A board is 71 cm in length and must be cut so that one piece is 15 cm longer than the other piece. Find the length of each piece. Round your answers to the
nearest centimeter, if necessary.

For equation B → 2A, the rate of reaction becomes:

-Δ[B]/Δt = (1/2) Δ[A]/Δt

Correct option: c

The rate of reaction may be defined as the change in concentration of any of the products or reactants per unit of time. The pace at which reactants change into products is known as the rate of reaction or reaction rate. It goes without saying that the pace at which chemical reactions take place varies greatly.

The given reaction is:

B → 2A

rate of reaction in terms of A:

rate = (1/2) d[A]/dt

rate of reaction in terms of B:

rate = -d[B]/dt

So,

rate = -d[B]/dt = (1/2) d[A]/dt

Correct option: c

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Answer:

Graphical form: Ax-b=4 simplifies to Ax-b-4=0

Text form: Ax-b=4 simplifies to Ax-b-4=0

Cartoon (animation) form: simplify_cartoon%28+Ax-b=4+%29

For tutors: simplify_cartoon( Ax-b=4 )

Step-by-step explanation:

A person who has owned a Roth IRA for five years may withdraw money from the account to buy their first home. The individual has to meet certain requirements and can't withdraw more than $10,000 per person.

A Roth IRA is a type of individual retirement account that allows for tax-free withdrawals of contributions at any time, without penalty or taxes. After five years of ownership, a person who has a Roth IRA may withdraw money from the account to buy their first home. This withdrawal is known as a "first-time homebuyer distribution."

However, there are certain rules and limitations to be aware of when withdrawing money from a Roth IRA for a first home purchase. The individual must be a first-time homebuyer, defined as someone who has not owned a home in the past two years. Additionally, the maximum amount that can be withdrawn for a first home purchase is $10,000 per person.

It's important to note that while contributions to a Roth IRA can be withdrawn tax-free and without penalty, earnings on those contributions may be subject to taxes and penalties if withdrawn before age 59 and a half.

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Option C) The given set of data is distributed as 3,3,5,4,3,2, 5,6,5 ther are 2 peeks showing that the data si bimodally distributed.

A function called data distribution identifies all potential values for a variable and assesses its relative frequency (probability of how often they occur). Any population with dispersed data is referred to as a distribution.

Being monomodal refers to having a one mode. In mathematics, unimodality more broadly refers to the existence of only one greatest value that is somehow specified.

Two modes comprise a bimodal distribution. In other words, two processes with distinct distributions' results are combined into a single collection of data. The distribution sometimes goes by the name "double-peaked." For instance, consider the distribution of data for two production shifts in a manufacturing facility.

The given set of data is distributed as 3,3,5,4,3,2, 5,6,5 ther are 2 peeks showing that the data si bimodally distributed.

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The length of b1 is given as follows:

b1 = 5 units.

The area of a trapezoid is obtained adding the bases, multiplying by the height, and dividing by 2.

For the trapezoid in this problem, the parameters are given as follows:

Hence the length of b1 is obtained as follows:

3(3 + b1)/2 = 12

9 + 3b1 = 24

3b1 = 15

b1 = 15/3

b1 = 5 units.

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Answer:

Step-by-step explanation:

In this case, the median would be a better measure of the center than the mean. The median is the value in the middle of a set of data when the values are arranged in order from least to greatest. In this case, there are 60 households, so the 31st household would be the median. Since 29 houses are worth $280,000 and one house is worth $2,500,000, the 31st house must be worth $315,000.

The mean, on the other hand, is calculated by adding up all the values and dividing by the number of values. The mean in this case would be significantly influenced by the one high-value household worth $2,500,000, leading to an estimate of the center that is much higher than the other values. In this situation, the median provides a better representation of the "typical" value among the majority of the households.

Answer:

  P(x) = x²(x +1)(x -2)²

Step-by-step explanation:

You want the 5th degree polynomial with leading coefficient 1 that has roots of 0 and 3, each with multiplicity 2, and a root of -1.

You recall that a polynomial with root p has (x -p) as a factor. A root that is repeated m times has multiplicity m.

You recall that an exponent is used to signify the number of times a factor is repeated.

The factored form of P(x) is then ...

  P(x) = (x -2)²(x -0)²(x -(-1)) . . . . . roots 2 and 0 repeated twice, root -1

  P(x) = x²(x +1)(x -2)²

__

Additional comment

If you like, you can multiply it out and collect terms. The result will be ...

