Doug has 8 square pieces of wood. Each piece of wood has a side length of s centimeters. The total area of all eight pieces of wood is 200 square centimeters. Create a quadratic equation Dounfg can use to find the side length of each piece of wood.

Answer:

2.44

Step-by-step explanation:

Answer:

The Correct answer is C

y>7

Answer:9/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

3 x 3/8 = 1 1/8

The equation we need to solve to find the width of the rectangular frame is 9x² + 42x - 120 = 0.

Finding the factors of a polynomial statement is the process of factoring in algebra. A term or expression that, when multiplied by another term or expression, yields the original polynomial is referred to as a factor. In algebra, factoring is helpful because it makes equations simpler and easier to answer. For instance, if the equation x square - 4 = 0 is provided, it can be factored as (x + 2)(x - 2) = 0, and the zero product property can then be used to find x. Calculus uses factoring extensively to determine the roots of functions and to make complex equations simpler.

The area of the rectangle is given as:

A = lw

Now, for the given expression of length and breadth we have:

(3x + 8)(3x + 6) = 168

Thus,

9x² + 42x + 48 = 168

9x² + 42x - 120 = 0

Hence, the equation we need to solve to find the width of the rectangular frame is 9x² + 42x - 120 = 0.

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We can expect to ask about 2-3 students before finding someone who prefers a salad for lunch, on average.

Calculating the possibility or probability that a specific event will occur uses the concept of probability.

It is a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the event.

Fractions, decimals, and percentages can all be used to express probabilities.

Assuming that each student's preference for lunch is independent of the others, the probability of any given student preferring a salad is 20% or 0.2.

The probability of the first student you ask preferring a salad is 0.2. If they don't prefer a salad, you move on to the next student.

The probability of the second student preferring a salad, given that the first student didn't, is also 0.2. The probability of neither of the first two students preferring a salad is (1-0.2) × (1-0.2) = 0.64.

In general, the probability of the nth student preferring a salad, given that none of the previous n-1 students did, is also 0.2. The probability of none of the first n-1 students preferring a salad is (1-0.2)ⁿ-¹.

So the expected number of students you must ask before finding someone who prefers a salad is:

E(x) = 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ...

This is an infinite series, but we can approximate it by truncating it after a certain number of terms. Let's say we stop after 10 terms:

E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2)

E(x) ≈ 2.48

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Answer:1/10

Step-by-step explanation:

In order to solve this, you need to read the question carefully. If you have 1 whole divided into 10 equal parts you need to divide 1 by 10.

The visualization for this is 1 ÷ 10, which translates to 1/10

A tip to remember is that ÷ looks a bit like a fraction with the numbers replaced with dots!

The probability of selecting no Republicans is approximately 0.2102, or about 21.02%.

What is probability?

Probability is a measure of the likelihood of an event occurring.

There are a total of 22 members in the group, consisting of 10 Democrats, 9 Republicans, and 3 Independents.

To find the probability of selecting no Republicans, we need to consider the possible ways in which two members can be selected without any Republicans being chosen.

There are two cases to consider:

The first person selected is not a Republican, and the second person selected is also not a Republican.

The first person selected is a Republican, and the second person selected is not a Republican.

Case 1: The probability of selecting a non-Republican member on the first draw is (10 + 3)/22, since there are 10 Democrats and 3 Independents out of 22 members. After the first member is selected, there are 21 members left, including 9 Republicans. The probability of selecting another non-Republican member on the second draw is (10 + 3 - 1)/(22 - 1), since there is one fewer member in the group after the first draw. Therefore, the probability of selecting no Republicans in this case is:

(10 + 3)/22 * (10 + 3 - 1)/(22 - 1) = 13/77

Case 2: The probability of selecting a Republican member on the first draw is 9/22, since there are 9 Republicans out of 22 members. After the first member is selected, there are 21 members left, including 10 Democrats and 3 Independents. The probability of selecting a non-Republican member on the second draw is (10 + 3)/(22 - 1), since there is one fewer member in the group after the first draw and we cannot select the Republican member again. Therefore, the probability of selecting no Republicans in this case is:

9/22 * (10 + 3)/(22 - 1) = 27/418

The total probability of selecting no Republicans is the sum of the probabilities in the two cases:

13/77 + 27/418 = 0.2102 (rounded to four decimal places)

Therefore, the probability of selecting no Republicans is approximately 0.2102, or about 21.02%.

