Your factory makes tires. It costs you $175,000 to pay for the lease each year. The cost to make a tire includes labor and materials, but comes to $53 per tire.
A) Write the equation of the line that represents your annual costs based on how many tires you make. Be sure to label you variables.
B) How many tires do you need to sell to break even if you sell them for $89 per tire.

The required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching to infinity.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
Given expression,

= 3ˣ

put x = 4
= 3⁴ = 81

Now put x = -4
= 3⁻⁴
= 1/3⁴

= 1/81

Since x gets larger as x = 0, 1, 2, 3, and so on 3ˣ get 1, 9, 27, 81 and so on approaching to infinity.

Thus, the required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching infinity.

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The candidates received ;

Person A = 734 votes

Person B = 793 votes

Person C = 798 votes

From the information given, we have that;

Now, substitute the values

Person A + Person B + Person C = 2325

Person B - 59 + Person B + Person + B = 2325

Let Person B = x

x -59 + x + x + 5 = 2325

collect like terms

3x = 2325 +54

Add the like terms

3x = 2379

Make 'x' the subject of formula

x = 2379/3

x = 793 votes

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At the school play, 225 adult tickets were sold.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The number of adult tickets sold be 'x',

Therefore, The number of student tickets would be 'x - 68'.

Therefore, The expression can be formed as,

x + (x - 68) = 382.

2x - 68 = 382.

2x = 450.

x = 225.

So, The number of adult tickets sold is 225.

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Answer:

The fraction 14/16 is greater than 7/8.

Step-by-step explanation:

On solving the provided question, we can say that by fraction, 4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

by fraction

4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.

16/12+9/12+8/12+9/12=42/12=3 and 1/2 cups.

20/3.5=5.7 or 6

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Answer:

50:7

Step-by-step explanation:

You just put ":" in between the numbers requested.

Step-by-step explanation:

answer, verified answer

The probability that their average length is less than 10 inches is; 5.71%

The formula for z-score is;

z = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

x' = 10 inches

μ = 9.7 inches

σ = 1.2 inches

n = 40

Thus;

z = (10 - 9.7)/(1.2/√40)

z = 0.3/0.1897367

z = 1.58

From online p-value from z-score calculator, we have;

P(z < 1.58) = 0.0571 or 5.71%

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The amount of force between two objects 10 mm away from each other is G[tex]m_1m_2[/tex] / 100.

All physical things with mass are drawn to the gravitational force, which can be thought of as an attracting force. It is the known natural force that is by far the weakest.

Given:

Distance = 10 mm

As, the Gravitation force between two objects

F = G[tex]m_1m_2[/tex] / r²

or, F = G[tex]m_1m_2[/tex] / 10²

F = G[tex]m_1m_2[/tex] / 100

Also, the force between two objects decreases as the far they are apart from each other.

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The Question attached is Incomplete/ inappropriate, the Complete Question is

What would be the amount of force between two objects 10 mm away from each other having the [tex]m_1[/tex] and [tex]m_2[/tex]?

The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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Answer:

It would be a little over 2 hours or so since 16:41 is just 4:41.

2 hours and 16 minutes

Step-by-step explanation:

You're welcome.

Translation the graph of the function  [tex]y=f(x)[/tex]a units to the right gives you the function [tex]y=f(x-a)[/tex]

If the graph of the function [tex]f(x)=3^{x}[/tex] is translated 6 units to the right, then the function becomes

[tex]g(x)=f(x-6)=3^{x-6}[/tex]

Answer: correct choice is A

Answer:yo no se como ablar ingles

Step-by-step explanation: perdoname

The US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We can use the formula for the margin of error for a 95% confidence interval:

margin of error = z× (standard deviation / √n)

where z is the z-score for a 95% confidence interval, which is 1.96.

a. The desired margin of error is $0.10:

0.10 = 1.96(0.25 /√n)

