HELP

A family is building a firepit for their yard that is shaped like a rectangular prism. They would like for the firepit to have a volume of 134.4 ft3. If they already have the length measured at 6.4 feet and the height at 3 feet, what is the width needed to reach the desired volume? 4 feet 7 feet 67.2 feet 115.2 feet

The longest segment that can be drawn to connect two vertices is 10 cm

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

Represent the smallest length with x

So, we have

SA = 2 * (x(x + 1) + x(x + 2) + (x + 1)(x + 2))

Substitute the known values in the above equation, so, we have the following representation

2 * (x(x + 1) + x(x + 2) + (x + 1)(x + 2)) = 484

So, we have

(x(x + 1) + x(x + 2) + (x + 1)(x + 2)) = 242

When solved using a graph, we have

x = 8

So, we have

Longest edge = 8 + 2

Longest edge = 10

Hence, the longest segment that can be drawn to connect two vertices is 10 cm

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Answer:Whats the question like what am I solving I will answer if i have a problem to solve

Step-by-step explanation:

If the random number is less than the winning probability of 0.0028, the player wins $20 and we add that to the amount variable.

Otherwise, the player loses $1 and we subtract that from the amount variable.

To simulate this scenario in Python.

Here's a possible implementation:

import random

# Set the seed number

random.seed(77)

# Initialize the starting amount and the number of bets

amount = 18

num_bets = 0

# Loop until the player runs out of money

while amount >= 1:

   # Increment the number of bets

   num_bets += 1

   # Check if the player wins

   if random.random() < 0.0028:

       amount += 20 - 1  # The net earnings are $10

          # Otherwise, the player loses $1

   else:

       amount -= 1

# Report the total number of bets

print(f"Total number of bets: {num_bets}")

In this implementation, we use the random module in Python to simulate the outcome of each bet.

We set the seed number to 77 to ensure that the results are reproducible.

We initialize the starting amount to $18 and the number of bets to 0. We then loop until the player runs out of money (i.e., the amount variable is less than $1).

Inside the loop, we increment the number of bets by 1 and simulate the outcome of the bet using random.

random() which returns a random float between 0 and 1.

If the random number is less than the winning probability of 0.0028, the player wins $20 and we add that to the amount variable.

Otherwise, the player loses $1 and we subtract that from the amount variable.

After the loop ends, we print the total number of bets.

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Answer:

Step-by-step explanation:

The Conjugate Roots Theorem states that imaginary roots come in pairs. If -8i is a root of the polynomial, then so is +8i.

If both -8i and +8i are factors, we rewrite them as (x + 8i) and (x - 8i) in factored form. Since imaginary terms aren't accepted, you can FOIL these to get a quadratic with no imaginary terms.

x2 - 8ix + 8ix - 64i2

Simplify. Replace i2 with -1 because √-1 = i

x2 - 64(-1)

x2 + 64

The quadratic x2 + 64 has roots -8i and 8i. You can use the quadratic formula to verify this.

Now, let's tackle the rest of the polynomial. If x2 + 64 is a factor of the polynomial

x4 + 10x3 + 85x2 + 640x + 1344, divide it out to see what is left. I will use long division of polynomials. Note, I am using the square root symbol as a division symbol.

x2 + 10x + 21

x2 + 64 √ (x4 + 10x3 + 85x2 + 640x + 1344)

x4 + 64x2

_____________

10x3 + 21x2

10x3 + 640x

__________

21x2 +1344

21x2 + 1344

___________

0

There is no remainder, meaning x2 + 64 went in evenly. The quotient left when we divide out x2 + 64 from

x4 + 10x3 + 85x2 + 640x + 1344 is x2 + 10x + 21. Factor the quotient to get (x + 7)(x + 3).

x4 + 10x3 + 85x2 + 640x + 1344 = (x2 + 64)(x + 7)(x + 3)

You can check this factored form by FOILing out, and you should get the original polynomial.

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:

2.44

Step-by-step explanation:

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!

Answer:are you trying to solve for R or? sorry if im wrong i have hard time paying attention in math

Step-by-step explanation:

if you are the answer is in exact form its r= 161/24 in decimal form its r=6.7083  and in mixed number form its r= 6 17/24

Answer:

cube.................

According to the given data the z-score corresponding to an IQ score is [tex]2.64[/tex].

A z-score (or standard score) is a measure of how many standard deviations an observation or data point is away from the mean of its distribution.

It is calculated by subtracting the mean of the distribution from the observed value, and then dividing the difference by the standard deviation of the distribution.

Given ; Data in the problem

∴μ[tex]= 99[/tex] , σ[tex]= 11[/tex] , [tex]x = 128[/tex]

so, z - score =( [tex]x -[/tex]μ)/σ

                    [tex]\frac{(128-99)}{11} \\=\frac{29}{11} \\= 2.64[/tex]

Therefore the z-score corresponding to an IQ score of [tex]128[/tex] is approximately  [tex]2.64[/tex]

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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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Answer:

A I'm pretty sure

Step-by-step explanation:

To find the expected value, we need to multiply each possible outcome by its probability and add up the results.The probability of drawing a ball with $1 is 5/10 = 0.5.

