Two numbers (x & y) add up to 20 and have a difference of 6.
a. Set up a system of equations for this problem.
b. Solve for the values of x & y.
c. Verify that these are the correct values of x & y.

Answer:

Below

Step-by-step explanation:

This is an exercise in 'completing the square'

x^2 - 6x -3      

   take 1/2 of the x coefficient  (6) square it and add it and subtract it

x^2 - 6x + 9    - 9   - 3        Now you can reduce the underlined portion

(x-3)^2      - 12          a = 3   b= -12          Done

Answer: A = 6

Step-by-step explanation: Here to help! So, if "a" wants to know the numerator of the fraction, all you have to do is to multiply 0.6 by 10, and that would get you 6/10. 6/10 is equivalent to 60% or 0.6. :))))

The perimeter of the square is 12√2 units

A square is a quadrilateral that has all it's sides equal and all it's angles equal. The sum of interior angles of a square is 360°. This means that each angle of a square is 90°.

The perimeter of a square is obtained by adding all the sides.

Therefore the perimeter of a square = 4l

A (-1,4) and B ( 2,7)

line AB = √2-(-1))² + (7-4)²

AB = √ 3²+3²

AB = √9+9

AB = √18 units

therefore since the sides of a square are equal, the perimeter = 4× √18

= 4×3√2

= 12√2 units

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Answer:

Option A. 12√2 units

Step-by-step explanation:

Answer:

1.55 x [tex]10^{15}[/tex]

or 1,550,000,000,000,000

Step-by-step explanation:

2.5 x 1.034 x [tex]10^{3}[/tex] x 6 x [tex]10^{11}[/tex]

15.51 x [tex]10^{14}[/tex]

1.551 x [tex]10^{15}[/tex]

The angular speed of the wheel is 0.314 rad/sec and the linear speed of the car is 8.164 feet/second .

Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ/ t

one revolution = 360°

180° = π

360° = 2π

3 revolution = 3× 2π = 6π

1 minute = 60 ×1 = 60s

angular speed = 6× 3.14/60

= 0.314 rad/s

The linear velocity =

V = wr

r = d/2

r = 52/2 = 26 feet

V = wr

V = 0.314× 26

V = 8.164 feet/second

Question: A Ferris wheel at a carnival has a diameter of 52 feet. Suppose it turns at a rate of 3 revolutions per minute. i. What is the angular speed of the wheel.

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C. An IQ score of 80 is more unusual than an IQ score of 120

is the false answer

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

Firstly we need to find the probability of the test score to be less than 90(P<90) then we will continue finding the probability of the IQ score to be between 90 and 110(90<P<110) then we find the probability of the IQ score being more than 110 (P>110).

For P<90

Firstly we compute this using a scientific calculator where we choose the stat option and enter the mean of 100 and a standard deviation of 10, so we check if we make the normal random variable(X) to be 90 the outcome or answer for that is 0.16 so now we know the probability of the IQ score to be less than 90 is 16% chances.

For 90<P<110

then we check with the same method what will be the probability for an IQ score to be between 90 and 110 for a mean of 100 and a standard deviation of 10 we again check a normal  random variable(X) of 110 to see what will be the probability of P<110 which we find an answer of 0.84 which is 84% chances so now therefore the probability of an IQ score to be more than 110 is 0.

therefore this tells us an IQ score of 120 is more unusual than an IQ score of 120.

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Is your 2050 prediction realistic?

No, the 2050 prediction is not realistic because the literacy rate cannot exceed 100%

Given data is

x0=1976, y0=63.2

x1=2001, y1=86.7

x2=2012, y2=94.5

Then the Lagrange interpolation formula is

[tex]y - y_1 = \frac{y_2 - y_1}{x_2 -x_1} (x - x_1)[/tex]

Here we have to interpolate to predict the literacy rate in 1992.

i.e. x=1992.

It lies between 1976 and 2001.

Then

x1=1976, y1=63.2

x2=2001, y2=86.7

Then interpolation function become

[tex]63.2 + \frac{23.5}{25}(16)[/tex]

= 63.2 + 15.04 = 78.24

i.e. The predicted literacy rate in 1992 is 78.24%.

Now, to find the literacy rate in 2050, we have to use extrapolation.