√n = 1.96×0.25 / 0.10

√n= 4.9

n = 4.9^2

n = 24.01

So the appropriate sample size for a margin of error of $0.10 is at least 25.

b. The desired margin of error is $0.07:

0.07 = 1.96 (0.25 / √n)

√n = 1.96 × 0.25 / 0.07

√n= 6.97

n = 6.97²

n = 48.53

So the appropriate sample size for a margin of error of $0.07 is at least 49.

c. The desired margin of error is $0.05:

0.05 = 1.96 (0.25 / √n)

√n= 1.96 × 0.25 / 0.05

√n= 9.8

n = 9.8²

n = 96.04

So the appropriate sample size for a margin of error of $0.05 is at least 97.

Therefore, the US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.

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The values of x and y for the parallelogram PQRS are respectively, 2 & 7

Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.

Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.

Given that,

The parallelogram PQRS has diagonals PR and SQ that intersects at T,

T is the midpoint of PR and T is the midpoint of SQ

If T is the midpoint of PR, then PT = TR

Given  PT = y and TR = 3x+1

y = 3x+ 1 _____(i)

Also, If T is the midpoint of SQ, then ST = TQ

Given QT=3y and TS=4x+13

3y = 4x+ 13 ____(ii)

Substitute equation 1 into 2;

3y = 4x+ 13

3(3x+1) = 4x+ 13

open the parenthesis

9x+3 = 4x+13

club like terms

9x-4x = 13-3

5x = 10

x = 10/5

x = 2

Substitute x = 2 into equation 1

From 1; y = 3x+1

y = 3(2)+1

y = 6+1

y = 7

Hence, the values are x = 2 and y = 7

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The complete questions :

Parallelogram PQRS has diagonals PR and SQ that intersect at T find the values of x and y PT=y TR=3x+1 QT=3y TS=4x+13

The equation of line passing through the points (-2, 4) & (4, 2) is :

y = -1/3 x + 6

The value of b = 6

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

To find the equation of the line passing through the two points (-2, 4) and (4, 2), we can use the point-slope form of a line. The point-slope form of a line is given by:

y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is any point on the line.

To find the slope of the line, we can use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the two given points.

Plugging in the values for the given points, we get:

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

m = -2 / 6

m = -1/3

Next, we can use one of the given points to write the equation in point-slope form:

y - 4 = -1/3 (x - (-2))

y - 4 = -1/3 x + 2

y = -1/3 x + 6

This is the equation of the line passing through the two given points (-2, 4) and (4, 2).

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Answer: 50 Cups

Step-by-step explanation:

16 cups in a gallon. so times that by 2, which equals 32. There are four cups in one quart so times 4 by 4 which is 16 and add to 32. 16 + 32 = 48

Two cups in a pint so add 2 to 48 which is 50

Answer:

You will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

Step-by-step explanation:

To convert between gallons, quarts, and pints, we need to use the following conversions:

1 gallon = 4 quarts

1 quart = 2 pints

Here's the step-by-step process to convert the given volume to cups:

Convert gallons to quarts: 2 gallons * 4 quarts/gallon = 8 quarts

Add the number of quarts from step 1 to the number of quarts given: 8 quarts + 4 quarts = 12 quarts

Convert pints to quarts: 1 pint * 1 quart/2 pints = 0.5 quarts

Add the number of quarts from step 3 to the number of quarts from step 2: 12 quarts + 0.5 quarts = 12.5 quarts

Convert quarts to cups: 12.5 quarts * 2 cups/quart = 25 cups

Therefore, you will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.

Answer:

26 kangaroos on the farm
32 goats on the farm

Step-by-step explanation:

To find the number of goats and kangaroos on the farm, we need to determine the number of legs each animal has. Let's say that there are 'g' goats and 'k' kangaroos.

Since each goat has 4 legs, the total number of legs for all the goats is 4g. Similarly, since each kangaroo has 2 legs, the total number of legs for all the kangaroos is 2k.

