Correct each of the following errors by circling the error, describing what is wrong, entering what should be there instead, and entering the correct answer.

1. (3x²)(-2x⁴)=3(-2)x²•⁴=6x⁸

2. 4a²•3a⁵=(4+3)a²+⁵=7a⁷

3. x⁶•x•x³=x⁶+³=x⁹

4. 3⁴•2³=6⁴+³

The total volume of compost required for 16 bowls is 67,493.33 cm³

The total weight of compost required for 16 bowls is 155,906.67 gm

The total amount of polythene required for 16 bowls is: 6400π cm²

(i) The volume of compost required per bowl can be calculated as follows:

V = (4/3)πr^3, where r is the radius of the sphere

The radius of each bowl can be calculated as:

r = (d/2) - t, where d is the diameter (21 cm) and t is the thickness (0.5 cm)

So, r = (21/2) - 0.5 = 10 cm

Plugging the value of r into the formula for volume:

V = (4/3)πr^3 = (4/3)π * 10^3 = 4186.67 cm³

The total volume of compost required for 16 bowls is:

16 * 4186.67 = 67,493.33 cm³

The total weight of compost required for 16 bowls is:

67,493.33 cm³ * 2.31 gm/cm³ = 155,906.67 gm

(ii) To find the total amount of polythene required to cover the outer surface of 16 bowls, we first need to calculate the surface area of one bowl.

The surface area of a sphere can be calculated as follows:

A = 4πr^2

Plugging the value of r into the formula for surface area:

A = 4πr^2 = 4π * 10^2 = 400π cm²

The total amount of polythene required for 16 bowls is:

16 * 400π cm² = 6400π cm²

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Check the picture below.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad P(\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 2 +8}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies (2~~,~~5)[/tex]

Answer:

Step-by-step explanation:

1/4 is one bow.

1/4 *4 is 1 yard.

mel can make 4 bows.

The statement "The margin of error is a key component of a confidence interval, as it reflects the uncertainty in the estimate due to sampling error." is true

A confidence interval is a range of values that likely contains the true value of a population parameter, such as the mean or proportion. It is created by taking a sample from the population and calculating a point estimate, such as the sample mean or proportion.

To account for this uncertainty, we use the concept of a margin of error, which represents the maximum amount by which the point estimate could be off from the true parameter.

The sample size refers to the number of observations in the sample. The larger the sample size, the more precise the estimate is likely to be, since there is less variability and sampling error.

The level of confidence refers to the degree of certainty that the true parameter lies within the confidence interval. A higher level of confidence means a wider interval, since we need to be more certain that the true parameter is included.

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Answer:

20 + .50M   = 10 + .80M     subtract .50M, 10 from both sides

10  = .30M     divide both sides by .30

10 / .30  = M   =  about 33 + 1/3 miles driven equalize the cost

[Jana used  " -.50M"  in the original set up instead of  " +.50M"   ]

Step-by-step explanation:

Answer:[tex]\sqrt{6}[/tex]

Step-by-step explanation:

The distance between 2 points is given by:

[tex]\sqrt{(x2-x1)+(y2-y1)}[/tex]

Let (6,3) be (x1, y1) and (8,7) (x2,y2).

=[tex]\sqrt{(8-6)+(7-3)}[/tex]

=[tex]\sqrt{2+4}[/tex]

=[tex]\sqrt{6}[/tex]

Hope this helps :)

[tex]\sqrt{p^1^2-16p^6+80}[/tex]

A pic down below is given:

The probability of getting one club and one heart is 0.127.

p= [tex]\frac{13*13*2*1}{52*51}[/tex]=0.1275

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

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Using the equation  [tex]C =a (1 - r)^{t}[/tex] , 179.75 grams will remain after 2 hours

What is Exponential Decay?

Exponential Decay is the process of reducing an amount by a consistent percentage rate over a period of time using the formula [tex]C = a(1-r)^{t}[/tex]

Where a = 480 grams

r = 15.1% = 0.151

t = 2 hours

C = 480(1 - 0.151)^2

C = 480(0.849)^2

C = 346 grams

Therefore, 346 grams will remain after 2 hours

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The fuel consumption per liter of Lilly's car is  12.5 kilometers per liter .

Average mileage The average mileage of a vehicle is the ratio of the distance traveled by the vehicle and the total amount of fuel used for that distance.

You can specify:

where (d) is the distance traveled and (n) is the fuel consumption.

Lily's car consumes 8 liters per 100km. This is your car's mileage or efficiency.

average mileage = 100/8 = 12.5 kilometers per liter

Therefore, the fuel efficiency in kilometers per liter of a Lily car with a fuel efficiency of 8 liters per 100 kilometers is 12.5 kilometers per liter.

Complete Question - Lily’s car has a fuel efficiency of 8 liters per 100 kilometers. What is the fuel efficiency of Lily’s car in kilometers per liter ?

