Simplify algebraic expression

Answer:

C is a function

Step-by-step explanation:

for a relation to be a function each value of x must map to exactly one unique value of y

A

2 → 5 and 2 → 2 ← not a function

B

- 1 → 6 and - 1 → 7 ← not a function

C

all values of x map to exactly one unique y ← function

D

3 → 1 and 3 → 2 ← not a function

On solving the provided question, we can say that difference of cylinder between the height of the soap 8 cm.

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

[volume of cylinder]=pi*r²*h- =  h=[volume of cylinder]/(pi*r²)

Volume=5652 cm³

r=7.5 cm, so,  h= [tex][5652]/(3.14*7.5²) = h=32 cm[/tex]

the height of the soap in the full dispenser is 32 cm

the height when 4,239 cubic centimeters of soap remains in the dispenser is h  [tex]=[4239]/(3.14*7.5²) = h=24 cm[/tex]

the difference is [tex]32-24 = 8 cm[/tex]

the answer is

8 cm

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If Swimming Pool On a certain hot summers day, 498 people used the public swimming pool. The number of children is 325 and the number of adult is 173.

Children = x

Adults = y

x + y = 498  Equation .....1

1.50x + 2.50y = 920  Equation ...2

Multiply (1) by 2.50

2.50x + 2.50y = 1,245  Equation  Equation ....3

1.50x + 2.50y = 920  Equation ...2

Subtract (2) from (3)

1x = 325

x = 325/1

x = 325 (Children)

Substitute x = 325 in (1)

x + y = 498

325 + y = 498

y = 498 - 325

y = 173 (Adult)

Therefore 325 children and 173 adults swam at the pool.

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Answer:

the answer us on the attatched documet

Step-by-step explanation:

can u just give me the brainliest

Answer: Choice D

Step-by-step explanation: A dilation would result in a similar triangle because multiplying by the scale factor will create proportional sides. However, this will change the size of the triangle, making it not congruent.

Answer:

D.

Step-by-step explanation:

Congruent means that the triangles are exactly the same in shape and size.

Dilating the triangle is the only answer that will change its size.

Answer:

From Least to Greatest

-9, 1/25, 0.25, 9/20, 11/20, 9

Step-by-step explanation:

Answer:

-9, 0.25, 9/20, 11/20, 9, 9 1/25

Step-by-step explanation:

You can convert everything in decimals or into fractions with a common denominator. Using what you have, you then put them in order.

I converted them all into decimals, getting:

-9, 0.55, 0.25, 0.45, 9, 9.04

Then I put them in order

-9, 0.25, 9/20, 11/20, 9, 9 1/25

The score interval that is within one standard deviation of the mean is

(70 , 80).

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.

Some of the properties of the standard deviation are:

1. It cannot be negative

2. It is only employed to calculate the spread or dispersion around a data set's mean

3. It displays the degree of deviation  from the mean value

4. The larger the spread, the more standard deviation, with data of about the same mean.

Given,

 The mean of the test μ = 75

The standard deviation σ = 5

We are asked to find the scores within one standard deviation of the mean.

This means that the scores should be in the interval ( μ - σ , μ + σ )

μ - σ = 75 - 5 =70

μ + σ = 75 + 5 = 80

Therefore the scores should be in the interval = ( 70,80), which is within one standard deviation of the mean.

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Consequently, this student's quiz results have a median, or "middle," value of 16.

When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.

Here,

the median, or "middle" value in a data set. Your data must be in numerical order in order to calculate the median.

Exam results:

9, 13, 20, 15, 18, 17

Number the rows and columns.

9, 13, 15, 17, 18, 20

Calculate the "middle" value:

9, 13, 15, 17, 18, 20

If there are two middle values, put them together and divide by two.

15 + 17 = 32

32/2 = 16

Consequently, this student's quiz results have a median, or "middle," value of 16.

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The farmer should expect to harvest 17,500 pounds of spinach from the field.

What is a function?

A function is a mathematical relation between a set of inputs (called the domain) and a set of possible outputs (called the range). The inputs are usually denoted by variables and the outputs are usually denoted by the value of a function. A function assigns exactly one output to each input.

In the given problem, g(z) = 400z - z^2 is a function that describes the area of a field in square feet, where z represents the width of the field in feet.

Given that the width of the field is 50 feet, we can substitute this value into the function to find the area of the field:

g(50) = 400(50) - 50^2 = 20,000 - 2,500 = 17,500 square feet

We know that the farmer will plant spinach in this field and expect to harvest 1 pound of spinach per square foot. Therefore, the total number of pounds of spinach the farmer should expect to harvest from the field is:

1 pound/square foot * 17,500 square feet = 17,500 pounds

Hence, the farmer should expect to harvest 17,500 pounds of spinach from the field.