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The range of a function refers to the set of all possible output values that the function can produce for its corresponding input values. In this case, the function is:

f(x) = 6x / (x^2 - 9)

To find the range of this function, we need to consider the restrictions on the denominator (x^2 - 9) that would make the function undefined.

The denominator (x^2 - 9) can be factored as a difference of squares:

x^2 - 9 = (x + 3)(x - 3)

So, the function is undefined when the denominator is equal to zero, i.e., when:

(x + 3)(x - 3) = 0

This occurs when x = -3 or x = 3.

Now, we need to consider the behavior of the function as x approaches these values. As x approaches -3 or 3 from the left, the function becomes increasingly negative, and as x approaches -3 or 3 from the right, the function becomes increasingly positive. This is because the numerator (6x) remains constant while the denominator approaches zero, resulting in a very large positive or negative value for f(x).

Since the function can approach arbitrarily large positive or negative values as x approaches -3 or 3, respectively, the range of the function is (-∞, ∞), which represents all real numbers except for the values -3 and 3. In interval notation, the range of the function can be written as:

Range of f(x): (-∞, ∞) \ {-3, 3}

Answer:

invest full 800$

Step-by-step explanation:

I would advise my friend to invest the full $800 in his new IRA. While buying a couple of pairs of sneakers may provide immediate satisfaction, investing in an IRA can have long-term financial benefits.

If we assume an average annual return of 8% for his IRA, then the $800 investment would grow to approximately $4,536 after 30 years. On the other hand, if he only invests $400 and spends the remaining $400 on sneakers, then the investment would only grow to approximately $2,268 after 30 years.

Thus, by investing the full $800, my friend would have a potential gain of over $2,268 compared to if he only invested $400. Furthermore, investing in an IRA can provide tax benefits and potentially reduce his taxable income, providing additional financial benefits.In summary, while it may be tempting to use some of the money for immediate gratification, investing the full $800 in an IRA can provide long-term financial benefits that outweigh the short-term satisfaction of purchasing a couple of pairs of sneakers.

Answer:

4

Step-by-step explanation:

you have to multiply 4 times 4 to get 16.

The total surface area of the given figure is 320 units² respectively.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

The area is a two-dimensional measurement of the size of a flat surface, whereas surface area is a three-dimensional measurement of the exposed surface of a solid object.

The main distinction between area and surface area is this.

So, the surface area of the cylinder: r = 3

[tex]A=\pi rh+2\pi r^{2}[/tex]

Now, calculate:

[tex]A=2\pi 3*10+2\pi 3^{2} \\A=245 units^{2}[/tex]

The surface area of the cone:

[tex]A = \pi r(r=h^{2} +r^{2} )[/tex]

Insert values as follows:

[tex]A=\pi r(3+\sqrt{4^{2} +3^{2} } )\\A=75.39822[/tex]

Rounding off: 75 units²

The total surface area of the given figure: [tex]75+245=320 units^{2}[/tex]

Therefore, the total surface area of the given figure is 320 units² respectively.

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Answer:

Hibah's store developed a leak in the roof during a rainstorm, causing a circular puddle to form on the sales floor. The radius of the puddle increased by 0.1 cm per minute. The rain stopped by 7 am, when the morning shift arrived and discovered the puddle. The employees cleaned up the puddle and placed a bucket under the leak.

I hope that's what your looking for :)

Answer:

  (b)  7 feet

Step-by-step explanation:

You want the width of a fire pit with a volume of 134.4 ft³ if it is 6.4 feet long and 3 feet high.

The volume of the pit is given by ...

  V = LWH

Solving for W, we have ...

  W = V/(LH) . . . . . . . . . divide by the coefficient of W

Then the width needed to give the desired volume is ...

  W = (134.4 ft³)/((6.4 ft)·(3 ft)) = 7 ft

The width needed is 7 feet, choice B.

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The quadratic equation which is as represented in the graph and required to be determined is; y = -(x - 1) (x - 5).

It follows from the task content that the quadratic equation which correctly represents the given graph is to be determined.

Recall from the graph that the zeroes are at; x = 1 and x = 5.

Therefore, the equation will take the form;

y = a (x - 1) (x - 5)

To determine the value of a, the pair of coordinates; (2, 3) is used, where, x = 2 and y = 3.

Therefore, 3 = a (2-1) (2 - 5)

a = 3 / -3; a = -1.

Ultimately, the quadratic equation as required to be determined is; y = -(x - 1) (x - 5).