Since, 2050 is not in between any of the given data, we will have to take last two datas.

i.e.

x1=2001, y1=86.7

x2=2012, y2=94.5

And x=2050.

Then our extrapolation formula become

[tex]86.7 + \frac{7.8}{11} (49)[/tex]

= 86.7 + 34.75

=121.45

i.e. The literacy rate in 2050 is 121.45%.

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The perimeter of this parallelogram is equal to 236/10 or 23 6/10 meters.

In Mathematics, a parallelogram simply refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

Mathematically, the perimeter of a parallelogram can be calculated by using this mathematical expression;

Perimeter = A + B + C + D

Where:

A, B, C, and D represents the length of sides of a parallelogram.

Substituting the given parameters into the perimeter of a parallelogram  formula, we have the following;

Perimeter = 3 3/10 + 8 5/10 + 3 3/10 + 8 5/10

Perimeter = 33/10 + 85/10 + 33/10 + 85/10

Perimeter = 66/10 + 170/10

Perimeter = 236/10 or 23 6/10 meters.

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Answer:

Step-by-step explanation:

The wooden frame is a cuboid

and the volume of a cuboid = Length x Width x Depth

Therefore,

The volume of this wooden frame = (8 feet) x (5 feet) x (4 feet)

                                                         = 160 cubic feet

The purchasing rate for the sand is $20 per cubic meter (which is NOT the same as cubic feet)

Unit conversion has to be applied then:

1 foot = 0.3048 meters

1 cubic feet = (0.3048 meters) x (0.3048 meters) x (0.3048 meters)

                                           1 cubic feet = [tex]0.3048^{3}[/tex] cubic meters

Therefore:                     160 cubic feet = (160)([tex]0.3048^{3}[/tex]) cubic meters

                                                                 Cost of sand:
                                                          1 cubic meter = $20

     Therefore:             (160)([tex]0.3048^{3}[/tex]) cubic meters = $(20)(160)([tex]0.3048^{3}[/tex])

                                                                                = $90.61

                                                           = $91 (Rounded to the nearest dollar)

It will cost Andrea $91 to purchase sand for the sandbox

If knowing the probability of an event occurring is known then it can be turned into one's favour as well as it can be obstructed if not in favour.

A way to determine the likelihood of something occurring is through probability. Many things are hard to predict with 100 percent certainty. We can only predict the likelihood of an event occurring or how likely it is using it. A probability can be between 0 and 1, with 0 signifying an impossibility and 1 signifying a certainty.

If the likelihood of an event occurring is known, one can attempt to influence the outcome in accordance with the likelihood.

The possibility of altering the likelihood that the event will go in one's favour is another useful tool.

Therefore, being aware of the probability can be beneficial.

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To better understand the relationship between education level and organic produce sales, we need to have data on these variables.

The data would typically be in the form of a table or a graph, with education level on one axis and organic produce sales on the other. Once we have the data, we can look at the pattern of the points to determine the relationship between education level and organic produce sales. If there is a positive relationship between the two variables, then as the education level increases, we would expect to see an increase in organic produce sales. This positive relationship could be represented by a line that slopes upward from left to right on a graph.

The slope of the line represents the rate of change of organic produce sales with respect to education level. A steep slope would indicate that even small changes in education level lead to significant changes in organic produce sales, while a shallow slope would suggest that changes in education level have little effect on organic produce sales.

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Angle of triangle AFC is 37°

An angle is the formed when two lines meet at the same vertex. It is measured is degrees. There are three types of angles based on their measurements.

From the given figure consider ABCF as trapezium,

Given that angle of triangle BCF is 37°

Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non-parallel side, add up to 180°

Therefore, ∠BCF + ∠CBF = 180°

                                  ⇒∠B = 180° - 37°⇒143°

Similarly ∠A = ∠B = 143°

⇒∠A+∠F=180°

⇒∠F=180°-143° ⇒ 37°

Hence, m∠AFC = 37°.

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The point (-5,-3) reflected over the y-axis is (5, -3).

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

(-5, -3)

Along y-axis:

(x, y) → (-x, y)

So,

(-5, -3) → (-(-5), -3) = (5, -3)

Thus,

(5, -3) is the reflected point.