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The farmer should expect to harvest 17,500 pounds of spinach from the field.

What is a function?

A function is a mathematical relation between a set of inputs (called the domain) and a set of possible outputs (called the range). The inputs are usually denoted by variables and the outputs are usually denoted by the value of a function. A function assigns exactly one output to each input.

In the given problem, g(z) = 400z - z^2 is a function that describes the area of a field in square feet, where z represents the width of the field in feet.

Given that the width of the field is 50 feet, we can substitute this value into the function to find the area of the field:

g(50) = 400(50) - 50^2 = 20,000 - 2,500 = 17,500 square feet

We know that the farmer will plant spinach in this field and expect to harvest 1 pound of spinach per square foot. Therefore, the total number of pounds of spinach the farmer should expect to harvest from the field is:

1 pound/square foot * 17,500 square feet = 17,500 pounds

Hence, the farmer should expect to harvest 17,500 pounds of spinach from the field.

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SAS congruence theorem should be used.

Option (B) is correct.

What is the SAS congruence theorem?

In Euclidean geometry, the SAS congruence theorem states that if two triangles have two sides of one triangle congruent (equal in length) to two sides of the other triangle, and the included angle is congruent, then the triangles are congruent. This theorem is often abbreviated as SAS, and is used in combination with other congruence theorems, such as ASA and SSS, to prove that triangles are congruent.

In the given picture, we can say both triangles has the same side of length 7 and along with it, one more side is of equal length.

and both triangles are having the right-angle,

so we can say that we can prove these triangles congruent by using SAS congruence theorem.

Hence, SAS congruence theorem should be used.

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Answer:

1 - 5 < y < 5

I hope you pass your assignment

The range of solutions for the given inequality is -5<y<5.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -6<1/3(6y + 12)<14.

Here, -6<(2y + 4)<14

-6<(2y + 4)

Subtract 4 on both the sides of an inequality, we get

-10<2y

Divide 2 on both the sides of an inequality, we get

-5<y

(2y + 4)<14

Subtract 4 on both the sides of an inequality, we get

2y<10

Divide 2 on both the sides of an inequality, we get

y<5

So, -5<y<5

Therefore, the range of solutions for the given inequality is -5<y<5.

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0.08/0.2 and 0.2/0.8 are not proportional.

A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.

Given are two numbers, 0.08/0.2 and 0.2/0.8

Checking for if they are proportional or not,

0.08/0.2

Multiplying denominator and numerator by 100,

8/20 = 2/5

And,

0.2/0.8 = 1/4

Since, 0.08/0.2 ≠ 0.2/0.8

Hence, 0.08/0.2 and 0.2/0.8 are not proportional.

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An inverse relation and function is the opposite of a relation and functions.

An ordered pair collection is referred to as a relation. Let's think about the two sets A and B. The cartesian product of A and B, indicated as A x B, is the set of all ordered pairs of the form (x, y), where x A and y B. A relation is any subset of the cartesian product A x B.

The inverse function f-1 takes each element in the range of an original function f and transfers it to the equivalent element in the function's domain. F must be one-to-one and onto since we are mapping the function f backward.

An onto function only has one output for each input, but a one-to-one function only has one input in the domain for each output in the range. This implies that each input has precisely one input for each output in order to have both.

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The probability that at least 12 buy their lunch =  0.887

Given that 73% of students buy their lunch.

⇒ p = 0.73

And q = 1-p

q =  0.27

sample size (the number of student selected) n = 19

We need to calculate the probability that at least 12 buy their lunch.

i.e., P(x ≥ 12)

We use binomial distribution formula, P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

P(X ≥ 12)

= P(X= 12) + P(X= 13) + P(X= 14) + P(X= 15) + P(X= 16) + P(X= 17) + P(X= 18) + P(X= 19) [tex]=~ ^{19}C_{12}(0.73)^{12}(0.27)^{7} + ^{19}C_{13}(0.73)^{13}(0.27)^{6}+ ^{19}C_{14}(0.73)^{14}(0.27)^{5} + ^{19}C_{15}(0.73)^{15}(0.27)^{4} + ^{19}C_{16}(0.73)^{16}(0.27)^{3} + ^{19}C_{12}(0.73)^{17}(0.27)^{2}+ ^{19}C_{12}(0.73)^{18}(0.27)^{1}+ ^{19}C_{12}(0.73)^{19}(0.27)^{0}[/tex]

= 0.1207 + 0.1757 + 0.2036 + 0.1835 + 0.1240 + 0.0592 + 0.0178 + 0.0025

= 0.887

The required proability is  0.887

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Mean distance for group A = 6.01 miles and for group B = 2.17 miles.

