5x - 4y = 27; - 2x + y = 3

The equation of a circle whose center is at the origin and passes through (7, 8) is x² + y² = 113

Circle is a round geometry whose all points constitute form a path having a constant distance (radius) from a fixed point (center of the circle).

The standard form for the equation of a circle is (x − h)² + (y − k)² = r², where (h,k) is the center of the circle, and r is the radius.

Center = (h,k) = (0,0)

Point = (7,8)

Now we input those values into the equation:

(x − h)² + (y − k)² = r²

(x − 0)² + (y − 0)² = r²

x² + y² = r²

Next, we have to determine the radius. It can be done by applying Pythagoras' Theorem. Look at the picture:

x² + y² = r²

7² + 8² = r²

49 + 64 = r²

113 = r²

Then we go back to the previous equation, and we get:

x² + y² = r²

x² + y² = 113

Thus, the equation of a circle whose center is at the origin and passes through (7, 8) is x² + y² = 113

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The graph shows a maximum wolf population size of 500 individuals, which occurred in 2017.

The graph depicts the magnitude of the wolf population in a certain location during the previous 25 years. The population size is shown to have changed over time, with the peak population count of 500 people happening in the year 2017. A population size of 450 people, which is a little less than the highest population level, was then reached in 2018. The year 2000 saw the lowest population size, with only 200 people living there. In 2017, there were 500 people in the population, which had grown considerably over the years. This suggests that over the past 25 years, the wolf population has been growing which occurred in 2017.

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The complete question is

based upon the data presented in the graph, which of the following best identifies the highest wolf population size which occurred in 2017?

Answer: 83 inches

Step-by-step explanation:

1. 12 inches = 1 foot

2. 12x6=72 inches

3. 72+11=83 inches

Answer:

The answers are

False

True

True

Thank you

The type of observational study in the following scenario is considered as prospective study.

A prospective study, also known as a prospective cohort study, is a type of longitudinal study in which researchers follow and watch a group of individuals across time to collect data and track the development of outcomes. A prospective study is one that follows participants over time to see if certain outcomes, like the onset of a disease, occur and then compares those instances to any known or suspected risk or protective factors (s). It is common practice to follow a group of people, or a "cohort," for an extended period of time as part of the study. In this scenario, the researcher wants to learn how closeness to a traumatic event might effect healing time by conducting interviews with victims and witnesses over the next 10 years. Hence, it fits the criteria for a prospective observational study.

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The salesperson's gross earnings for a week, based on the informations, equals to $1,195.

An employees' gross pay is what they earn before taxes, benefits, and other payroll deductions are deducted from their pay. It is opposite of net pay, also known as take-home pay which is the amount left over after all withholdings are deducted.

Data

Weekly base salary of $600 on a quota of $4500.

On the next $2000, she receives a commission of 11 %.

On any additional sales, the commission rate is 15%.

Gross earning is computed as:

= Base salary + (First sales *11%) + (Additional sales*15%)

= $600 + ($2,000*11%) + ($2,500 * 15%)

= $1,195

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The angles ∠1 and ∠2 are vertical angles. Vertical angles are congruent and according to the definition of congruency, ∠1 = ∠2.

The completed table used to prove that ∠1 ≅ ∠2 is presented as follows;

Statement     [tex]{}[/tex]                                 Reasons

1. m∠1 + m∠3 = 180° [tex]{}[/tex]                     1. Linear pair angles are supplementary

m∠2 + m∠3 = 180°

2. m∠1 + m∠3 = m∠2 + m∠3 [tex]{}[/tex]       2. Substitution

3. m∠1 = m∠2[tex]{}[/tex]                                3. Subtraction property

4. ∠1 ≅ ∠2                  [tex]{}[/tex]                   4. Definition of congruency

Two angles are congruent if the measures of the each angle are equivalent.