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The twins are 6 years old, and the oldest sister is 13 years old (since they were born seven years after their older sister).

7.3% of women under the age of 35. 6.9% of females aged 35 to 37. 6.8% of women aged 38 to 40 were female. 5.1% of females aged 41 to 42.

Starting out, let's assign some variables.

Let x represent the sister's older sister's age in years.

The twins' age is then x – 7. (since they were born seven years after their older sister).

We are told that the product of the three siblings' ages is 2693 more than the sum of their ages. This can be expressed algebraically as:

x(x - 7)(x - 7) = x + (x - 7) + (x - 7) + 2693

Simplifying this equation gives:

x³ - 21x² + 98x - 2693 = 0

We can see that x = 13 is a root of the equation, since:

13³ - 21(13)² + 98(13) - 2693 = 0

This means that (x - 13) is a factor of the equation.

We can use polynomial division or synthetic division to divide the equation by (x - 13) and obtain a quadratic equation:

x² - 8x + 207 = 0

The solutions of this quadratic equation are:

x = (8 ± sqrt(8² - 4(1)(207))) / 2 = 4 ± sqrt(241)

Since x represents the age of the older sister, which must be a positive integer, the only valid solution is:

x = 13

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Answer:

roughly 88 but 87.9645943005...

Step-by-step explanation:

First, the formula for the circumference of a circle is 2pi(r), so plugging in 14 yards, you get 28pi roughly 88 but for an actual answer 87.9645943005

The cost to wax the floor will be $2,184.03.

What is the area of any geometrical shape?

The area of a geometrical shape is a measurement of the extent of a two-dimensional surface. It is the measure of the amount of space inside the shape, which can be expressed in square units, such as square inches, square feet, or square meters.

Rectangle: area = length x width

Trapezoid: area = ((base1 + base2) / 2) x height

To find the area of the floor, we need to split the shape into two parts: a trapezoid on top and a rectangle on bottom.

The area of the trapezoid is: (33 + 19) / 2 * 14 = 385 square feet

The area of the rectangle is: 33 * 28 = 924 square feet

The total area is: 385 + 924 = 1309 square feet

Multiplying by the cost per square foot, we get:

1309 * 1.67 = 2184.03

Hence, the cost to wax the floor will be $2,184.03.

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A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, we can be multiply two polynomials step by step.

Distribute each term of the first polynomial to every term of the second polynomial.

Combine like terms by adding the coefficients of the terms that have the same variables raised to the same powers.

Simplify the result by arranging the terms in descending order of the exponent of the variable.

For example, let's say you want to multiply (2x + 3) and (x - 4):

(2x + 3) * (x - 4) = 2x * x - 2x * 4 + 3 * x - 3 * 4

Simplify the terms: 2x^2 - 8x + 3x - 12

Combine like terms: 2x^2 - 5x - 12

Therefore, the product of (2x + 3) and (x - 4) is 2x^2 - 5x - 12.

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Answer:

A.   112 units^2

Step-by-step explanation:

64 + 32 + 12 + 4 = 112

Heyy! Johnny Sins back with another answer for yall!

Lets see here....

The perimeter of a rectangle can be found by adding the lengths of all four sides. If the length of the rectangle is three times its width, we can write the expression for the length as 3w. Therefore, the expression for the perimeter would be:

P = 2(width) + 2(length)

P = 2w + 2(3w)

P = 2w + 6w

P = 8w

So the perimeter of the rectangle can be represented by the expression 8w.

___________________________________________________________

Pretty easy huh? Well no worries just give me 5 stars and a thanks. 2 buttons. So simple huh?

Love, Johnny Sins :)

The two points that would lie on the graph of function g are (-2,-12) and (1,30). The solution has been obtained by using functions.

What is a function?

An association between a number of inputs and a single output for each input is known as a function. A function is often written as f(x), where x stands for the input. A function is typically expressed as y = f(x).

We are given that f(x) passes through the points (-2,-4) and (1,10).

So, it means that

For x = -2,  f(-2) = -4

Similarly,

For x = 1, f(1) = 10

We are given g(x) = 3f(x)

So, on substituting the obtained values of f(x) in the g(x) function, we get

For x = -2,

⇒g(-2) = 3f(-2)

⇒g(-2) = 3(-4)

⇒g(-2) = -12

Similarly,

For x = 1,  

⇒g(1) = 3f(1)

⇒g(1) = 3(10)

⇒g(1) = 30

Hence, the two points that would lie on the graph are (-2,-12) and (1,30).

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Question: An exponential function, f, passes through the points (-2,-4) and (1,10). Which two points would lie on the graph of function g if g(x)=3f(x)?

The length of the hypotenuse BC in right  angled triangle ABC is 3.605 units.

