1. Match each equation with an equivalent equation. Some of the answer choices are
not used.
A. 3x + 6 = 4x+7
B. 3(x + 6) = 4x+7
C. 4x + 3x = 7-6
1.9x = 4x +7
2. 3x + 18 = 4x+7
3.3x = 4x + 7
4. 3x1 = 4x
5.7x = 1

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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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.

An equation of the line that passes through two points (x1,y1) and (x2,y2) can be found using the slope-intercept form:

Slope intercept form: what is it?

Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope of the line, we use the following formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the points given, we get:

m = (10 - 1) / (0 - 3) = -9/3

To find the y-intercept, we can use either of the given points and the slope:

b = y - mx

Plugging in the coordinates of the point (3,1) and the slope, we get:

b = 1 + (9/3) * 3 = 4

So the equation of the line that passes through (3,1) and (0,10) is:

y = -3x + 4

It's also possible to use the point slope form of a linear equation, which is y-y1=m(x-x1)

y - 1 = -3(x-3)

y = -3x + 9

Both equations are valid and represent the same line.

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The volume of the solid that is in the parabola is 3.48[tex]\pi[/tex] after integration will carried out.

Parabola is a U shape curve whose eccentricity is 1.

The equation of parabola is y = 2-3x² and the x axis.

The cross section is perpendicular to y axis and the square.

The parabola is passes through the x axis put y = 0 in the equation of parabola.

0 = 2-3x²

x = [tex]\sqrt{\frac{2}{3} }[/tex]

Volume of the solid = [tex]\pi r^{2}h[/tex]

here r = y and h = dx

[tex]\pi (2-3x^{2} )^{2} dx=dv\\dv = \pi (9x^{4}-12x^{2} +4)dx\\[/tex]

Now, integrate the given equation to get the volume of the solid.

∫dv = ∫π(9x⁴-12²+4)dx

Put limits [tex]\sqrt[2]{\frac{2}{3} }[/tex] to 0

After integration and putting the limit we got V = 3.48[tex]\pi[/tex].

Hence, the volume of the solid is 3.48π.

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The complete question is:

Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y = 2 − 3x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.

Answer: 83 inches

Step-by-step explanation:

1. 12 inches = 1 foot

2. 12x6=72 inches

3. 72+11=83 inches

The coordinates of the midpoint of the segment whose endpoints are H (-2, 4) and K (2, –3) is (0,1/2)

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

x = [tex]\dfrac{p+m}{2}[/tex]

and y =[tex]\dfrac{q+n}{2}[/tex]

Given;

The endpoints= H (-2, 4), K (2, –3)

X coordinate of midpoint;

-2+2/2=0

Y coordinate of midpoint;

4-3/2=1/2

Therefore, the midpoint will be (0,1/2)

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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:

Is it 0? sorry if this is wrong

Step-by-step explanation:

Answer:

f(g(0)) = -2

Step-by-step explanation:

We have our two equations, f(x) and g(x).

We work our way from the inside to the outside. Our inside equation is g(0). If we match g(x) to that, that would mean x = 0. So on that g(x) graph, when the x=0, the graph intercepts the y axis at y = 1.

Now that we know that g(0) = 1, we can plug that into the original equation, making it f(1) instead of f(g(0)). Now that we have f(1), we can go to our f(x) equation.

Matching the equations, it shows the x=1. On our f(x) graph, we'll find x=1 and trace down or up (down in this case) to the point where the graph intercepts at that point. Thats where we can then trace that point to the y axis and we see that our line hits the y axis at -2, making that the answer.

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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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 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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Answer:

X/4=3/6

Start off by cross multiplying the tops and bottoms, so X/4=3/6 turns into 6X=12. Now divide by 6 on both sides.

6X=12      X=2

Answer:

2

Step-by-step explanation:

Cross Multiple and Divide

X. 3

----. = ----

4. 6

So what you want to do is multiply diagonally:

(6)(X) = 6X

(3)(4) = 12

Now that we have our two answers, we put an equal sign between them.

6X = 12

Now to get X alone. Since it's being multiplied by 6, you want to do the opposite and divide.