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The total amount of acid in the final equation solution is 700% + 420% = 1120%, which is 40% of the total volume:

In arithmetic equations, the identical sign (=) is used to denote the equivalence of two assertions. It is demonstrated that using mathematical methods, which have acted as manifestations of reality, it is feasible to compare different numerical factors. For fact, the equal sign splits the number 12 into two separate parts, even if the answer is y + 6 = 12. It is possible to determine how many letters are also present on either end of this character.

Here,

Let x be the number of liters of pure acid solution needed, and y be the number of liters of 20% acid solution needed to make 28 liters of a 40% acid solution.

x + y = 28 (total volume of the solution)

100x + 20y = 40(28) (total amount of acid in the solution)

Simplifying the second equation, we get:

100x + 20y = 1120

Dividing both sides by 20, we get:

5x + y = 56

Now we can solve the system of equations by substitution or elimination. Here we will use the substitution method.

Solving the first equation for y, we get:

y = 28 - x

Substituting this expression for y into the second equation, we get:

5x + (28 - x) = 56

Simplifying and solving for x, we get:

4x = 28

x = 7

So the technician needs 7 liters of pure acid solution and 21 liters of 20% acid solution to make 28 liters of a 40% acid solution.

To check this answer, we can calculate the amount of acid in each solution and verify that the total amount of acid in the final solution is indeed 40%.

7 liters of pure acid solution contain 7 × 100% = 700% acid.

21 liters of 20% acid solution contain 21 × 20% = 420% acid.

The total amount of acid in the final solution is 700% + 420% = 1120%, which is 40% of the total volume:

1120% ÷ 28 liters = 40%

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9.03 divided by 0.15 is equal to 60.2.

The opposite of multiplication in arithmetic is called division. It's used to determine how many times one quantity is contained inside another. Division is done by dividing the dividend by the divisor, which can be done visually by using the division sign () or a fraction bar (/). The quotient, which shows how many times the dividend can be divided by the divisor, is the operation's output. For instance, if you split up eight apples into four equally sized pieces, each piece would contain two apples. This division is denoted by the equation 8/4 = 2, where 8 is the dividend, 4 is the divisor, and 2 is the quotient.

The division of 9.03 by 0.15 can be calculated as follows:

9.03 ÷ 0.15 = 9.03 / 0.15

= 60.2

So, 9.03 divided by 0.15 is equal to 60.2.

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The time that is taken by the colony is 23 years.

The exponential growth function can be used to account for the exponential increase in the number of the organisms that are to be found in the colony.

Given that we have that;

P=Poe^rt

P = Number at time t

Po = Number initially present

r = rate of growth

t = time taken

Thus;

3480 = 1120e^0.0498t

3480/1120 = e^0.0498t

3.1 = e^0.0498t

ln(3.1) = 0.0498t

t = ln3.1/0.0498

t = 23 years

There are 23 years

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The original cost of the sweater is $60.

Percentage is simply defined as the parts of a number per fraction of 100.

Percentage is usually denoted by the symbol '%'.

Percentage of a number in a whole can be calculated by dividing the number by the whole and then multiply with 100.

Given that,

A sweater is on sale for a 20% discount. The amount of the discount is $12.

Percentage of discount = 20%

Amount of the discount = $12

Let x be the original cost of the sweater.

20% of x = 12

0.2x = 12

x = 60

Hence the original price of the sweater was $60.

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Answer:8k

Step-by-step explanation:i did the test and got it write

The Height is 10 inch and radius is 10 inch.

Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. While capacity can be measured in virtually any other unit, such as litres, gallons, pounds, etc., volume is measured in cubic units.

Given:

Volume = 10,000π in³

Volume of b= π r² h

So, 10,000π= π r² h

10,000 =  r² h

r² h = 10 x 10 x 10

r² h = 10² x 10

Now, comparing the values

r= 10 inch and h= 10 inch

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H is a subgroup of G since it is closed under the group operation, contains the identity element and inverses of its elements.

A subset H of a group G is a subgroup of G if it satisfies the following three properties:

1. Closure: H is closed under the group operation, that is, if α, β∈H then αβ∈H.

2. Identity element: H contains the identity element e of G.

3. Inverses: For each element α∈H, its inverse (or reciprocal) α−1 is also an element of H.

In this case, the subset of G consisting of elements of finite order (H) satisfies all of these three properties. Since H is closed under the group operation, if α, β∈H then αβ∈H. The identity element of G, e, is also an element of H since the order of the identity element is always 1, which is finite. Finally, for each element α∈H, its inverse α−1 is also an element of H since the inverse of a finite order element is also of finite order. Therefore, by satisfying all of the three properties of a subgroup, H is indeed a subgroup of G.