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Answer: 21/12 =7/4

Step-by-step explanation:

The scale factor is the ratio of the lengths of corresponding sides in the preimage and the image. For example, the length of A'B' is 21 units, and the length of AB is 12 units. Therefore, the scale factor is 21/12 =7/4

The expression (x³y⁴)⁻²/(x⁻²y) is the same as x⁻⁴y⁻⁹

Exponents are a way of expressing the repeated multiplication of a number by itself.

Here are the rules of exponents:

Here we have

The expression (x³y⁴)⁻²/(x⁻²y)  

The above expression can be simplified as follows

Using the above exponent rules

=>  (x³y⁴)⁻²/(x⁻²y)                  

=>  (x³⁽⁻²⁾y⁴⁽⁻²⁾) /(x⁻²y)                 [ By the Power Rule: (aᵇ)ⁿ = aᵇⁿ ]

=>  (x⁻⁶y⁻⁸) /(x⁻²y)              

=>  (x⁻⁶ · x² · y⁻⁸ · y⁻¹)                 [ By the Quotient Rule:  aᵇ / aⁿ = a⁽ᵇ⁻ⁿ⁾ ]

=>  (x⁻⁶⁺² y⁻⁸⁻¹)                           [ By the Product Rule: aᵇ × aⁿ = a⁽ᵇ⁺ⁿ⁾ ]

=>  (x⁻⁴y⁻⁹)  

Therefore,

The expression (x³y⁴)⁻²/(x⁻²y) is the same as x⁻⁴y⁻⁹

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The period of the parent cosine function, y = cos(x) is 1

From the question, we have the following parameters that can be used in our computation:

The parent cosine function, y = cos(x)

For a parent cosine function, y = cos(x), the period is always 1

This is the general rule of the cosine sinusoidal function

Hence, the period of the parent cosine function, y = cos(x) is 1

The graph of the cosine function is added as an attachment

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Answer: 3/100 as a decimal is 0.03.

Step by step explanation: 3 hundredths means 3 out of 100, which can be represented as = 1003 = 0. 03.

Let's use the variables w and l to represent the current ages of the wool and linen tapestries, respectively.

From the problem, we know that:

w = l + 32 (the wool tapestry is 32 years older than the linen tapestry)

w - 20 = 2(l - 20) (twenty years ago, the wool tapestry was twice as old as the linen tapestry)

We can simplify the second equation by distributing the 2:

w - 20 = 2l - 40

Now we can substitute the first equation into the second equation to eliminate w:

(l + 32) - 20 = 2l - 40

Simplifying this equation, we get:

l + 12 = 2l - 40

Adding 40 to both sides:

l + 52 = 2l

Subtracting l from both sides:

l = 52

Now we can use the first equation to find w:

w = l + 32 = 52 + 32 = 84

Therefore, the present age of the wool tapestry is 84 years old, and the present age of the linen tapestry is 52 years old.

So the answer is option (b) 84, 52.

The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

It is a scale among 0 and 1 that represents the probability or likelihood of an event happening. In many disciplines, including statistics, physics, economics, law, and computer science, probability theory is extensively used. Many situations, such as games of chance, weather predictions, medical diagnoses, and more, can be explained using the concept of probability. The mathematical computation of probabilities, the analysis for random variables, and the conclusion-making process are all included in the study of probability.

given

The likelihood that 162 or more kids in a randomly chosen sample of 340 pupils will have received a referral in that particular year can be calculated using the normal distribution.

Calculating the sample proportion is necessary:

The predicted value of p is equal to the 0.34 underlying proportion of referred pupils. It is possible to compute the sample proportion's standard deviation as follows:

P equals sqrt[p(1-p)/n] = sqrt[0.34(1-0.34)/340] = 0.031

Calculate the z-score to determine the likelihood of locating 162 or more kids with referrals:

[tex]z = (0.476 - 0.34) / 0.031 = 4.39[/tex]

The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

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The correct answer is option A: As x decreases in value, y increases in value. As x increases in value, y increases in value.

A mathematical object called a function accepts inputs (often represented by the symbol x) and creates outputs (typically represented by the symbol y or f(x)). An equation can be used to describe a function, although a function is not always defined by an equation.

It may incorporate one or more variables, but it does not always indicate how those variables are related.

For instance, even if the equation 2x + 3 = 7 involves the variable x, it does not define a function.

Given the function starts at (-3, 0) and extends upwards and to the right.

Thus, if x approaches negative infinity, the function cannot take on negative values, so the graph approaches the x-axis but never touches or goes below it.

Hence, the correct answer is option A: As x decreases in value, y increases in value. As x increases in value, y increases in value.