  P(x) = x⁵ -3x⁴ +4x²

From the Venn diagram, the values that come under set A are A = { h,p,d,t,x }.

The area of mathematical logic known as set theory examines sets, which are essentially collections of objects. Set theory is a branch of mathematics that primarily deals with objects that are pertinent to mathematics as a whole, despite the fact that any kind of object can be gathered into a set.

Given that the Venn diagram consists of the values for set A and set B. The values which come under set A of the Venn diagram can be written as below,

A = { h,p,d,t,x }.

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Discrete values are the data values which are quantitative and the number of values is finite or countable.

What is discrete data?

In a count involving integers, there are only a finite number of potential values. It is impossible to break this kind of data into separate components. Discrete data consists of discrete variables that are non-negative, finite, numerical, and countable.

We are given interval, discrete, categorical and continuous values.

Of these, we need to find that which type of data values are quantitative and the number of values is finite or countable.

Interval data is quantitative but not countable because interval can range from infinity to infinity.

Discrete data is both quantitative and countable.

Categorical data is qualitative and not quantitative.

Continuous data is quantitative but not finite.

Hence, discrete values are the data values which are quantitative and the number of values is finite or countable.

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The relationship is not a function.

What is Function?

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given that,

A mapping diagram represents a relationship that contains three different input values and four different output values.

Let A be the set of input values and B be the set of output values.

Number of elements in A = 3

Number of elements in B = 4

This means that 3 elements in A has four elements as image in B.

Thus, an element in A must have two different images in B.

But by the definition of functions, there can't be more than one image for an element in set A.

Hence the given relationship is not a function.

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The total surface area of the triangular pyramid is 936 cm²

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The surface area of the triangular prism is the sum of the individual area of the surface. Hence:

Surface area = (0.5 * 24 cm * 18 cm) + (0.5 * 24 cm * 18 cm) + (24 cm * 7 cm) + (18 cm * 7 cm) + (30 cm * 7 cm) = 936 cm²

The total surface area is 936 cm²

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The correlation coefficient r is -0.7642

The equation of least square line is

y = -0.37x + 305.98

Correlation describes the strength of an association between two variables, and is completely symmetrical, the correlation between A and B is the same as the correlation between B and A.

Given,

Games won: 109,119,107,67,79,63,65,90

Batting average: 259,267,264,288,277,288,269,277

calculation is done by calculator and attached below.

Hence, Correlation coefficient is - 0.7642

Least square line:

y = -0.37x + 305.98

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first off let's check how much is 5% of hmmm say "x"

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of x}}{\left( \cfrac{5}{100} \right)x}\implies 0.05x[/tex]

so if we increase "x" by that much, that's just "x + 0.05x" = 1.05x.  Now, let's find how much is 5% of that

[tex]\stackrel{\textit{5\% of 1.05x}}{\left( \cfrac{5}{100} \right)1.05x}\implies (0.05)(1.05x)\implies 0.0525x \\\\\\ \stackrel{\textit{now let's add that, to 1.05x}}{1.05x~~ + ~~0.0525x}\implies 1.1025x[/tex]

so our "x" went up by 0.1025x, now let's conver that to a percent, 0.1025 * 100 = 10.25%.

The equation of the line is y = 4 and the y-coordinate of every point along this line is 4.

The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y-axis, also known as the y -intercept.

Given that, we need to find an equation of a line passing through given points,

Considering two points, (-3, 4) and (1, 4)

We know that, the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by,

(y-y₁) = (y₂ - y₁ / x₂ - x₁)(x-x₁)

Here, (x₁, y₁) and (x₂, y₂) = (-3, 4) and (1, 4)

Therefore, the equation =

y-4 = 4-4 / 1+3(x+3)

y-4 = 0

y = 4

Since, the slope is zero and y-intercept is 4 that mean, the line given is parallel to x-axis,

Hence, all the y coordinates will be 4.

Hence, the equation of the line is y = 4 and the y-coordinate of every point along this line is 4.

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Answer:

A. 5 to 8
B. 13 to 8

Step-by-step explanation:

Answer:

look at the screenshot

Step-by-step explanation:

A permutation is a collection of things where the arrangement is important. In general, a permutation of a set in mathematics is the rearranging of its members into a sequence or linear order if the set already has an ordered structure.

A permutation is a grouping of items where the order is crucial.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order.

The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

Contrasted with combinations, which are selections of a few members of a set independent of order, are permutations.