So remember to divide on both sides to get rid of the 6.

6X divided by 6 is just X.

12 divided by 6 is 2

We got our answers, put the equal sign in-between

X = 2

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 b1 = -21, b2 =33, and b3 = 6 in the given matrix.

A collection of integers lined up in rows and columns so to produce a rectangular array is called a matrix. The elements, or inputs, of the matrix are the integers.

A single matrix is created through matrix multiplication, sometimes referred to as matrix product and the multiplication of two matrices. This kind of binary operation is used. A scalar multiplication occurs when an integer is multiplied by a matrix. Scalar multiplication is the process of multiplying a matrix by a scalar value.

For the given matrix multiply each term of the matrix with 3 to obtain the value of b1. b2, and b3.

[tex]3\left[\begin{array}{ccc}-7\\11\\2\end{array}\right] = \left[\begin{array}{ccc}-21\\33\\6\end{array}\right][/tex]

Hence, the value of b1 = -21, b2 =33, and b3 = 6.

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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 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).

That since exact value of sin(A-β) depends on the cos(-β) value, which we miss, we are not able to determine the value.

To determine (A-β), we can use trigonometric identities.

Tan(A) = 3/4 and sin() = 4/5 in Quadrant III.

The identification can be used for:

tan(A) = cos/sin(A) (A)

Sin(A) in this instance equals 3/4. * cos(A) (A)

We can adopt a different guise.

(A-sin) = sin (A)

(cos) - (cos (A)

Sin(β), so sin(A-) = (3/4 * cos(A)) (sin()) - cos()) (cos(A))

sin(A-β) = (3/4) - (4/5) * (sin(A) * (cos(A) * cos())

We can now apply the double angle formula.

cos(2A) = sin2 + cos2(A) (A)

Therefore, cos(A) = (1 - sin(A)2), and sin(A-) = (3/4) * (± √(1 - (3/4)^2) * cos(β)) - (4/5) * (3/4)

sin(A-β) = (3/4) * (± √(1 - (9/16)) * cos(β)) - (3/5)

The formula for sin(A-) is (3/4) * ((7/16) * cos()) - (3/5)

That since exact value of sin(A-) depends on the cos(-) value, which we miss, we are not able to determine the value.

Therefore, using the equation given, it is impossible to figure out the precise value of (A-β).

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The medians and IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.

a. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 4.

b. The medians and IQRs of distributions (1) and (2) are the same; both have a median of 6 and an IQR of 2.c. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 3 and an IQR of 2, while distribution (2) has a median of 8 and an IQR of 2.

d. The medians and IQRs of distributions (1) and (2) are different; distribution (1) has a median of 50 and an IQR of 50, while distribution (2) has a median of 500 and an IQR of 400.

The median IQRs of two distributions can be compared to determine how the distributions differ. If the medians and IQRs are the same, the distributions are similar. If the medians and IQRs are different, the distributions are not the same.

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Answer:

Step-by-step explanation:

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

= 6

Two points should be noted: The 15% is first calculated using your annual gross wage rather than your take-home pay. Second, the business match is not included in your 15%.

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If the spin lands on the space where the contestant wins nothing, then x = 0.

If the spin lands on a space where the contestant wins $1, then x = -1 + 1 = 0. If the spin lands on a space where the contestant wins $4, then x = -2 + 4 = 2.

The expected value of x can be calculated as follows:

E(x) = (333/555) × 0 + (111/555) × (-2 + 1) + (111/555) × (-2 + 4) = (111/555) * 2 = 0.4.

So, on average, the player's net gain per spin is 40 cents.

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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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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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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 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 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 standard deviation of is equal to the standard deviation multiplied by, and the anticipated value of is equal to the mean.

The mean, which is the average of the random variable, is equal to the expected value of. It is determined by summing up all of the random variable's values and dividing the total number of values in the set. The result of multiplying the standard deviation by is the standard deviation of. By taking the square root of the variance, the standard deviation—a measurement of the range of data points from the mean—is created. By dividing the total of the squares of the deviations between each data point and the mean, the variance is computed.

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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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