On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 1, negative 3) and (0, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 3) and (1, negative 3). Everything to the right of the line is shaded.
A school is planning for an addition in some open space next to the current building. The existing building ends at the origin. The graph represents the system of equations that can be used to define the space for the addition. What is the system of equations that matches the graph?

y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1

Answer:

13

Step-by-step explanation:

60 - 47 = 13

a) Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

Compound interest is a method of calculating interest on a principal amount that includes not only the initial principal but also the accumulated interest from previous periods.

a. The formula for periodic deposits, assuming a fixed interest rate and the same amount of deposit made at the end of each period, is:

Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

Where:

A = Financial goal

P = Initial deposit (assumed to be 0 in this case)

r = Annual interest rate (as a decimal)

n = Number of compounding periods per year

t = Time (in years)

Substituting the given values, we have:

Periodic Deposit = (210000 - 0*(1 + 0.035/12\()^{(12\times 13)}\) * (12 / ((1 + 0.035/12\()^{(12\times 13)}\) - 1))

= $543.15 (rounded to the nearest cent)

Therefore, the periodic deposit needed to reach the financial goal of $210000, with a 3.5% annual interest rate compounded monthly over 13 years, is $543.15 at the end of each month.

b. To determine how much of the financial goal comes from deposits and how much comes from interest, we can use the following formula for the future value of an annuity:

FV = P * ((1 + r/n)ⁿᵗ - 1) / (r/n) + A * (1 + r/n)ⁿᵗ

Where:

FV = Future value of the annuity (i.e., the financial goal)

P = Initial deposit

A = Periodic deposit

r, n, t = Same as before

Substituting the given values and solving for P, we have:

P = (210000 - 543.15 * (1 + 0.035/12\()^{(12\times 13)}\) ) * (0.035/12) / ((1 + 0.035/12\()^{(12\times 13)}\) - 1)

= $60305.24 (rounded to the nearest cent)

Therefore, the amount of the financial goal that comes from deposits is $60305.24, and the amount that comes from interest is $210000 - $60305.24 = $149694.76.

Hence,

a) Periodic Deposit = (A - P*(1 + r/n)ⁿᵗ) * (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

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Step-by-step explanation:

m= -4-6/1--9= -1

6=-1(-9)+c

c= -3

y=mx+c

y= -x-3

Answer:

Total Surface Area Atot = 790.331 cm2

Lateral Surface Area Alat = 611 cm2

Top Surface Area Atop = 89.6657 cm2

Bottom Surface Area Abot = 89.6657 cm2

Step-by-step explanation:

The Length AB of the triangle ABC is 31.079m

Area is the total amount of space filled by a flat (2-D) surface or an object's shape.

A planar figure's area is the space that its perimeter encompasses.  Square units like cm²and m² are used to measure area. The area of a form is a two-dimensional quantity.

Area of oblique triangle: S(CAB)=AC*BC*sin(ACB)/2

Substituting the values;

AC=8.4m

S(ΔCAB)=100m²

(∠ACB)=40°

S(ΔCAB)=(8.4×BC×Sin40°)/2

100=(8.4×BC×Sin40°)/2

BC=37.041m

Law of cosines:

AB²=AC²+BC²-2AC×BC×cos(∠ACB)

Substitute  the values,

AC=8.4m, ∠ACB=40 ° , BC=37.041 we get:

AB²=8.4²+37.041²-2×8.4×37.041×cos40°

AB=31.079m

Hence, The Length AB of the triangle ABC is 31.079m.

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When a client who plays tennis is experiencing elbow discomfort and receives a diagnosis of tendinitis, epicondylitis, or tennis elbow, they may exhibit specific symptoms and signs associated with these conditions.

Tendinitis, also known as inflammation of the tendon, is a common diagnosis for tennis players. Symptoms may include pain and tenderness in the outer or inner side of the elbow joint, swelling, and limited range of motion. The pain is typically worsened during activities that involve gripping or twisting motions, such as gripping a tennis racket.