The details of the reasons used to prove that ∠1 = ∠2, are as follows;

Linear pair angles

Linear pair angles are adjacent angles that have a common side and for which the other non common sides of the two angles, together form a straight line.

Substitution property

The substitution property of equality states that if a = b then b can replace a in any expression or equation, with the value of the new expression remaining the same as the previous expression or both sides of the new equations remain equivalent.

Subtraction property

The subtraction property of equality states that the subtraction of the same amount from two quantities that have the same amount, will result in two new quantities that remain equivalent.

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Answer:

k-m+1

if you have 36 and 78 for example, you would do 78-36 to find how many numbers there are plus one. so, the answer is k-m+1

Jane typed all the natural numbers between m and k (where k>m), which implies she wrote all the positive integers between m and k, inclusive. Jane would have written the numbers 5, 6, 7, 8, 9, and 10 if m was 5 and k was 10.

Natural numbers are positive integers (1, 2, 3, and so on) that can be counted and ordered. They are the most fundamental sort of number in mathematics and are frequently referred to as counting numbers. Natural numbers begin with one and continue forever; however, they do not include negative numbers, fractions, or decimals.

Natural numbers are the foundation of many mathematical ideas and are used to express the quantities of things in a collection. Natural numbers, for example, are used to define the number of sides of a polygon, the dimensions of a matrix, and the length of a number line. They are also used to indicate how much time has elapsed.

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The multifactor productivity for a given operation is 6.16 fees generated per dollar of input.

The Break Even Point, or the inflection point at which a corporation starts to make a profit, is the amount of output required for a company's revenue to equal its total costs.

First, we need to calculate the revenue generated per week:

Potential leads per week = 3 employees x 4,000 leads/employee/week = 12,000 leads/week

Actual sign-ups per week = 12,000 leads/week x 7% = 840 sign-ups/week

Revenue per week = 840 sign-ups/week x $90/sign-up = $75,600/week

Next, we need to calculate the input costs per week:

Labor cost per week = 3 employees x $18/hour x 40 hours/week/employee = $2,160/week

Material cost per week = $1,300/week

Overhead cost per week = $8,800/week

Total input cost per week = $2,160/week + $1,300/week + $8,800/week = $12,260/week

Finally, we can calculate the multifactor productivity:

Multifactor productivity = Revenue per week / Input cost per week = $75,600/week / $12,260/week = 6.16

So the multifactor productivity for this operation is 6.16 fees generated per dollar of input.

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The numbers for the first eight beads that are white are; 1, 5, 9, 13, 17, 21, 25, 29

step1

Arithmetic Sequence

We are told that she strings in this order;

Now, after the first white bead, the next white bead is the 5th bead in total.

This means the difference in interval between white beads is; 5 - 1 = 4 beads

Thus, the numbers for the first eight beads that are white are

1, (1 + 4), (1 + 4 + 4), (1 + 4 + 4 + 4)…..

Thus, we have;

1, 5, 9, 13, 17, 21, 25, 29

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If the series JK has 12 2 I J K 30, the value of JK is 720

In order to find the value of JK, multiply the given values all through and then generate the answer in a simplified manner

JK=(12)(2)(30)

Multiply all the figures

JK = 12 X 2 X 30

JK = 720

Therefore, the correct answer is as given above. It can be concluded that the value of JK is 720 as a result of the multiplication.

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Answer:

Step-by-step explanation:

You want to use the graph to estimate the lower and upper quartiles of the lengths of the 16 fish that Jay measured.

The lower quartile is comprised of the 1/4 of the total number of fish that are the shortest. The graph shows that 4/16 of the fish are 10 inches or less, so the lower quartile is 10 inches.

The upper quartile is comprised of the 1/4 of the total number of fish that are the longest. The graph shows that 12/16 of the fish are 25 inches or less, so 4/16 of the fish are 25 inches or more. The upper quartile is 25 inches.

The lower and upper quartiles are 10 inches and 25 inches, respectively.

