plications Involving Factoring Polynomials Set up an algebraic equation and then solve. The width of a rectangle is 17 units less than the length. If the area is 60 square units, then find the dimensions of the rectangle. Length: units Width: units

The number of pounds of durian needed to produce 216 pounds of durian-flavored chocolate bars is 50 pounds.

We have,

To determine the amount of durian needed to produce 216 pounds of durian-flavored chocolate bars, we need to calculate the cost and compare it to the budget constraint.

Let's assume x represents the number of pounds of durian needed.

The cost of plain chocolate per pound is $3.50, so the cost of x pounds of plain chocolate is 3.50x dollars.

The cost of durian per pound is $15.75, so the cost of x pounds of durian is 15.75x dollars.

To ensure the cost does not exceed $4.50 per pound, we set up the inequality:

3.50x + 15.75x ≤ 4.50 x 216.

Combining like terms:

19.25x ≤ 972.

Dividing both sides by 19.25:

x ≤ 50.45.

Since we cannot have a fraction of a pound, we round down to the nearest whole number.

Therefore,

The number of pounds of durian needed to produce 216 pounds of durian-flavored chocolate bars is 50 pounds.

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angle = tan⁻¹(2,500 / 31,680)

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

When two rays collide at a given point, an angle is created. Indicated by the symbol is the "angle," also known as the "opening" between these two beams. Many angles, such as 60°, 90°, etc., are usually stated as numbers in degrees.

To find the angle of descent, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle:

tan(angle) = opposite / adjacent

In this case, the opposite side is the change in elevation, which is 2,500 feet, and the adjacent side is the distance traveled, which is 6 miles or 31,680 feet (since 1 mile = 5,280 feet).

So we have:

tan(angle) = 2,500 / 31,680

To solve for the angle, we can take the inverse tangent (or arctangent) of both sides:

angle = tan⁻¹(2,500 / 31,680)

Using a calculator, we get:

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

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The area οf the shaded regiοn will be (area οf bigger rectangle - area οf white rectangle) 5x²+7x-26.

A rectangle is a type οf quadrilateral, which is a fοur-sided pοlygοn. A rectangle has the fοllοwing prοperties:

It has fοur straight sides, which are perpendicular tο each οther (at right angles).

It has fοur right angles (90-degree angles).

Its οppοsite sides are equal in length and parallel tο each οther.

Its diagοnals are equal in length and bisect each οther.

Nοw,

Area οf shaded regiοn= area οf bigger rectangle - area οf white rectangle.

As Area οf rectangle= length × Breadth

then

Area of shaded region [tex]= (3x-4)(2x+2)-(x-3)(x-6)[/tex]

[tex]=6x^2+6x-8x-8 -x^2+6x+3x-18\\=5x^2+7x-26[/tex]

hence,

         The area οf the shaded regiοn will be 5x²+7x-26.

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Answer:

1/9

Step-by-step explanation:

I plugged it into a calculator.

Answer:

Step-by-step explanation:

4 - 2(1) = 2

i'm pretty sure, sorry if its wrong, pls do not report.

how i got it

4 - 2 = 2

2 x 1 = 2

                        4 - 2y = 2

                       4 - 2(1) = 2

Type the second one exactly how i did, don't put a symbol or space, just copy and paste it.

The amount of time each would require working alone is 6 hours for Bill and 4 hours for his father.

To find the time each person would require working alone, we can use the combined work rate formula: 1/t₁ + 1/t₂ = 1/t, where t₁ is the time for Bill's father, t₂ is the time for Bill, and t is the time they take working together.

We are given that t = 2 hours and 24 minutes, or 2.4 hours. We are also told that Bill's father can paint a room in 2 hours less than Bill, so t₁ = t₂ - 2.

Substituting these values into the formula, we get:

1/(t₂ - 2) + 1/t₂ = 1/2.4

Multiplying both sides by 2.4t₂(t₂ - 2) to clear the denominators gives us:

2.4t₂ + 2.4(t₂ - 2) = t₂(t₂ - 2)

Simplifying and rearranging gives us:

2.4t₂ + 2.4t₂ - 4.8 = t₂² - 2t₂

t₂² - 6.8t₂ + 4.8 = 0

Multiply the whole equation by 5 and factor.

5t₂² - 34t₂ + 24 = 0

(5t₂ - 4)(t₂ - 6) = 0

t₂ = -4/5 or t₂ = 6

Since t₂ cannot be less than 2 (because Bill's father takes 2 hours less than Bill), the only valid solution is t₂ = 6. Therefore, Bill would take approximately 6 hours to paint the room alone, and Bill's father would take approximately 4 hours (6 - 2) to paint the room alone.