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Natural numbers: 0.1 Whole numbers: 0, Integers: -7, -3, 0, 1, Rational numbers: -7.2, -3.0, 0.1, 3.5,Irrational numbers: √5, √64, Real numbers: -7.2, -3.0, 0.1, √5, 3.5, √64.

Natural numbers are the positive integers, 1, 2, 3, 4, 5, and so on. They are also known as the counting numbers or the positive integers. They are the numbers used for counting and measuring. Natural numbers are the building blocks of mathematics, and are used in the formation of other number systems, such as integers, rational numbers, real numbers, and complex numbers.

Natural numbers are also used in the formation of equations and formulas, as well as in the counting of objects, in the measurement of distances, and in many other areas of mathematics. Natural numbers are an important part of everyday life, and are used in everything from telling time to counting money.

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[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -5 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{since the leading coefficient is 2, let's a = 2}}{2(x+2)(x-5)=y} \\\\\\ 2\stackrel{\textit{F O I L}}{(x^2-3x-10)=y}\implies \boxed{2x^2-6x-20=y}[/tex]

Answer:

Step-by-step explanation:

The formula for the area of a triangle is:

1/2×base×height

If you know the area of the triangle and height you can apply the area formula:

A=1/2×base×height

in reverse to calculate the length of the base:

b=2A/h

given, h=60dam

A=18

so, b=2×18/60

b=36/60

b=0.6

The answer is 0.6

a) The 22nd percentile for incubation times of chicken eggs is of: 20.5 days.

b) The middle 95% of incubation times is in this following interval: (19.1, 23.5) days.

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 this problem are given as follows:

[tex]\mu = 21.3, \sigma = 1.1[/tex]

The 22nd percentile is the value of X when Z has a p-value of 0.22, hence X when Z = -0.77, thus:

-0.77 = (X - 21.3)/1.1

X - 21.3 = -0.77 x 1.1

X = 20.5 days.

The middle 95% of incubation times is obtained from X when Z = -1.96(2.5th percentile) to X when Z = 1.96(97.5th percentile), hence:

-1.96 = (X - 21.3)/1.1

X - 21.3 = -1.96 x 1.1

X = 19.1 days.

1.96 = (X - 21.3)/1.1

X - 21.3 = 1.96 x 1.1

X = 23.5 days.

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Answer:

3/8 feet²

---------------------------

Area of the rectangle is the product of its two dimensions:

Substitute the dimensions and find the area:

The new function of Jennifers's investment is f(t) = 50000 * (1.15)^t

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

Initial investment, a = 50000

Rate of growth, r = 15%

Using the above as a guide, we have the following:

f(t) = a * (1 + r)^t

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

f(t) = 50000 * (1 + 15%)^t

So, we have

f(t) = 50000 * (1.15)^t

Hence, the function is f(t) = 50000 * (1.15)^t

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Complete question

ennifer starts a new investment account that grows exponentially. Her financial advisor tells her the initial investment of $50,000 grows at a rate of about 15% annually.

Write a new function, N(t), that represents the amount of money in Jennifer’s new account after t years. Be sure to use correct notation

Answer:

A vertical line that passes through the coordinate (25, 0).

Equation of the vertical line is x = 25

Step-by-step explanation:

2x = 50

x = 25

Answer:

The formula for the surface area of a sphere with radius r is 4πr^2. Plugging in the given radius of 8, we get:

Surface area = 4π * 8^2 = 4π * 64 = 256π

Using an approximate value of π = 3.14, the surface area of the sphere is approximately:

256 * 3.14 = 803.84

Rounding to the nearest hundredth, the surface area of the sphere is approximately 803.84 square units.

Answer:

803.84cm²

Area of a sphere = 4πr²

When we put the given values we get

Area of a sphere = 4x3.14x8²

Area of a sphere = 4x3.14X16

                             = 804.25cm²

Rounding to the nearest hundredth we get,

803.84cm²