A triangle is said to be right angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle. Consequently, other names for this triangle include the right triangle and 90-degree triangle.

In right angle triangle if 90 degree angle is A then

[tex]AB^{2} +AC^{2} = BC^{2}[/tex]

And here length of altitude AB equals to 3 units and length of base  AC equals to 2 units And here length of hypotenuse BC equals to [tex]\sqrt{13}[/tex] units

[tex]AB^{2} +AC^{2} = BC^{2}[/tex]

[tex]3^{2} +2^{2} = \sqrt{13}[/tex]

[tex]\sqrt{13}[/tex]= 3.60555 unit

And here ans [tex]\sqrt{13}[/tex] is already give what we have to do just calculate the value of [tex]\sqrt{13}[/tex] which is = 3.605

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The fractions have values -

4. one-sixth plus five-sixths equals - Option 3 : 1

5. seven twelfths plus two-twelfths equals - Option 1 : 0

6. nine-tenths minus four-tenths equals - Option 4 : 2

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The first fractional statement is -

one-sixth plus five-sixths

The mathematical expression is -

1/6 + 5/6

Since the denominator is same just add the numerator.

(1 + 5) / 6

6/6

1

Therefore, the value is obtained as 1.

The second fractional statement is -

seven twelfths plus two-twelfths

The mathematical expression is -

7/12 + 2/12

Since the denominator is same just add the numerator.

(7 + 2) / 12

9/12

3/4

0.75 ≈ 0

Therefore, the value is obtained as 3/4.

The third fractional statement is -

nine-tenths minus four-tenths

The mathematical expression is -

9/10 - 4/10

Since the denominator is same just subtract the numerator.

(9 - 4) / 10

5/10

2

Therefore, the value is obtained as 2.

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4. Round each fraction to help you estimate the solution for the following equation:

one-sixth plus five-sixths equals

1. 0

2. one half

3. 1

4. 2

5. Round each fraction to help you estimate the solution for the following equation:

seven twelfths plus two-twelfths equals

1. 0

2. one half

3. 1

4. one and one half

6. Round each fraction to help you estimate the solution for the following equation:

nine-tenths minus four-tenths equals

1. one half

2. 1

3. one and one half

4. 2

The scaled dimensions of the kitchen, given the scale and the measurements, is 1. 26 cm x 0. 96 cm

1 meter on the scaled drawing would be 500 meters of the actual kitchen. This means that the scaled length would be:

= 6. 3 / 500

= 0. 0126 meters

The scaled width would be:

= 4. 8 / 500

= 0. 0096 meters

This can be converted to centimeters :

= 0. 0126 x 100 cm per meter

= 1. 26 cm

= 0. 0096 x 100

= 0. 96 cm

The scale dimensions would be:

1. 26 cm x 0. 96 cm

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Answer:

Step-by-step explanation:x=28

The sine, cosine, cosecant, and secant functions have a period 2π;

the tangent and cotangent functions have period π.

The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.

If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. The period is the interval between two occurrences of the wave.

The complete question is-

The sine, cosine, cosecant, and secant functions have period _______; the tangent and cotangent functions have period _______.

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a) The probability that no one reports the loss or theft of their credit cards is 0.0498.

b) The probability that every credit card is lost or stolen is practically zero.

c) The probability that exactly six people report the loss or theft of their cards is 0.1042

d) The probability that at least nine people report the loss or theft of their cards is 0.2142

a. To calculate the probability that no one reports the loss or theft of their credit cards, we can use the Poisson distribution with an average of λ = 0.02% * 15,000 = 3.

The probability that no one reports the loss or theft of their credit cards is:

P(X = 0) = e^(-λ) * (λ^0 / 0!) = e^(-3) * (1 / 1) = 0.0498 or approximately 5%.

b. The probability that every credit card is lost or stolen is:

P(X = 15000) = e^(-λ) * (λ^15000 / 15000!)

Since λ is very small, the probability of all 15000 credit cards being lost or stolen in a month is practically zero.

c. To calculate the probability that six people report the loss or theft of their cards, we again use the Poisson distribution with an average of λ = 3.

The probability that exactly six people report the loss or theft of their cards is:

P(X = 6) = e^(-λ) * (λ^6 / 6!) = e^(-3) * (3^6 / 720) = 0.1042 or approximately 10.4%.

d. To calculate the probability that at least nine people report the loss or theft of their cards, we need to sum the probabilities for X = 9, 10, 11, ..., 15, since there are only 15,000 credit cards in total.

The probability that at least nine people report the loss or theft of their cards is:

P(X >= 9) = Σ(i=9 to 15) P(X = i) = Σ(i=9 to 15) e^(-λ) * (λ^i / i!)

This is a tedious calculation to do by hand, but we can use a calculator or software to find that P(X >= 9) is approximately 0.2142 or 21.42%.