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Substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.

Pythagorean Theorem is a mathematical formula that states that the square of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the other two sides. It is expressed as a2 + b2 = c2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

The given diagram is a right triangle with two of its sides labeled in inches. To find the length of the third side (d), one must use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, d is the hypotenuse, so d2 = a2 + b2. Therefore, substituting in the given values for a and b, we can solve for d and find that it is approximately 9.48 inches.

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(1) The percentage of males that drive sports cars is 46.43 %.

(2) The percentage of all drivers that are male is 25 %.

(3) The percentage of sports car drivers that are male is 46.43 %.

(4) Yes, question 1 and question 3 are the same.

The percentage of males that drive sports cars is calculated as follows;

= 39 / 84  x 100%

= 46.43 %

The percentage of all drivers that are male is calculated as follows;

= 60 / 240  x 100%

= 25%

The percentage of sports car drivers that are male is calculated as;

= 39 / 84  x  100%

= 46.43 %

Thus, question 1 and question 3 are the same.

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Answer:

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be  the shape is 55 square miles.

Because a triangular has two or more extra sections, it is a polygon. It's shape is a simple rectangle. A triangular shape can only be distinguished from a parallelogram by its sides A, B, and C. A singular plane rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.

Here.

Two triangles with a base of 10 miles and heights of 7 miles and 4 miles can be formed from the composite design.

The following method can be used to determine a triangle's area:

A = (1/2)bh

where A represents area, B represents foundation, and H represents height.

We can calculate each triangle's area using the following formula:

=> Area of 1st triangle

=>  (1/2)(10)(7) = 35 square miles

=> Area of 2nd triangle

=>  (1/2)(10)(4) = 20 square miles

The two triangles' combined regions make up the composite shape's surface area.

55 square miles is the combined shape's area

=>  (35 + 20).

Consequently, the combined size of the two triangles in the shape is 55 square miles.

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The number line is plotted on the graph below

A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.

If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions

It displays information as a series of data points called 'markers' connected by straight line segments

Given data ,

Let the number line be represented by graph A

Now , the points on the graph are

A = { 4 , -3 , 1 }

The opposites of the number points A is given by

A' = { -4 , 3 , -1 }

The values of the sets A and A' are plotted on the line plot graph

Hence , the line plot is solved

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The Euclidean algorithm can be applied to Gaussian integers in the same way it is applied to ordinary integers. In this case, we are given x = 3+2i and y = 2-5i and we need to find q and r such that x = qy + r and d(r) < d(y).

First, we divide x by y to get a quotient and remainder:
x/y = (3+2i)/(2-5i) = (3+2i)(2+5i)/(2-5i)(2+5i) = (16+7i)/29 = 0.551724 + 0.241379i

Since q and r must be Gaussian integers, we round the real and imaginary parts of the quotient to the nearest integer to get q = 1 + 0i = 1.

Next, we multiply q by y and subtract from x to get the remainder:
r = x - qy = (3+2i) - (1)(2-5i) = 1+7i

Finally, we check that d(r) < d(y):
d(r) = 1^2 + 7^2 = 50
d(y) = 2^2 + (-5)^2 = 29

Since d(r) > d(y), we need to adjust our quotient and remainder. We can do this by subtracting 1 from the real part of q and adding y to the remainder:
q = 0 + 0i = 0
r = (1+7i) + (2-5i) = 3+2i

Now, d(r) = 3^2 + 2^2 = 13 < 29 = d(y), so our final answer is q = 0 and r = 3+2i.

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Answer: If you did 100 Joules of work to lift your backpack, then the work you did is equal to the force applied multiplied by the distance lifted. Let's say you lifted the backpack a distance of d meters with a force of F Newtons. Then:

100 J = F x d

Now, if half of everything falls out of your backpack, the force required to lift the backpack will be reduced by half, so the new force required will be F/2. The distance lifted remains the same. So the work done to lift the backpack using half the force is:

Work = (Force x Distance) / 2

= (F x d) / 2

But we know that F x d = 100 J, so we can substitute this in the equation above:

Work = (F x d) / 2

= 100 J / 2

= 50 J

Therefore, the work you will do to lift your backpack the same distance with half the force is 50 Joules.

Step-by-step explanation:

Answer:

A. The number of actual outcomes is 6 (since there are 6 sides to the block).

B. The number of all possible outcomes would be the number of ways the block could land on the table, which is also 6 (since each of the 6 sides is equally likely to face up).