There are six permutations of the set "1, 2, 3," for instance, represented as tuples: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1).

Therefore, a permutation is a collection of things where the arrangement is important. In general, a permutation of a set in mathematics is the rearranging of its members into a sequence or linear order if the set already has an ordered structure.

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The answer is -6.,  is the slope of the function.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

In order to determine the slope of the function, we have to know about linear function.

In any linear function, we can get its slope using two pairs of coordinates that belong to the linear function.

m=Slope of the linear function.

P1=(x1,y1)=First pair of coordinate.

P2=(x2,y2)=Second pair of coordinate.

In this case, we have many pairs of coordinates, so we choose two of them:

P_1=(-2,8)

P_2=(0,-4)

Then, we replace them in the slope formula:

m = y2-y1/x2-x1

   = -6

Finally, the slope of the function is -6.

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As h decreases, the value of (the change in x^2)/h increases, since 16h gets divided by a smaller value of h. For example, when h=0.1, (the change in x^2)/h = 16/0.1 = 160.

a. If h=1, then (the change in x^2)/h = 16/1 = 16

b. If h=0.1, then (the change in x^2)/h= 16/0.1 = 160

c. If h=0.01, then (the change in x^2)/h= 16/0.01 = 1600

d. If h=0.001, then (the change in x^2)/h= 16/0.001 = 16000

The change in x^2 refers to the difference in the value of x^2 when x is increased from 4 to 4+h. In other words, it is the difference between (4+h)^2 and 4^2. The change in x^2 is 16h, since (4+h)^2 = 16h + 4^2. To find (the change in x^2)/h, we simply divide 16h by h, which gives us 16. So, for each of the values of h given, when x is increased from 4 to 4+h, (the change in x^2)/h is 16. As h decreases, the value of (the change in x^2)/h increases, since 16h gets divided by a smaller value of h. For example, when h=0.1, (the change in x^2)/h = 16/0.1 = 160.

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The most accurate comment about the graph  data is: "China's steel production is increasing while its major competitors' production is declining."

Academics are using graphs to logically chart or graphically depict events or quantities. A graph point is a common way to depict how different things interact. The non-linear storage structure known as a graph is made up of nodes, also referred to as vertices, and lines. Glue ought to be used to connect the edges, also known as nodes , respectively.  (4.5).

Here,

The most accurate comment about the data is: "China's steel production is increasing while its major competitors' production is declining."

This is because the graph shows that China's steel production has been steadily increasing since the early 2000s, while the steel production of other major producers such as Japan, the United States, and Germany has been declining or stagnant. This trend is particularly evident after the global financial crisis of 2008-2009.

While it is true that Japan's steel production has increased and shows no signs of decreasing, this comment does not address the overall trend of declining steel production among major producers.

The other two comments are not accurate. The statement "By 2009, China’s tons of steel produced per US million ($) GDP was 50, about 10 tons less than Japan’s all-time high" is not supported by the graph, as there is no information about tons of steel produced per US million ($) GDP on the graph.

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Answer:

490

Step-by-step explanation:

80/100×the total number= 560

solved for the total number Which is equal 700

700×70% = 490

An interval that will include at least 5/9 of the sample values of wireworm counts obtained is (85,115).

Let us consider a random variable Y which follows the Poisson distribution with parameter λ=100

The Mean of the Poisson distribution of λ(μ)=100

The variance of the Poisson distribution σ²=100

We need to find an interval that will include at least 5/9 of the sample values.

We have the Mean of the Poisson distribution λ=100

The variance of the Poisson distribution is σ²=100

The standard deviation of the Poisson distribution is σ =√100=10

Now, consider Tchebysheff’s rule:

Let X be a random variable with finite expected value and finite non-zero variance then for any real number k > 0,

Pr(|X-μ|≥kσ)=≤1/k².

1-1/k²=5/9

1-5/9=1/k²

4/9=1/k²

k²=9/4

k=1.5

So the interval contains all the values within 1.5 standard deviations from the mean:

μ±1.5(σ)

100±1.5(10)

100±10

(85,115).

Hence, The interval is (85, 115).

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The probability that the scholarship will be awarded to a senior given that it will not be awarded to a freshman is 2/9.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of students = 100

Freshman = 10

Sophomores = 325

Juniors = 30

Seniors = 20

Graduate students = 15

Now,

The probability that the scholarship will be awarded to a senior given that it will not be awarded to a freshman.

This means,

We will subtract the freshman from the total number of students.