Adding these two quantities, we have:

4g + 2k = 180

Since each goat has 1 head, the total number of heads for all the goats is g. Similarly, since each kangaroo has 1 head, the total number of heads for all the kangaroos is k.

Adding these two quantities, we have:

g + k = 58

Now, we have two equations and two unknowns. To solve for 'g' and 'k', we can use substitution or elimination method.

Let's use substitution method:

From the second equation, we can find g:

g = 58 - k

Substituting this in the first equation, we get:

4(58 - k) + 2k = 180

Expanding and solving, we get:

232 - 4k + 2k = 180

232 - 2k = 180

-2k = -52

k = 26

So, there are 26 kangaroos on the farm. To find the number of goats, we can use the first equation:

g = 58 - k = 58 - 26 = 32

Therefore, there are 32 goats on the farm.

In these triangles, the largest angle and the largest side have been measured. This means that the two smaller sides and the two smaller angles are proportional to each other. This is known as the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. This means that the two smaller angles and the two smaller sides of the triangle must add up to be larger than the largest angle or side.

The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side. This means that two other inequalities can be written:

a > |c - b| and b > |c - a|,

where |x| is the absolute value of x. This means that the length of each side must be greater than the difference between the other two sides

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The identity to be used here is [ (a - b)² = a² - 2ab + b² ]

First, try to get the given expression in form of terms on the RHS of the above identity

[tex]\qquad \sf  \dashrightarrow \: 4y {}^{2} - 6yz + 9 {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2 {}^{2})( {y}^{2}) - 2(3)(y)(z) + (3 {}^{2} ) {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (3z) {}^{2} [/tex]

[ it's in form of a² - ab + b² now, add and deduct ab here ]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (9z) {}^{2} - (2y)(3z) + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - 2(2y)(3z) + (3z) {}^{2} + (2y)(3z)[/tex]

[ Apply the identity ]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + 6yz[/tex]

[ That's probably the answer, it can't be simplified more ]

To factorize the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex], we can use the quadratic formula.

We have the quadratic expression [tex]\sf\:ax^2 + bx + c \\[/tex], where $$\sf\:a = 4$$, $$\sf\:b = -6y $$, and $$\sf\:c = 9z^2 $$.

The quadratic formula states that for any quadratic equation of the form [tex]\sf\:ax^2 + bx + c = 0 \\[/tex], the solutions for $$\sf\:x $$ can be found using the formula:

[tex]\sf\:x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]

Applying this formula to our quadratic expression, we get:

[tex]\begin{align}\sf\:x &= \frac{-(-6y) \pm \sqrt{(-6y)^2 - 4(4)(9z^2)}}{2(4)} \\ &= \frac{6y \pm \sqrt{36y^2 - 144z^2}}{8} \\ &= \frac{6y \pm \sqrt{36(y^2 - 4z^2)}}{8} \\ &= \frac{6y \pm 6\sqrt{y^2 - 4z^2}}{8} \\ &= \frac{3}{4}y \pm \frac{3}{4}\sqrt{y^2 - 4z^2}\end{align} \\[/tex]

Thus, the factored form of the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex] is [tex]\sf\:(\frac{3}{4}y + \frac{3}{4}\sqrt{y^2 - 4z^2})(\frac{3}{4}y - \frac{3}{4}\sqrt{y^2 - 4z^2}) \\[/tex].

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

✨[tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

Right, Isosceles

Step-by-step explanation:

The little square in the corner means its right angled, so a right triangle. This also means that it cannot be acute or obtuse.

The two hash marks shows two sides are the same. So it is isosceles. This also means it cannot be scalene or equilateral.

The value of x in the triangle is 5 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The perimeter of a triangle is the sum of the whole three sides of the triangle.