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Answer:

Step-by-step explanation:

the answer is : 4,8,6,6,6

= 6

The experimental probability that the puppy would be named lemon or linus is 13/50. Option D

The experimental probability that the pupply would be named lemon or linus can be solved by

P(A) + P(B)

where P (A) is probability of lemon

P(B) is probability of linus

The total value in the frequency table is given as 10 + 13 + 3 + 14 + 10 = 50

P(A) = 3 / 50

P(B) = 10 / 50

The probability = 3/50 + 10/50

solve using the lcm method of solving fractions. There is a common denominator

3  + 10 / 50

= 13 / 50

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The value of x in the given polygon is 31 degrees.

An exterior angle is an angle created by the expansion of the neighboring side and one of the sides of a closed shape construction, such as a polygon. Regardless of the number of sides in the polygons, the sum of the measures of the outside angles is equal to 360 degrees.

The sum of the exterior angle of any polygon is 360 degrees.

So,

360 = 57 + 41 + 82 +x + 62 + 87

360 = x + 329

x = 31

Hence, the value of x in the given polygon is 31.

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The answers include the following below:

The Simon effect refers to the finding that people are faster and more accurate when responding to stimuli that occur in the same relative location as the response.

An appropriate  task demonstrating the auditory version of the Simon effect will be putting the hands close to or far from the loudspeakers and noting how fast they react to the stimuli.

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The Complete statement is : The location of proton in the atom is inside nucleus , has a charge of +1 elementary charge and the approximate mass of proton is 1.00727647 amu .

The Protons are the positively charged particles, the electrons are negatively charged particles and the neutrons have no charge.

In an atom there are equal number of protons and number of electrons . Thus the atom is electrically neutral in nature. The charge of the  proton is equal and opposite of an electron. So , proton has a unit positive charge.

The Protons are found inside the nucleus of atom , the proton carries the elementary charge of  1.00727647 amu (atomic mass units) , the charge on the proton is +1 .

The given question is incomplete , the complete question is

Answer the following questions about the Proton ,

The location of proton in the atom is  ______ , has a charge of ______ elementary charge and the approximate mass of proton is _____ amu .

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The words that can be changed into mathematical or arithmetic operators are

More = +, of  = *, if=Condition.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

The four basic arithmetic operations in Maths, for all real numbers, are:

Addition (Finding the Sum; ‘+’)

Subtraction (Finding the difference;  ‘-’)

Multiplication (Finding the product; ‘×’ )

Division (Finding the quotient; ‘÷’)

Now,

we can change

More = +, of  = *, if=Condition as only these makes sense according to mathematics actions.

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Answer: The statement given tells us that the Acme Company manufactures widgets and that the distribution of widget weights is bell-shaped. A bell-shaped distribution is also known as a normal distribution or a Gaussian distribution. This means that the majority of the data will cluster around the mean (average) value and the farther the data is from the mean, the less common it is.

The mean weight of the widgets is given as 51 ounces, which is the average weight of all the widgets manufactured by the company. The standard deviation is given as 10 ounces, which is a measure of how spread out the data is from the mean. A smaller standard deviation means that the data is more tightly clustered around the mean, while a larger standard deviation means that the data is more spread out.

This information allows us to make some predictions about the weights of the widgets. For example, we know that approximately 68% of the widgets will weigh between 41 ounces (mean - standard deviation) and 61 ounces (mean + standard deviation). Additionally, we know that approximately 95% of the widgets will weigh between 31 ounces (mean - 2standard deviation) and 71 ounces (mean + 2standard deviation) and 99.7% of the widgets will weigh between 21 ounces (mean - 3standard deviation) and 81 ounces (mean + 3standard deviation).

It is important to note that these predictions are based on the assumption that the distribution of widget weights is indeed bell-shaped. If that assumption is not true, these predictions may not be accurate.

Step-by-step explanation:

The sum of all the paintable integers is 757.

