate, dx/dt.

We determine the value of y:

8 / 2 = (x + y) / y

  8y = 2x + 2y

  6y = 2x

    y = x / 3

Then we substitute the value of y into the equation:

dy/dx = d(x/3) / dx

         = 1/3

Finally, we can get the rate dx/dt:

dx/dt = dy/dt * dx/dy

         = 4/9 * 3

         = 4/3

Thus, it can be concluded that the person is walking 4/3 meters per second.

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Answer:

(6-squarre root 8)^2 = 10.058874

On solving the provide question, we can say that by unitary method each person get = 24/14 = 1.7142857143 pounds of beef

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

a group of = 24 people

equally shared  = 14 pounds of ground beef.

each person get = 24/14 = 1.7142857143 pounds of beef

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The lengths of q and r are 2.5 , 2.5 respectively if the perimeter of an isosceles triangle pqr is 9 cm.

A triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.

here, Given that,

The perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm.

the length of side p is 4 cm

Let the lengths of q and r are x and y respectively.

The perimeter of an isosceles triangle  =  (p+2q)

So,

p+2q = 9

4+2q = 9

2q = 9-4

2q = 5

q = 5/2

q = 2.5 cm

Hence , the lengths of q and r are 2.5 , 2.5 cm respectively .

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Answer:

6y - 14

Step-by-step explanation:

simplify the expression

2y - 6 + 4 (y -2)

Distribute the 4 to each term in the parentheses.

2y - 6 + 4y -8

Combine like terms

2y+4y-6-8

6y - 14

Answer:

[tex] \sf \: 6y - 14 [/tex]

Step-by-step explanation:

Given expression,

→ 2y - 6 + 4(y - 2)

Let's simplify the expression,

→ 2y - 6 + 4(y - 2)

→ 2y - 6 + 4(y) - 4(2)

→ 2y - 6 + 4y - 8

→ (2y + 4y) + (-6 - 8)

→ (6y) + (-14)

→ 6y - 14

Hence, the answer is 6y - 14.

Answer: 14.7

Step-by-step explanation:

The remaining interior angle is [tex]135^{\circ}[/tex].

[tex]\frac{x}{\sin 19^{\circ}}=\frac{32}{\sin 135^{\circ}}\\ \\ x=\frac{32 \sin 19^{\circ}}{\sin 135^{\circ}} \\ \\ x \approx 14.7[/tex]

A reasonable prediction for the number of times a Red or Yellow Marble Draws = (7/20) x 180 = 126.

The total number of marbles in the bag is 20 (5 red, 6 blue, 3 green, 4 black, and 2 yellow). Therefore, the probability of drawing a red or yellow marble is 7/20. Applying this probability to the 180 times a marble is drawn and replaced, we can calculate that the number of times a red or yellow marble is likely to be drawn is 126 (7/20 x 180). This can be expressed as a formula as follows: Red or Yellow Marble Draws = (Number of Red and Yellow Marbles / Total Number of Marbles) x Number of Draws. In this case, Red or Yellow Marble Draws = (7/20) x 180 = 126.

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The minimum value of the expression is [tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex], with a, b, and c be positive real numbers.

What is the positive real number?

In mathematics, the set of positive real numbers is the subset of those real numbers that are greater than zero. The non-negative real numbers, also include zero.

We can simplify the expression as follows:

a^2 b^2 c = (ab)^2 c.

Now, we can use the AM-GM inequality to find the minimum value of the expression:

[tex][(ab)^2 c \ge \left(\frac{(ab)^2 + c}{2}\right)^2 = \left(\frac{(ab + c)^2 - 2abc}{4}\right)^2.][/tex]

As the minimum value is achieved when equality holds, we can set the equation to the original expression and simplify it.

[tex][(ab)^2 c \ge \left(\frac{(ab)^2 + c}{2}\right)^2 = \left(\frac{(ab + c)^2 - 2abc}{4}\right)^2.][/tex]

[tex]$a^2b^2c = \frac{(a^2b^2+ 2ab^2c+c^2b^2) - 2abc}{4}$[/tex]

[tex]$4a^2b^2c = (a^2b^2+ 2ab^2c+c^2b^2) - 2abc$[/tex]

4abc = (ab + c)(ab + c) - 2abc

4abc = (ab + c)^2 - 2abc

6abc = (ab + c)^2

so the minimum value is: [tex]$(\frac {(ab+c)^2}{6})^{\frac{1}{2}}$[/tex]

[tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex]

Hence, the minimum value of the expression is [tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex], with a, b, and c be positive real numbers.

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The line which passes through the points (2,-1) and (4,-1) has the slope-intercept equation as y = -1.

What is the slope-intercept form?

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

The line passes through point (x1,y1) = (2,-1) and (x2,y2) = (4,-1)

The formula to find slope is -

m = (y2-y1)/(x2-x1)

m = (-1+1)/(4-2)

m = 0/2

m = 0

Now use the slope and point (2,-1) to find the y-intercept.

y = mx + b

-1 = 0(2) + b

-1 = 0 + b

b = -1

Write the equation in slope-intercept form as -

y = mx + b

y = 0x + (-1)

y = -1

Therefore, the equation is obtained as y = -1.

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Answer:

Step-by-step explanation:

A polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 1, 3 is (x- -2)(x-1)(x-3) = x^3 - 6x^2 + 11x - 6

The value of 'x' for the given co exterior angles for the parallel lines PQ ans SR is found as: x = 30.

For the stated question:

(x + 12) + (3x + 48) = 180  (co exterior angles are supplementary)

4x + 60 = 180

4x = 180 - 60

4x = 120

x = 30

Thus, the value of 'x' for the given co exterior angles for the parallel lines PQ ans SR is found as: x = 30.

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All of the conditions for inference are met, so it is appropriate to construct a 99% confidence interval for the true proportion of all magazine subscribers who do not read the magazine they subscribe to.

Random sample: The sample of 100 magazine subscribers was selected randomly, so this condition is met.

10% condition: The sample size is 100, which is less than 10% of the population of all magazine subscribers, so this condition is met.

Large counts condition: To check the large counts condition, we need to calculate the expected number of subscribers who do not read the magazine they subscribe to, which is n × p = 100 × 0.38 = 38. Since this number is greater than 5, the large counts condition is met.

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Answer:

Random condition:

✔ met

10% condition:

✔ met

Large counts condition:

✔ met

Are the conditions for inference met?

✔ yes

These identities are not true and cannot be derived from the first identity.

What is trignomentry ?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of angles and circles, and to solve problems involving geometric shapes and measurements. Trigonometry is used in many fields such as physics, engineering, and navigation.

The statement "sin 0 + cos 0 = 1" is a correct foundational trigonometric identity. However, it is not possible to derive the identities "1+cot^2(0) = csc^2(0)" or "tan^2(0)+1 = sec^2(0)" by dividing through by cot^2(0) or by tan^2(0) respectively. These identities are not true, and are not a direct consequence of the first identity.

These identities are not true and cannot be derived from the first identity.

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A function f for f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3.

An easy definition of a function?

As a set of inputs with one output for each, a function is defined as a relationship between them.

              A function, expressed simply, is an association between inputs where each input is connected to one and only one output.

when it says something like f(1) = 0 it means that when x = 1, y = 0

so we know one point on the graph is (0,0)

when it says something like f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3

here is a picture of the tangent lines, then what a sketch of the function would be.

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