So,

Total students = 100 - 10 = 90

Seniors = 20

And,

Probability = 20/90 = 2/9

Thus,

The probability that the scholarship will be awarded to a senior is 2/9.

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Answer:

See below

Step-by-step explanation:

r = 4*2 = 8

q = 4√3

p = q = 4√3

s = √(4√3)^2 + (4√3)^2) = √96 = 4√6

If you purchase 200 shares for $70 a share ($14,000), and after a year the price falls to $60. the percentage return on your investment are:

27.21%,  49.11%, 78.57%.

If the margin requirement was 15%:

Total cost of the investment = $14,000 / (1 - 0.15)

Total cost of the investment = $16,471.43

After a year, Value of the investment =  200 * $60 = $12,000

Percentage return = ( $16,471.43 -12,000 ) / $16,471.43 * 100

Percentage return = 27.21%

If the margin requirement was 40%:

Total cost of the investment = $14,000 / (1 - 0.40)

Total cost of the investment  = $23,529.41

After a year, Value of the investment  =200 * $60 = $12,000

Percentage return = ( $23,529.41 -$12,000 ) / $23,529.41 * 100

Percentage return = 49.11%

If the margin requirement was 75%:

Total cost of the investment = $14,000 / (1 - 0.75)

Total cost of the investment = $56,000

After a year, the value of the investment = 200 * $60 = $12,000

Total cost of the investment =  ($56,000 - $12,000 ) / $56,000 * 100

Total cost of the investment = 78.57%.

Therefore  the percentage return on your investment are:

27.21%,  49.11%, 78.57%.

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The elements listed above that are required for an inverse trig problem to find a missing angle include the following:

A. A right triangle.

D. The length of at least 2 sides.

In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.

Generally speaking, the length of at least two (2) sides is an element that is required for an inverse trig problem in order to find a missing angle in a right angled triangle.

In conclusion, both a right triangle and the length of at least two (2) sides must be provided in order to find a missing angle in a right angled triangle.

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It will take 17 years and 10 months for the investment to grow to $4000.

Compound interest is computed as interest on the principle of an account plus any accrued interest.

Compound interest can be calculated using the following formula:

x = P (1+r/n

,where x = compound interest

P = principal (the initial deposit or loan amount)

r = annual interest rate

n = the number of compounding periods per unit of time

t = the number of time units the money is invested or borrowed for

Given:

Charmaine deposited $2000 into an account with a 3.9% annual interest rate, compounded quarterly.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.9/100

r = 0.039 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(4,000.00/2,000.00) / ( 4 × [ln(1 + 0.039/4)] )

t = ln(4,000.00/2,000.00) / ( 4 × [ln(1 + 0.00975)] )

t = 17.86 years

Hence, the time is 17 years and 10 months.

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Answer:

360

Step-by-step explanation:

If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360°

hope dis helpsssssss

Using the Pythagorean theorem and the Law of Cosines, we can solve for the lengths of each side in right triangle ABC.

The right triangle ABC with right angle at vertex B can be solved using the Pythagorean theorem. The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. In this case, side AC is the hypotenuse and side AB and BC are the two shorter sides.

We can determine the lengths of all three sides using the Pythagorean theorem and the information given. Side AB is equal to the square root of the sum of the squares of sides AC and BC. Since we are given that angle ABC is a right angle, we can determine that side BC is equal to the length of side AB. This means that the length of side AB is equal to the square root of the square of side AC. The length of side AC can be determined by finding the length of the dashed segment BD.

To find the length of dashed segment BD, we can use the Law of Cosines. The Law of Cosines states that in any triangle, the square of the length of a side is equal to the sum of the squares of the other two sides minus twice the product of the other two sides multiplied by the cosine of the angle opposite the side. In this case, we are finding the length of side BD. We can use the angle ABC and side AC to solve for the length of side BD.

Therefore, using the Pythagorean theorem and the Law of Cosines, we can solve for the lengths of each side in right triangle ABC.

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Answer:

1.C

2.D

3.A

4.A

Step-by-step explanation:

1. The negative must be outside to be reflected across the Y axis. Also you can never find the square root of a negative number

2.Its D because when you move to the right, you subtract on the inside. doing it outside would move it down

3. As I said in "2" to move up or down you have to keep the number outside. In this case it was down 3 so -3 ouside of the square root.

4. This is a combination of the two so right 4 and 4 four translates to -4 on the inside and -4 on the outside.

Hope it helps!