Epicondylitis, specifically lateral epicondylitis or tennis elbow, is characterized by pain and inflammation in the tendons that connect the forearm muscles to the outer side of the elbow. Symptoms typically include pain and tenderness on the outer side of the elbow, weak grip strength, and pain with wrist extension or lifting objects.

Common signs observed in these conditions may include localized swelling, redness, and warmth around the affected area. The client may also experience discomfort during specific movements, such as gripping objects or performing repetitive wrist and forearm motions.

It's important to note that a proper assessment and diagnosis should be made by a healthcare professional to accurately determine the client's condition and develop an appropriate treatment plan.  

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Answer:

4

Step-by-step explanation:

The formula of the area of a triangle is 1/2 times base times height

1/2 .4.2 equals 4

Answer:

2.3 mL

Step-by-step explanation:

This is called finding the volume by displacement. By subtracting the final volume and the initial volume you can determine how much the volume changed when the object was added. That change in voulme represents the volume of the object, so in this case:\

14.5-12.2 = 2.3 mL

The change in the volume of the object is, 2.3 mL.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

An object placed in a graduated cylinder raised the volume from 12.2 mL to 14.5 mL .

Here, An object placed in a graduated cylinder raised the volume from 12.2 mL to 14.5 mL .

Hence, The change in the volume of the object is,

⇒ 14.5 - 12.2 mL

⇒ 2.3 mL

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The function is given by f(x) = (1+x)/x, and the point is a=1.Using the limit formula to compute f'(a):

The formula for the derivative is given by: f'(a) = limh→0 (f(a+h) − f(a))/h

Substituting the given function into the formula and simplifying: f'(a) = limh→0 [f(a+h) − f(a)]/h

= limh→0 [(1+(a+h))/(a+h) - (1+a)/a]/h

= limh→0 [(a+h)/(a(a+h)) - a/(a(a+h))]/h

= limh→0 [((a+h)-a)/a(a+h)]/h

= limh→0 h/a(a+h)

= 1/a

Since a = 1, f'(1) = 1.

The equation for the tangent line at the point x = 1 is given by:

y = f(1) + f'(1)(x-1)

Substituting the given function into the equation, we get: y = f(1) + f'(1)(x-1)

= [(1+1)/1] + 1(x-1)

= 2 + x - 1

= x + 1

Therefore, the equation for the function's tangent line at the point x = 1 is y = x + 1.

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Step-by-step explanation:

that is

sum(2^r) for r=1 to n, plus sum(1/2) for r=1 to n.

and that is

sum(2^r) + n/2 for r=1 to n.

2^r is a geometric sequence with 2 being the common ratio (every new term is created by multiplying the previous term by 2).

and since r is starting at 1, the first term a1 = 2.

the formula for the sum of a finite geometric sequence is

Sn = a1×(1 - r^n) / (1 - r)

with r being the common ratio .

so, in our case

Sn = 2×(1 - 2^n) / (1 - 2)

Sn = (2 - 2^(n+1)) / -1 = 2^(n+1) - 2

and so, in total we get

2^(n+1) - 2 + n/2 = 2^(n+1) + (n - 4)/2

JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Answer:

When you multiply the variables with different exponents, you add. When you multiply an exponent with another exponent, you multiply.

Step-by-step explanation:

Answer above

The sum of 9/10 and 5/6 is 26/15.

The sum of two fractions can be calculated only if the denominator (the bottom number) is the same. Here, in 9/10, 10 is the denominator and in 5/6, 6 is the denominator. To equate two denominators LCM(least common multiple) should be done.

LCM of 10 and 6 is 30.

To convert is to multiply each by the bottom number of the other over the other

9/10 + 5/6

= 9/10×3/3 + 5/6×6/6

=27/30 + 25/30

=52/30

=26/15 or 1 11/15

Therefore, the sum of 9/10 and 5/6 is 26/15 or 1 11/15.

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The sum of 9/10 and 5/6 equals 26/15.

Only if the denominator (the bottom number) is the same can two fractions' total be calculated. In this case, the denominator in 9/10 is 10 and in 5/6 is 6. The LCM (least common multiple) method should be used to equate two denominators.