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Answer:

To find the perimeter of the rectangle, we need to add up the lengths of all four sides.

The horizontal sides of the rectangle have a length of 3 - (-1) = 4 units.

The vertical sides of the rectangle have a length of 3 - (-3) = 6 units.

Therefore, the perimeter of the rectangle is:

2(4 units) + 2(6 units) = 8 units + 12 units = 20 units.

Therefore, the perimeter of the rectangle is 20 units. Answer: 20 units.

The perimeter of the rectangle is 20 units.

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

We have,

Using the distance formula, the length of the side between (-1,3) and (3,3).

= √[(3 - (-1))² + (3 - 3)²]

= √16

= 4

Similarly, the length of the side between (3,3) and (3,-3).

= √[(3 - 3)² + (3 - (-3))²]

= √36

= 6

The length of the side between (3,-3) and (-1,-3) is also 4, and the length of the side between (-1,-3) and (-1,3) is 6.

Now,

The perimeter of the rectangle.

= 4 + 6 + 4 + 6

= 20

Thus,

The perimeter of the rectangle is 20 units.

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The height of the kite from the ground when the angle is 50 degrees is 232 feet.

The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.

Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.

To find the height of the kite above the ground we use the trigonometric identity of tangent.

Thus, we have:

tan(50°) = h/200

Now, using cross multiplication:

h = 200 tan(50°) ≈ 232 feet

Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.

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New fixed charge: R80.70 * 1.15 = R92.805

Thato bought 5 items with the following prices and discounts:

Item 1: R100 with a 10% discount

Item 2: R200 with a 5% discount

Item 3: R300 with a 20% discount

Item 4: R400 with no discount

Item 5: R500 with a 15% discount

VAT rate: 15%

3.1.1 Thato bought 5 items.

3.1.2 Calculate the total discount paid on the items that she bought:

Item 1: R100 * 10% = R10

Item 2: R200 * 5% = R10

Item 3: R300 * 20% = R60

Item 4: R400 * 0% = R0

Item 5: R500 * 15% = R75

Total discount: R10 + R10 + R60 + R0 + R75 = R155

3.1.3 Calculate the total including VAT paid on this transaction:

Total price before discount: R100 + R200 + R300 + R400 + R500 = R1500

Total price after discount: R1500 - R155 = R1345

Total VAT: R1345 * 15% = R201.75

Total including VAT: R1345 + R201.75 = R1546.75

Sliding scale for water consumption:

0 - 6 kl: R0/kl

7 - 12 kl: R12/kl

13 - 35 kl: R15/kl

Above 35 kl: R20/kl

Now we can answer the questions:

3.2.1. Calculate the cost if Thato uses 35 kl of water:

7 - 12 kl: 6 kl * R12/kl = R72

13 - 35 kl: 23 kl * R15/kl = R345

Total water consumption cost: R72 + R345 = R417

Total cost including fixed charge: R417 + R80.70 = R497.70

3.2.2 Calculate the new fixed charge if it is increased by 15%:

New fixed charge: R80.70 * 1.15 = R92.805

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On solving the provided question ,we can say that As a result, option C—domain: 4 x 12; range: 44 f(x) 396—is the proper response.

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

The packing expenses in cents for transporting a book with the specified dimensions are represented by the function f(x) = 2.75x2.

Option B is invalid because the minimal value of x is 0 and the base of the cuboid cannot be negative.

The cuboid's measurements in the diagram also imply that its base length ranges from 4 to 12 inches, hence the function's domain is 4 x 12.

At x = 4, where f(4) = 2.75(4)2 = 44, and x = 12, where f(12) = 2.75(12)2 = 396, f(x) has its minimum and maximum values, respectively. As a result, the function's range is 44 f(x) 396.

As a result, option C—domain: 4 x 12; range: 44 f(x) 396—is the proper response.

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Answer: 36 m²

Step-by-step explanation:

A = bh

b=4

h=9

A=(4)(9) =36 m²

i. The second angle that will make the 2 angles complementary is 33^o.

ii. The second angle that will make the 2 angles supplementary is 123^o.

Complementary angles are measure of given angles whose addition gives a right angle i.e 90^o. While two or more angles are supplementary when their addition produces 180^o.

a. To find the second angle that will make the 2 angles complementary, we have;

let the second angle be represented by x, then;

x + 57 = 90

x = 90 - 57

  = 33

x = 33^o

b. To find the second angle that will make the 2 angles supplementary, we have;

let the second angle  be represented by y; so that;

y + 57 = 180

y = 180 - 57

  = 123

y = 123^o

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