In statistics, the mean is the average of all data values given in a data set.

Mean is calculated by adding all the data value and then divided the sum by the total amount of data.

distance in miles for Group A       distance in miles for group B

         11.5                                                  2

          8                                                  

                                                                2.5

         9.2                                                3.23

         6.8                                                 1.3

          4.5                                                1.8

          4.8                                                2.4

         2.5                                                 3

         0.76                                               1.5

                                                                1.8

now mean value for group A = sum of data value/ number of data value

  mean distance = (11.5 + 8 +9.2 +6.8 +4.5+ 4.8+2.5+0.76) / 8

  mean distance for group A = 6.01 miles

mean distance for group B = (2+2.5+3.23+1.3+1.8+2.4+3+1.5+1.8)/ 9

 mean distance = 2.17 miles

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Answer:

Step-by-step explanation:

We have, C(x) = 0.005x3 – 0.02x2 + 30x + 5000

Clearly, the marginal cost, MC (x) = \(\frac{d}{d x}\)C(x)

= \(\frac{d}{d x}\)(0.005x3 – 0.02x2 + 30x + 500)

= 0.005 × 3x2 – 0.02 × 2x + 30 + 0

= 0.015x2 – 0.04x + 30

Now, marginal cost when 3 units arei produced

MC(3)= 0.015(9) – 0.04(3) + 30

= 0135 – 0.12 + 30= 30.015

Tyler drove 40 miles in one hour.

To find how far Tyler drove in one hour, we need to divide the total distance he traveled (52 21/32 miles) by the total time it took him (1 2/3 hours). To do this, we first need to convert the time to a common denominator, which in this case is 32. We can convert 1 2/3 hours to 32/3 hours by multiplying the numerator and denominator of 2/3 by 32/32.

So, we have:

(52 21/32) miles / (32/3) hour = (52 21/32) miles * (3/32) hour

                                                = (52 21/32) * (3/32)

                                                = (52 213/3232)

                                                = (52 63/32) miles/hour

                                                = 40 miles/hour

So, Tyler drove 40 miles in one hour.

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The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.

What is iteration ?

iteration can be defined as the repeating itself to perform a particular task.

Given

X2 is when n=1

X2 = X1+1 = X1 ^ 3 - 5/10

because X1 = -1

so X2  = -1-5/10 = -6/10 = -0.6

X3 is when n=2

X3 = X2+1

= X2 ^ 3 -5/10

because X2 = -3/5

so X3 could be

X3 = (-0.6*-0.6*-0.6) - 5 / 10

X3 = -0.041600

Hence, The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.

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Therefore , the solution of the given problem of trigonometry  comes out to be surface x² + y² + z² = p².

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.

Here,

Given:

p = sinθ sin∅

To Locate:

the equation's surface

Solution:

adding p to both sides of the equation

p sinθ sin∅ = p²

p sinθ sin∅ = p²

p sinθ sin∅ =y

x²+y²+z²=y

x² + y² - y+ z² = 0

x²+ (y - 1/2)²+ z² = 1/4

r² =1/4, r= √1/4,

The surface of the sphere having a radius of 1/2 and a center at (0, 1/2, 0) is designated as 1/4.

Sphere-centered coordinates

x = sin p sin

y = sin(p), sin(p),

z = p cos∅

x² + y² + z² = p²

Therefore , the solution of the given problem comes out to be surface

x² + y² + z² = p².

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Answer:

gay

Step-by-step explanation:

gayayayayayayaydyfyfaygaygagya

The coeficient of y² in the expression is the number 3

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

3y² + 4x

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.

3 is the coefficient of y²

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Answer:

C = $30 + $0.05M

Step-by-step explanation:

We know that renting the car will cost $30, regardless of whether you drive it any where or not

So far

C = $30

On the end of this equation, we want to be able to add another value, that can vary depending on the quantity of M (number of miles)

The second value is $0.05 multiplied by how many miles are travelled

Also expressed as $0.05M

Finally, just fix the two parts together

Answer:

Step-by-step explanation:

We know that renting the car will cost $30, regardless of whether you drive it any where or not

So far

C = $30

On the end of this equation, we want to be able to add another value, that can vary depending on the quantity of M (number of miles)

The second value is $0.05 multiplied by how many miles are travelled

Also expressed as $0.05M

Finally, just fix the two parts together

C = $30 + $0.05M

The average rate of the given function is 2.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is h(x)=-x²-x+5 and the interval is -6≤x≤2.

x={-6, -5, -4, -3, -2, -1, 0, 1, 2}

y=-x²-x+5

When x=-2

y=-(-2)²-(-2)+5

y=-4+4+5

y=5

When x=-1

y=-(-1)²-(-1)+5

y=5

When x=0

y=5

When x=1

y=-1-1+5

y=3

When x=2

y=-(2)²-(2)+5

y=-1

Now, rate using (1, 3) and (2, -1), we get

m =(-1-1)/(2-3)

m=2

Therefore, the average rate of the given function is 2.