30 is the LCM of 10 and 6.:

By multiplying each by the bottom number of the other over the other, you may convert.

9/10 + 5/6

= 9/10×3/3 + 5/6×6/6

=27/30 + 25/30

=52/30

=26/15 or 1 11/15

As a result, 9/10 plus 5/6 equals 26/15.

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A shear transformation in R2 is a linear transformation that displaces points in a shape. It is represented by a 2x2 matrix that captures the effects of the transformation. In the case of vertical shear, the matrix will have a non-zero entry in the (1,2) position, indicating the vertical displacement along the y-axis. For the given matrix | 1 k |, | 0 1 |, where k represents the shearing factor, the presence of a non-zero entry in the (1,2) position confirms a vertical shear. This means that the points in the shape will be shifted vertically while preserving their horizontal positions. In contrast, if the non-zero entry were in the (2,1) position, it would indicate a horizontal shear. Shear transformations are useful in various applications, such as computer graphics and image processing, to deform and distort shapes while maintaining their overall structure.

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(a) The profit of the firm at the current employment levels of 25 units of labor and 50 units of capital can be calculated by subtracting the total cost from total revenue.

The total revenue is given by the output multiplied by the market price, which is $2. The total cost is the sum of the wage cost (W) and the rental cost of capital (R), multiplied by their respective quantities.

Profit = Total Revenue - Total Cost

Profit = (Output * Price) - (Wage * Labor + Rental * Capital)

Given that the output is determined by the production function Y = 100K^(1/2) + 40L^(1/2), the profit can be calculated as follows:

Profit = (100K^(1/2) + 40L^(1/2)) * $2 - ($8 * 25 + $10 * 50)

(b) The profit-maximizing quantity of capital for this firm can be determined by setting the marginal revenue product of capital (MRPK) equal to the rental cost of capital (R). MRPK represents the additional revenue generated by employing an additional unit of capital.

MRPK = R

The marginal revenue product of capital can be calculated as the partial derivative of the production function with respect to capital (K), multiplied by the market price (P):

MRPK = (∂Y/∂K) * P

Using the production function Y = 100K^(1/2) + 40L^(1/2), we can calculate the marginal revenue product of capital as follows:

MRPK = (∂Y/∂K) * P = (50K^(-1/2)) * $2

Setting this equal to the rental cost of capital (R) of $10, we have:

(50K^(-1/2)) * $2 = $10

Simplifying the equation, we find:

K^(-1/2) = 1/5

Squaring both sides of the equation, we get:

K = 25

Therefore, the profit-maximizing quantity of capital for this firm is 25 units.

(c) To raise profits, the firm should decrease its capital employment from 50 to 25 units. This is because the profit-maximizing quantity of capital is determined to be 25 units, as calculated in part (b). By employing fewer units of capital, the firm can reduce its rental cost while still maintaining the optimal level of capital for production. As a result, the firm can lower its total cost and increase its profit. Employing more capital beyond the profit-maximizing level would lead to diminishing returns, where the additional costs outweigh the additional revenue generated. Therefore, reducing capital employment to the optimal level of 25 units would be the most favorable decision for the firm to maximize its profits.

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Total number of employee working for four hours per shift for the manager is 2 people.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event. The probability of an event can not be more than the number 1.

The probability of failure of an event is equal to the difference of the 1 to the success of the event.

Here, the manager records the number of hours, X, each employee works on his or her shift and develops the probability distribution below.

Probability Distribution

Hours Worked: X     Probability: P(X)

           3                         0.1

           4                           ?

           5                        0.14

           6                         0.3

           7                        0.36

           8                       0.06

As, the probability of an event can not be more than the number 1. Thus, the sum of all the probabilities will be equal to 1.

Let suppose the probability of people working for four hour is x. Therefore,

\(0.1+x+0.14+0.3+0.36+0.06=1\\x+0.96=1\\x=1-0.96\\x=0.04\)

Now, the total number of people work for the manager is 50. Therefore, total number of people working for 4 hours are,

\(0.04\times50=2\)

Hence, total number of employee working for four hours per shift for the manager is 2 people.