Note that it is impossible for any of h,t,u to be 1, since then each picket will have been painted one time, and then some will be painted more than once.

h cannot be 2, or that will result in painting the third picket twice. If h=3, then t may not equal anything not divisible by 3, and the same for u. Now for the fourth and fifth pickets to be painted, t and u must be 3 as well. This configuration works, so 333 is paintable.

If h is 4, then t must be even. The same for u, except that it can't be 2 mod 4. Thus u is 0 mod 4 and t is 2 mod 4. Since this is all mod 4, t must be 2, and u must be 4, in order for 5,6 to be paintable. Thus 424 is paintable.

h cannot be greater than 4, since if that were the case then the answer would be greater than 999, which would be impossible for the AIME.

Therefore, the sum of all paintable numbers is 757.

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The domain restriction for f(x)/g(x) is x ≠ 0 or -3

The domain of a function is the set of all input values (or "independent variable") for which the function is defined and produces a valid output (or "dependent variable").

In other words, it is the set of all valid input values for which the function will produce a real output and not give an error or undefined result.

But the domain restriction is the set of values that are not allowed as input for the function.

f(x)/g(x) = (x+26)/(14x²+42x)

In order to find the Domain restriction for f(x)/g(x), equate the denominator g(x) to zero and solve for x. That is:

14x²+42x = 0

14x(x + 3) = 0

14x = 0 or x + 3 = 0

x = 0 or x = -3

Thus, the Domain restriction is x ≠ 0 or -3

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Answer:

D.[tex]\sqrt[32]{2}[/tex]

I think this is right becuse V=l*w*h which is 64=4*4*4

Answer:

Part 1

(a) There were 2798 patients who only had the protein for Lyme.

Part 2

(b) There were 2516 patients who only had the normal protein.

Part 3

(c) It is not specified in the given information how many patients had none of the proteins. It is only specified that 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease; 1884 had the protein for CFS and Lyme; 408 had the protein for CFS only; 2602 had the protein for CFS; 1731 had the normal protein as well as the one for Lyme; 2798 had the protein for Lyme; 2516 had the normal protein. Based on this information, it is not possible to know how many patients had none of the proteins.

Answer: There are no patients who had none of the proteins.

Step-by-step explanation: Part 1

(a) There were 408 patients who only had the protein for Lyme.

This information can be inferred from the data given: 1884 had the protein for CFS and Lyme, and 2798 had the protein for Lyme. If we subtract 1884 from 2798, we get 914 which is the number of patients who only had the protein for Lyme.

Part 2

(b) There were 2516 patients who only had the normal protein.

This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, and 2602 had the protein for CFS. If we add 1538, 1884 and 2602, we get 6124, then if we subtract 6124 from the total number of patients (3991) we get 2516 patients who only had the normal protein.

Part 3

(c) There were 0 patients who had none of the proteins.

This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, 408 had the protein for CFS only, 2602 had the protein for CFS, 1731 had the normal protein as well as the one for Lyme, 2798 had the protein for Lyme, and 2516 had the normal protein. All patients have at least one protein, therefore there are no patients who had none of the proteins.

Answer: A cubic polynomial function has the form f(x) = ax^3 + bx^2 + cx + d.

A horizontal tangent line is a line that is parallel to the x-axis and it occurs at a critical point of the function, where the derivative of the function is 0.

We know that a cubic function has 3 critical points and thus 3 derivative that could be 0, so to find the equation of the cubic function we will use these two points to find the value of a, b, c, and d.

We know that the critical points of a cubic function are found by solving f'(x) = 0, where f'(x) is the derivative of the function, so we have:

f'(x) = 3ax^2 + 2bx + c = 0

Now we can use the two points to find the value of a, b, c, and d.