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The circle equations for circles with diameters of 12 units that lie on the y-axis are:

We want to find the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis, now, remember that the general equation for a circle of radius R and a center (a, b) is:

(x - a)^2 + (y - b)^2 = R^2

If we want a circle that lies on the y-axis, then a = 0, and if the diameter is 12 units, then the radius is R = 6 units.

Then the equation is something like:

x^2 + (y - b)^2 = 6^2 = 36

The two circle equations with this form are:

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The maximum height reached by the ball is 20 units at 1.2 unit time.

The extrema of a function are the maxima and minima. The highest and minimum values of a function inside the specified ranges are known as maxima and minima, respectively. Absolute maxima and absolute minima are terms used to describe the function's maximum and minimum values, respectively, throughout its full range.

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.

The equation is given as

h = [tex]-10t\x^{2} + 24t + 5.6[/tex]

Differentiating both side with respect to t we get

[tex]\frac{dh}{dt} = -20t + 24[/tex]

To reach maximum value [tex]\frac{dh}{dt} = 0[/tex]

⇒20t = 24

⇒ t = 1.2

So the maximum height reached = [tex]-10 *(1.2)\x^{2} + 24*1.2 + 5.6 = 20[/tex]

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A)  13 meters

B)  2.3 centimeters

=================================================

Work Shown:

Part A

The ruler diagram shows the building on paper is 6.5 cm wide. The right side of the building lines up with the midpoint marker between 6 and 7.

1 cm = 2 m

6.5*(1 cm) = 6.5*(2 m)

6.5 cm = 13 m is the width of the building in real life

Or you can solve it like this

(1 cm)/(2 m) = (6.5 cm)/(x meters)

1/2 = 6.5/x

1*x = 2*6.5

x = 13

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

Part B

(1 cm)/(2 m) = (x cm)/(4.6 m)

1/2 = x/4.6

1*4.6 = 2*x

4.6 = 2x

x = 4.6/2

x = 2.3 centimeters is the height of the building in the drawing

Therefore the expression simplified using only positive exponents is 10h^4v^22.

An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ. For example, 2⁻⁴ = 1 / (2⁴) = 1/16.

A mathematical procedure called multiplication shows how many times a number has been added to itself. The multiplication symbol (x) or (*) are used to denote it. A mathematical process that shows how many equal amounts add up to a given number is called division.

To simplify the expression using only positive exponents, we need to make sure that all the exponents are positive.

We can simplify the expression:

(2h^7v^-3)/(5h^-4v^5)^-5

= (2h^7v^-3)/(1/(5h^-4v^5)^5)

= (2h^7v^-3) * (5h^4v^25)

= 10h^4v^22

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The radius of convergence R = 1/b

The radius of convergence for a power series is given by the formula:

1/R = lim sup |bn|^(1/n)

In this case, the radius of convergence is given by:

1/R = lim sup |bn|^(1/n) = lim sup b^(1/n) = b^(1/n) as b > 0.

So R = 1/b

As for the interval of convergence, it is the set of values of x for which the series converges. The series converges when |x-a| < R, and diverges when |x-a| > R. So the interval of convergence is (a-R, a+R) which is (a-1/b, a+1/b)

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Answer:

(- 1, 9 )

Step-by-step explanation:

6x - y = - 15 → (1)

x + 2y = 17 → (2)

multiplying (1) by 2 and adding to (2) will eliminate y

12x - 2y = - 30 → (3)

add (2) and (3) term by term to eliminate y

13x + 0 = - 13

13x = - 13 ( divide both sides by 13 )

x = - 1

substitute x = - 1 into either of the 2 equations and solve for y

substituting into (2)

- 1 + 2y = 17 ( add 1 to both sides )

2y = 18 ( divide both sides by 2 )

y = 9

solution is (- 1, 9 )

A semi-circular protractor with a diameter of 15 cm has the perimeter of 38.5 cm.

What is the perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

The formula for perimeter of a semi-circle is -

πr+2r

Where r is the radius of the semi-circle.

The diameter d of semi-circle is 15 cm.

The radius of the semi-circle is -

r=d/2

r=15/2

r=7.5 cm

Plugging the values in the equation -

=πr+2r

=(3.14)(7.5)+2(7.5)

=23.5+15

=38.5 cm

Therefore, the value for perimeter is obtained as 38.5 cm.

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