C. The probability that the block will land with either the T, C or R facing up is the probability of landing on any one of those 3 sides. Since there are 3 such sides, and each side is equally likely to face up, the probability is 3/6 or 1/2.

Answer:

11.97 lb

Step-by-step explanation:

To find the force that the rope must exert on the cart to keep it from rolling down the ramp, we need to resolve the forces acting on the cart along the direction of the ramp and perpendicular to the ramp.

First, we resolve the weight of the cart into its components. The weight of the cart acting vertically downwards can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.

The component perpendicular to the ramp is given by:

W_perp = W * cos(theta) = 40lb * cos(15°) = 38.6lb

The component parallel to the ramp is given by:

W_parallel = W * sin(theta) = 40lb * sin(15°) = 10.4lb

where W is the weight of the cart, and theta is the angle of inclination of the ramp.

Next, we resolve the force exerted by the rope into its components. The force exerted by the rope can be resolved into a component perpendicular to the ramp and a component parallel to the ramp.

The component perpendicular to the ramp is given by:

F_perp = F * cos(phi) = F * cos(60°) = 0.5F

The component parallel to the ramp is given by:

F_parallel = F * sin(phi) = F * sin(60°) = 0.87F

where F is the force exerted by the rope, and phi is the angle of inclination of the rope.

To keep the cart from rolling down the ramp, the force exerted by the rope must balance the weight of the cart along the direction of the ramp. That is,

F_parallel = W_parallel

0.87F = 10.4lb

Solving for F, we get:

F = 11.97lb

Therefore, the force that the rope must exert on the cart to keep it from rolling down the ramp is approximately 11.97lb.

P(X = 1) = (50 choose 1) * (0.06)^1 * (0.94)^49 ≈ 0.198

And so on for the other values of X.

An example of independent random variables X and Y such that P(X < Y) = 1 is X = 0 and Y = 1. Since X is always less than Y, the probability that X is less than Y is 1.

The probability of a person ordering both a Quarter Pounder and a Diet Coke is p1*p2 = 0.2*0.3 = 0.06. Since each person orders independently of all others, the number of people ordering both a Quarter Pounder and a Diet Coke follows a binomial distribution with parameters n = 50 and p = 0.06. Therefore, the PMF of X is:

P(X = x) = (50 choose x) * (0.06)^x * (0.94)^(50-x)

for x = 0, 1, ..., 50.

Using the above formula, we can calculate the probability of X taking on any value between 0 and 50. For example, the probability of X = 0 is:

P(X = 0) = (50 choose 0) * (0.06)^0 * (0.94)^50 = 0.94^50 ≈ 0.076

The probability of X = 1 is:

P(X = 1) = (50 choose 1) * (0.06)^1 * (0.94)^49 ≈ 0.198

And so on for the other values of X.

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An equation which Lupe should use include the following: k = 2p/x².

In this exercise, you are required to make "k" the subject of formula in the given mathematical expression by using the following steps.

p = 1/2kx²

By multiplying both sides of the mathematical expression by 2, we have the following:

2p = kx²

By dividing both sides of the mathematical expression by x², we have the following:

k = 2p/x²

In conclusion, we can reasonably infer and logically deduce that the spring constant can be calculated by using k = 2p/x².

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Answer: Here are three specific examples of public health problems that epidemiologists may investigate:

Obesity: Epidemiologists may investigate the causes and risk factors for obesity, as well as the prevalence and trends in obesity rates over time. They may also evaluate the effectiveness of interventions to prevent or treat obesity, such as diet and exercise programs, policy changes, or medical treatments.

Environmental exposures: Epidemiologists may investigate the health effects of exposure to environmental toxins, such as air pollution, lead, or pesticides. They may evaluate the risks associated with exposure to these toxins, identify populations that are particularly vulnerable, and assess the effectiveness of interventions to reduce exposure or mitigate health effects.

Injury prevention: Epidemiologists may investigate the causes and risk factors for injuries, such as motor vehicle crashes, falls, or firearm injuries. They may identify populations that are at higher risk for injuries, evaluate the effectiveness of injury prevention programs or policies, and develop strategies to reduce the incidence or severity of injuries.

Step-by-step explanation:

The solution set of the equation is {0}

A. The values of the variable that make a denominator zero are [tex]x = 3[/tex] and [tex]x = -3[/tex]. This is because when [tex]x = 3[/tex] or [tex]x = -3[/tex], the denominator of the fraction [tex]x^2 - 9[/tex] becomes zero, causing the entire equation to become undefined.