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The length of one side of the box is 10 inches.

Suppose that: The side length of the considered cube is L units.

Then, we get the Volume of that cube = L³ cubic units.

The volume of a cube is of the form V =  L³, where L is the side length.

Given that the shipping box has a volume of 1,000 cubic inches.

Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:

1000 =  L³

Cube root both sides:

L = \(\sqrt[3]{1000}\)

Therefore, each side is 10 inches.

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Answer:

i think its c. srry if im wrong

Step-by-step explanation:

Answer:

A = 8

Step-by-step explanation:

For the equation to have infinitely many solutions , then the terms on both sides must be the same.

Qw require the x- terms on the right side to be 6x

Ax - 2x = 6x ( consider the coefficients )

A - 2 = 6 ( add 2 to both sides )

A = 8

Answer:

$16

Step-by-step explanation:

Given data

Flat Charge= $5

Fee per hour= $10

The expression describing the total cost is

C= 5+10h

For C=$165, we can find h as

165=5+10h

165-5=10h

160=10h

h= 16

Hence the cost per hour would be $16

Rates of increase from slowest to fastest.

Here's the correct order: 1. O(log(n)) 2. O(n) 3. O(n*log(n)) 4. O(n^2) 5. O(2^n) 6. O(n!)

The complexity of an algorithm refers to the amount of time and space resources required to execute it. In other words, it describes how efficient an algorithm is in solving a particular problem.

This order represents the increasing complexity and runtime of the algorithms, starting with the slowest rate of increase and ending with the fastest rate of increase.

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The numbers which are divisible by 3 are countless. We determine it by the divisibility rules.

A number is called divisible by others whenever it is divided properly and   obtain a whole number as an outcome. As example 125 can be divided by 5 and we get the whole number 25 so 125 is said divisible by 5.

On the other hand, 225 cannot be divided by 10 and we get a decimal number. So, 225 is not divisible by 10.

A number is said to be divisible by 3 if the sum of the digits is divided by 3. Suppose we are given two number 308 and 492.

At first, we will sum the digit of each number, 3+0+8 = 11

the sum of the digit of 492 = 4+9+2 = 15

we cannot divide 11 by 3 but 15 is divided by 3. Hence, 492 is divisible by 3.

So, there are countless number which are divisible by 3.

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The statement that is false of quadrilaterals is C. Adjacent angles in a parallelogram are complementary.

In the tapestry of geometrical relationships, adjacent angles within a parallelogram are not bestowed with the nature of complementarity. Rather, they exhibit a distinct quality known as supplementary.

Unlike the enchanting dance of complementary angles, which combine to form a sum of 90 degrees, adjacent angles in a parallelogram intertwine their measures to yield a sum of 180 degrees. The allure of the parallelogram resides in the congruence of its opposite angles, not the complementarity of its adjacent angles.

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The order of the angles from the least measure to greatest measure is ∠HGB, ∠ECD, ∠FGH and ∠GBH. The solution has been obtained by using the properties of angles.

What is an angle?

When two rays or lines share an endpoint, they form an angle, which is a figure in plane geometry.

We are given that CEFH is a parallelogram. We know that the adjacent angles of a parallelogram are supplementary.

So,

⇒∠FEC + ∠HCE = 180°

⇒124° + ∠HCE = 180°

⇒∠HCE = 56°

We know that angles on a straight line form a linear pair.

So,

⇒∠BCH + ∠HCE + ∠ECD = 180°

⇒90° + 56° + ∠ECD = 180°

⇒∠ECD = 34°

We know that the opposite angles of a parallelogram are equal.