We know that the point (1,-2) is on the graph of the function, so we can substitute it into the equation to find d:

f(1) = a + b + c + d = -2

And we know that the point (-1,2) is on the graph of the function, so we can substitute it into the equation to find d:

f(-1) = -a + b - c + d = 2

Now we can use these two equations to find the value of a, b, and c:

a + b + c + d = -2

-a + b - c + d = 2

2a + 2d = 0

a = -d

-a + b - c + d = 2

b - c = 4

3ax^2 + 2bx + c = 0

3(-d)x^2 + 2bx - c = 0

Now we can use these equations and the critical points to find the value of a, b, c, and d

3(-d)x^2 + 2bx - c = 0, (1,-2) => 3d+2b-c = 0

3(-d)x^2 + 2bx - c = 0, (-1,2) => 3d-2b+c = 0

b-c = 4

Solving these equations, we have:

a = -1/3

b = 1

c = -5/3

d = -2

And the equation for the function is:

f(x) = -1/3x^3 + x^2 - 5/3x - 2

We can now sketch the graph of the function by using the information that we have. The cubic function will have an vertex of symmetry at (0,-2) and two horizontal tangent lines at (1,-2) and (-1,2) .

Since a < 0, the function is concave down, so the graph will be opened downwards and will have a local minimum at (0,-2) .

It is important to note that this is one possible equation for a cubic function that has horizontal tangent lines at (1, −2) and (−1, 2), but there may be other possibilities.

Step-by-step explanation:

Answer:

Step-by-step explanation: 21

The solution for the given differential equation is  [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex].

We have given a differential equation:

[tex]\frac{d}{dx}(C_1e^{12x})[/tex]

since C1 is a constant,

=[tex]C_1\frac{d}{dx} (e^{12x})[/tex]

we know that [tex]\frac{d}{dx} (e^{ax}) = e^{ax}\frac{d}{dx} (ax)[/tex]

= [tex]C_1e^{12x}(12) = 12C_1e^{12x}[/tex]

Therefore, [tex]\frac{d}{dx}(C_1e^{12x}) = 12C_1e^{12x}[/tex]

Now, let y = [tex]C_1e^{12x}[/tex]

Therefore, [tex]\frac{dy}{dx} = 12C_1e^{12x} = 12y[/tex]

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The complete question is:

Fill in the blank. The symbol C represents a constant. [tex]\frac{d}{dx}C_1e^{12x}[/tex]= ____ Write this result as a linear first-order differential equation that is free of the symbol C1 and has the form dy/dx = f(x, y).

The probability that they’re will be between 33 and 45 with part time jobs in a randomly selected group of 300 is given as follows:

B. 0.736.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution in this problem are given as follows:

p = 0.13, n = 300.

Hence the mean and the standard deviation are given as follows:

Using continuity correction, the probability of X between 33 and 45 is (32.5 < X < 45.5), which is the p-value of Z when X = 45.5 subtracted by the p-value of Z when X = 32.5, hence:

X = 45.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (45.5 - 39)/5.82

Z = 1.12

Z = 1.12 has a p-value of 0.8686.

X = 32.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (32.5 - 39)/5.82

Z = -1.12

Z = -1.12 has a p-value of 0.1314

Hence:

0.8686 - 0.1314 = 0.736 (approximately).

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The charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s] is given by q(t) = q0 + (t)I,

The charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s] is calculated by the formula q(t) = q0 + (t)I, where q0 is the initial charge and I is the current.

The charge q(t) that crosses the dashed line going from left to right in the time interval (0, t) [s] is given by q(t) = q0 + (t)I, where q0 is the initial charge and I is the current. To calculate q(t), we need to first calculate the initial charge q0 and then calculate the current I. To calculate q0, we need to integrate the current I over the time interval (0, t). To calculate q(t), we need to know q0 and I. Then, we can calculate q(t) by multiplying t by I and adding it to q0. For example, if q0 = 3 C and I = 2 A, then q(t) = 3 + (t)(2) = 3 + 2t C.

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