B. To find the solution of the equation, we can first multiply both sides by the common denominator, [tex]x^2 - 9[/tex]:

[tex](5/x+3-3/x-3)(x^2-9) = (5x/x^2-9)(x^2-9)[/tex]

Simplifying and combining like terms, we get:

[tex]5x - 9 - 3x + 9 = 5x[/tex]

[tex]2x = 5x[/tex]

Subtracting [tex]5x[/tex] from both sides, we get:

[tex]-3x = 0[/tex]

Dividing by -3, we find that the solution of the equation is x = 0.

Therefore, the solution set of the equation is {0}.

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Answer:

1st one: (x-7)

2nd: (-x+7)

3rd: (5x+3)

Step-by-step explanation:

1: you subtract like terms so first you do 3x-2x which is x and do -2-5 and get -7 so its (x-7)

2: do 2x-3x and get (-x) and then do 5-(-2) and get 7 so the answer is (-x+7)

3: first do 2x+3x and get 5x and then do 5+(-2) and get 3 so the answer is (5x+3)

Answer:

Step-by-step explanation:

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

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

( 2x + 5 ) + ( 3x - 2 ) = 2x + 5 + 3x - 2 = 5x + 3

Answer:

Both of the shapes correspond with one another.

(For explanation, look to the second image. Brainly would not let me submit that for an unknown reason)

(It is my explanation)

Good luck!

Answer:

go to the y and go all the way down to two i think

a)1.746

b)0.119

To compare the null hypothesis that the population mean of the increase in sales is at least 50 units against the observed mean of 41.3 units, we will use both the critical value approach and the p-value approach.

For the critical value approach, we need to use the standard deviation of 12.2 units as well as the sample size of 20 supermarkets. This gives us a critical value of 1.746. As the observed mean (41.3 units) is less than 1.746 standard deviations away from the mean of 50 units, we can conclude that the null hypothesis cannot be rejected at the 5% level of significance.

For the p-value approach, we will use the same sample size and standard deviation. This gives us a p-value of 0.119, which is greater than the 5% level of significance. Thus, we can also conclude that the null hypothesis cannot be rejected at the 5% level of significance.

It is important to note that we are assuming that the data is normally distributed, and that there is no bias in the sample.

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The graph is shown in the image attached.

To solve an equation by graphing, you need to graph the equation on a coordinate plane and find the points where the graph intersects the x-axis. These points correspond to the solutions of the equation, which are the values of x that make the equation true here.

Therefore, to solve the equation by graphing, we plot the graph, locate the points where the graph intersects the x-axis, and read the solutions from the graph.

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According to the solving  the value of given function h’(5) h’(5) = [2f’(5)g(5)] / g(5)² + f(5) / g(5)²

A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output. Every function has a domain and a codomain, or range. A function is typically represented by the notation f(x), where x represents the input.

To find the value of h’(5), we need to find the derivative of h(x) first. We can use the product rule and the quotient rule to do that:

h(x) = f(x)g(x) + f(x)/g(x)

h’(x) = f’(x)g(x) + f(x)g’(x) + [g(x)f’(x) – f(x)g’(x)] / g(x)² (by the quotient rule)

h’(x) = [f’(x)g(x) + g(x)f’(x)] / g(x)² + [f(x)g’(x) – f(x)g’(x)] / g(x)² + f(x) / g(x)²

h’(x) = [2f’(x)g(x)] / g(x)² + f(x) / g(x)²

Now we can find h’(5) by plugging in x = 5:

h’(5) = [2f’(5)g(5)] / g(5)² + f(5) / g(5)²

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Answer: its D

i suck at explaining but ik its D

B

-6

...................

Answer: Less than three would be like 2 or 1 or any negative number.

Step-by-step explanation: Three munis anything is less than the 3 you had to start with.

Answer: D

Step-by-step explanation: Disregard the $ and solve algebraically.

[tex]4x+36\leq 52[/tex]

[tex]4x\leq 52-36[/tex]

[tex]4x\leq 16[/tex]

[tex]x\leq 4[/tex]

Answer: Choice D is the correct answer :)

Step-by-step explanation:

The expression is not a polynomial, as it's exponent is not an integer number.

An expression represents a polynomial when these following conditions are satisfied:

The exponent for this problem is of [tex]5\sqrt{7}[/tex], which is a non-integer exponent, hence the expression is not a polynomial. Any integer exponent would make the expression in fact represent a polyonomial.

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