The probability of drawing a ball with $2 is 2/10 = 0.2.

The probability of drawing a ball with $30 is 3/10 = 0.3.

The expected value is:

(0.5 * 1) + (0.2 * 2) + (0.3 * 30) = 0.5 + 0.4 + 9 = 9.9

However, the person paid $10 to play, so we need to subtract that from the expected value:9.9 - 10 = -0.1

Therefore, the expected value of this game is -$0.10. Answer choice (A) is correct.

Answer: $9.50

Step-by-step explanation:

The total number of possible outcomes of shirt and pants are

Red shirt and shorts

Red shirt and jeans

Red shirt and slacks

Blue shirt and shorts

Blue shirt and jeans

Blue shirt and slacks

Given data ,

John has one red shirt, one blue shirt, one pair of shorts, one pair of jeans, and a pair of slacks

Now , total number of possible outcomes of shirt and pants are

A = 2 x 3 = 6 outcomes

Red shirt and shorts

Red shirt and jeans

Red shirt and slacks

Blue shirt and shorts

Blue shirt and jeans

Blue shirt and slacks

Hence , the possible outcomes are solved

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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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Using functions, we can find that the given equation is a quadratic equation so, the graph will be a parabola.

Option B is correct.

Simple functions like linear and quadratic functions are simple to graph. The fundamental concept behind graphing functions is to locate the shape, if at all possible. A line would be the graph of a linear function of the type f(x) = axe + b, for instance; a parabola would be the graph of a quadratic function of the form f(x) = ax² + bx + c.

By replacing some random x values into the function, one can locate some spots on it by determining the corresponding y values for each value.

Here in the question,

Given equation will be:

-(x+3)(x + 1)

Solving it we get:

= -x² -x + 3x + 3

= -x² + 2x + 3

So, graph for this function will be a parabola as the function is a quadratic function.

Therefore, the graph of the function will be the 2nd graph. Option B is correct.

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The correct answer is C.  320×pi

What occurs when something is rotated around a pole? What kind of shape is the point closest to the pole making?

Obviously, a circle.

that means rotating the rectangle around the x-axis creates a round object (with the bottom area being a circle).

so, all answers about a prism (rectangular bottom shape) are automatically wrong.

again, just imagine to rotate a small sheet of paper around a pole (the x-axis acts like one in this scenario).

the result is solid with a circular bottom area, and it maintains this shape all the way to the top.

it is a cylinder!

and what is its radius?

well, the outermost point of the rectangle is 8 points away from the x-axis. when we rotate this rectangle, that attribute remains, of course. and every point on the side surface of the resulting cylinder has the same distance from the central x-axis : 8.

so, the radius is 8.

and the volume of a cylinder is

ground area × height = pi×r² × height

in our case

pi×8² × 5 (the width or "height" of the rectangle) = pi×64 × 5 = 320×pi

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Based on the information, we lack credible evidence to assume an association between a student's academic success and if they are either a boarder or day student at a significance level of 0.05.

The statistic for the chi-square test is given as follows:

X² = ∑ [(observed value - expected value)² / expected value]

Through employing a significance level of 0.05, accompanied by 1 degree of freedom (due to two categories and three degrees of performance), the critical value for the chi-square distribution is calculated at 3.84.

The computed chi-square test statistic is measured to be:

X² = [(130-147.43)²/147.43] + [(180-195.57)²/195.57] + [(240-222.57)²/222.57] + [(305-289.43)²/289.43] + [(100-111.43)²/111.43] + [(200-188.57)²/188.57]

X² = 5.61

Given that 5.61 is lower than 3.84, we dismiss the null hypothesis. Ultimately, we lack credible evidence to assume an association between a student's academic success and if they are either a boarder or day student at a significance level of 0.05.

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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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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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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

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:

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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Answer: 36 m²

Step-by-step explanation:

A = bh

b=4

h=9

A=(4)(9) =36 m²

It would take 211 months for the bank account to double in value at a 4.1% APR compounded monthly.

We are going to use the rule of 72 which states that the number of years it takes for an investment to double is approximately equal to 72 divided by the annual interest rate.

The annual interest rate is 4.1% compounded monthly.

Monthly interest rate = 4.1% / 12

Monthly interest rate = 0.0034166667

Now we can use the rule of 72:

Doubling time = 72 / (0.0034166667 x 100)

Doubling time = 210.731705261

Doubling time = 211 months.

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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:

4

Step-by-step explanation:

you have to multiply 4 times 4 to get 16.

In linear equation, 330 will be defective sporting goods.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Based on the given conditions, formulate = 37500 * 77 ÷ 8750

                  Simplify fraction(s)  = 30 * 11

      Calculate the product or quotient: 330

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The complete question is -

A Sporting goods company makes footballs with an alligator logo. Of the 8,750 footballs produced in one week, 77 were defective. If the company produces 37500 footballs in one month , how many do you predict will be defective ?