Hence,

x + 2x + 3 + x + 9 = 32

4x + 12 = 32

subtract 12 from both sides of the equation

4x + 12 = 32

4x + 12 - 12 = 32 - 12

4x = 20

divide both sides of the equation by 4

x = 20 / 4

x = 5

Therefore,

x = 5

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Answer:

x = 5, y = 1

Step-by-step explanation:

For x :

Substitute y into the equation : 5x + 3 ( -1/5x + 2 ) = 28

Simplify : 22/5x + 6 = 28

Isolate x : x = 5

For y :

Substitute x for 5 : y = -1/5 * 5 + 2

Solve: y = 1

The solution to the question on the equilibrium of the cheese and bagels have been given below

a) If the equilibrium price of cream cheese and the equilibrium quantity of bagels have both risen, this could be caused by a fall in the price of flour, one of the inputs used to produce bagels.

This decrease in the cost of production would cause the supply of bagels to increase, leading to a rightward shift in the supply curve. At the same time, the demand for bagels would increase as consumers substitute away from other breakfast foods and toward bagels, leading to a rightward shift in the demand curve.

These two shifts would result in a higher equilibrium price for cream cheese, since bagels and cream cheese are complements. The increased demand for bagels would lead to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward.

The diagram below illustrates this relationship. The initial equilibrium is at point A, with a price of P1 and a quantity of Q1. After the decrease in the price of flour, the supply curve for bagels shifts rightward to S', and the demand curve for bagels shifts rightward to D'. The new equilibrium is at point B, with a higher price of P2 and a higher quantity of Q2. The increase in the demand for bagels leads to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward to D'''. The new equilibrium for cream cheese is at point C, with a higher price of P3 and a higher quantity of Q3.

b) If the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen, this could be caused by a rise in the price of milk, one of the inputs used to produce cream cheese.

This increase in the cost of production would cause the supply of cream cheese to decrease, leading to a leftward shift in the supply curve. At the same time, the demand for cream cheese would decrease as consumers substitute away from cream cheese and toward other breakfast foods, leading to a leftward shift in the demand curve.

These two shifts would result in a higher price for cream cheese, but a lower quantity of bagels consumed. The decreased demand for cream cheese would lead to a decrease in the demand for bagels, causing the demand curve for bagels to shift leftward.

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The relation is a function only if for element x in Set X, there is only one element in Set Y so, the choice B shows the relation.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

When a relation will be called as a function .

Consider there be a relation R from a set X to a set Y .

Since the relation will be called a function if each element of set X is related to exactly one element in set Y.

which is, an element x in X, there is only one element in Y that x is related to.

Therefore , the correct option is B.

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The value of f(3) is 2.

Option B is the correct answer.

A function has an input and an output with a relationship between them.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 1/4 x [tex]2^x[/tex]

Substitute x = 3.

f(3) = 1/4 x 2³

f(3) = 1/4 x 8

f(3) = 2

Thus,

The value of f(3) is 2.

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Answer:

D

Step-by-step explanation:

ASA = 2 non included angles + 1 included side

by knowing angle c is congruent to angle z we can prove the triangles are congruent by ASA postulate.

The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

AC = XZ

∠ A = ∠ X

Now, To prove the triangles are congruent by ASA , we get;

AC = XZ

∠ A = ∠ X

⇒ ∠ Z = ∠ C

or, ∠ B = ∠ Y

Thus, The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

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Answer:

2nd answer : it is equivalent but not completely factored

Step-by-step explanation:

the "pulling out" of 3 as factor was completely correct.

but

3(x² - 4) can be further factored.

remember :

(a + b)(a - b) = (a² - b²)

therefore,

(x² - 4) = (x + 2)(x - 2)

and then

3(x + 2)(x - 2)

would be a complete factorization.

Answer: B) The expression is equivalent, but is not completely factored

Step-by-step explanation:

Answer: D, 3x+12

Step-by-step explanation: Distributing a number means that you have to multiply the number by all of the numbers inside the parentheses. 3*x is 3x, and 3*4 is 12.  3x+12 is 3x+12.