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In the given right angle triangle the measure of tanL, sinL, and cosL is 73.74°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecent/hypotenuse and

tan = opposite/adjacent.

Given, A right-angled triangle has side lengths 7, 24, and 25.

Here, Hypotenuse is 25, Adjacent is 7 and opposite is 24.

Now, tan = opposite/adjacent.

tanL = 24/7.

L = tan⁻¹(24/7).

L = 73.74°.

Similarly,

sinL = 24/25.

L = sin⁻¹(24/25).

L = 73.74°.

And,

cosL = 7/25.

L = cos⁻¹(7/25).

L = 73.74°.

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A 5-card poker hand is dealt from a standard deck of cards and the number of distinct ways are there to form a hand with two pairs are 1326 ways.

To solve this problem, we got to use permutations and the combinations. Given that a 5-card poker hand is dealt from a standard deck of cards  and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.

Here 4 suits with 13 different kinds for each and every suit , so number of total outcomes are 13*4 = 52

Here we use combinations, and given that a 5-card poker hand is dealt from a standard deck of cards  and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.

The number of distinct ways are there to form a hand with two pairs are given by, C(52,2)

(52 * 51) / 2

(26 * 51)

1326 ways

Therefore, the  number of distinct ways are there to form a hand with two pairs are 1326 ways.

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The triangle is scalene triangle as none of the sides of a triangle are equal to each other.

Triangles are classified into three types on the basis of its sides.

Equilateral triangle =  If all sides of a triangle are equal then it is known as equilateral triangle.

Isosceles triangle =  If any two sides of a triangle are equal then it is known as isosceles triangle.

Scalene triangle = If none of the sides of a triangle are equal then it is known as scalene triangle.

The question states that a triangle has side lengths 35cm, 46cm, and 68cm

so, none of the side are equal so the given triangle is scalene triangle

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Answer:

y <= 40

Step-by-step explanation:

Let's call the number of people traveling by van "x", and the number of people buying train tickets "y". We know that the total number of people in the group is 40, so we can write the equation:

x + y = 40

And we also know that the van can hold up to 12 people, so we can write the inequality:

0 <= x <= 12

Now, to find the number of train tickets, we just need to substitute

x = 40 - y into the second inequality:

0 <= 40 - y <= 12

Expanding and solving for y, we get:

0 <= 40 - y <= 12

-40 <= -y <= -28

y >= 28

y <= 40

So the number of train tickets needed (y) is equal to or greater than 28 and equal to or less than 40.

Answer:

Inequality:    12 + x ≤ 40

Solution:   x ≤ 28

Step-by-step explanation:

Let x be the number of train tickets that the group will need.

As the van holds 12 people and the rest will buy train tickets, an expression for the total number of people is:

If the group is up to 40 people then 12 + x will be less than or equal to 40:

Therefore, the inequality that can be used to find the number of train tickets that the group will need is:

To solve the inequality, subtract 12 from both sides:

⇒ 12 + x - 12 ≤ 40 - 12

⇒ x ≤ 28

Therefore the number of train tickets that the group will need is less than or equal to 28 tickets.

The function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Consider the equation :

y = 30.5(0.7)ˣ

Plug in x=0,

y= 30.5(0.7)⁰ = 30.5 *1 = 30.5

The point is (0,30.5)

Similarly, when we plug in x=1 and x=2, we get y=21.35 and y=14.95 respectively

The other 2 points in (x, y) form are (1,21.35) and (2, 14.95)

These points are matching with the points on the graph

So, the function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

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Answer:

y = (4/3)x - 2

Step-by-step explanation:

y intercept is (0, -2)

slope is 4/3

The appropriate measure of variation (spread) for these data is the standard deviation, which is 2.287.

The appropriate measure of variation (spread) for these data is the standard deviation. Standard deviation is a measure of how much the data values vary from the mean (average) of the data set. It is calculated by taking the square root of the variance, which is the average of the squared differences between each data value and the mean.

To calculate the standard deviation for this data set, follow these steps:

1. Find the mean of the data set by adding up all of the data values and dividing by the total number of values. In this case, the mean is (4 + 7 + 2 + 3 + 4 + 2 + 1 + 3 + 9 + 8 + 5 + 1 + 3 + 2 + 3 + 2 + 4 + 3 + 6 + 5) / 20 = 3.65

2. Find the variance by subtracting the mean from each data value, squaring the result, and then finding the average of these squared differences. The variance for this data set is ((4 - 3.65)^2 + (7 - 3.65)^2 + (2 - 3.65)^2 + ... + (6 - 3.65)^2 + (5 - 3.65)^2) / 20 = 5.2275

3. Take the square root of the variance to find the standard deviation. The standard deviation for this data set is sqrt(5.2275) = 2.287

Therefore, the appropriate measure of variation (spread) for these data is the standard deviation, which is 2.287.

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