So,

⇒∠FEC = ∠FHC

⇒∠FHC = 124°

Now,

⇒∠FHC + ∠FHG = 180°

⇒∠FHG = 56°

Using the angle sum property of triangle, we get

⇒∠FHG + ∠FGH + ∠GFH = 180°

⇒56° + ∠FGH + 87° = 180°

⇒∠FGH = 37°

∠GHB = 124°     (Vertically opposite angles)

∠CHB = 56°     (Vertically opposite angles)

Using the angle sum property of triangle, we get

⇒∠BCH + ∠CHB + ∠HBC = 180°

⇒90° + 56° + ∠HBC = 180°

⇒∠HBC = 34°

∠GBH = 44°    (Straight line angle)

∠HGB = 12°     (Angle sum property of triangle)

Hence, order of the angles from the least measure to greatest measure is ∠HGB, ∠ECD, ∠FGH and ∠GBH.

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=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

--------------

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Answer:

x=6.566084 or x=−1.066084

Step-by-step explanation:

Let's solve your equation step-by-step.

−4

x

−1=

7

2

−x+

3

x

+1

−4

x

+−1=

7

2

+−x+

3

x

+1

Multiply all terms by x and cancel:

−4+−1x=

7x

2

+(−x)(x)+3+1x

−x−4=−x2+

9

2

x+3(Simplify both sides of the equation)

−x−4−(−x2+

9

2

x+3)=−x2+

9

2

x+3−(−x2+

9

2

x+3)(Subtract -x^2+9/2x+3 from both sides)

x2+

−11

2

x−7=0

For this equation: a=1, b=-5.5, c=-7

1x2+−5.5x+−7=0

x=

−b±√b2−4ac

2a

(Use quadratic formula with a=1, b=-5.5, c=-7)

x=

−(−5.5)±√(−5.5)2−4(1)(−7)

2(1)

x=

5.5±√58.25

2

x=6.566084380618436,−1.0660843806184368

Check answers. (Plug them in to make sure they work.)

x=6.566084(Works in original equation)

x=−1.066084(Works in original equation)

Answer:

x=6.566084 or x=−1.066084

Answer:

\(4\sqrt[3]{2}\)

Step-by-step explanation:

\(\sqrt[3]{128} = \sqrt[3]{64 (2)} = 4\sqrt[3]{2}\)

The probability that demand during this period will exceed 25 gallons depends on the distribution of demand.

To calculate the probability of a stockout during the replenishment lead-time, we need to consider the distribution of demand during this period. If the demand follows a known probability distribution, such as the normal distribution, we can use statistical methods to estimate the probability.

First, we need to determine the parameters of the distribution, such as the mean and standard deviation of the demand during the lead-time. Once we have these parameters, we can calculate the probability of demand exceeding 25 gallons using the cumulative distribution function (CDF) of the chosen distribution.

For example, if the demand during lead-time follows a normal distribution with a mean of 20 gallons and a standard deviation of 5 gallons, we can use the normal distribution table or statistical software to find the probability of demand exceeding 25 gallons.

Alternatively, if we have historical data on demand during lead-time, we can use that data to estimate the probability. We can calculate the proportion of instances where the demand exceeded 25 gallons and use this as an estimate of the probability of a stockout during the lead-time.

Overall, the probability of a stockout during replenishment lead-time depends on the distribution of demand and can be determined using statistical techniques or historical data.

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Answer:

12

Step-by-step explanation:

5^2 + x^2 = 13^2

x = 12

Answer:

12

Step-by-step explanation:

Use Pythagorean theorem

\(a^2 +b^2 =c^2\)

c= always hypotenuse/ longest side/ side across from right angle = 13

a= 5

\(5^2+b^2=13^2\)

\(25+b^2=169\)

Subtract 25 from 169

\(b^2= 144\)

Square root both sides

b= 12

--------

it's also a special triangle known as a 5, 12, 13 triangle

Answer:

I don't see any attachement or a picture or anything

Step-by-step explanation:

The answer is D

Answer:

y = ac / (a - b - c)

Step-by-step explanation:

y(a - b) = c(y + a)

Distribute

ay - by = cy + ac

Subtract cy from both sides

ay - by - cy = ac

Factor out y

y(a - b - c) = ac

Divide both sides by (a - b - c)

y = ac / (a - b - c)