The table below shows how long it took Tamara to swim different distances.
Time
(in minutes) (x)
0.5
1.25
2.0
2.0
2.5
Distance
(in meters) (y)
50
100
200
225
300
A. List the domain and range values.
B. Is the relation a function? Explain. Use the table to support your argument.

the volume of a region bounded by the curve and the -axis between is 19.47787445 cubic units.

What is volume of cone?

The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.

So the

V = (1/3)πr²h.

V = π ∫ (x^2)^2 dx - π ∫ 0 dx = π ∫ (x^4) dx - 0 = π (x^5 / 5)

Evaluating from 2 to 1 yield the following:

π (2^5 / 5 - 1^5 / 5) = π (32/5 - 1/5) = 31π/5 cubic units, approximately equal to 19.47787445 cubic units

Hence, the volume of a region bounded by the curve and the -axis between is 19.47787445 cubic units

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Answer: y=8x+7

Step-by-step explanation:

8 is the difference between the numbers (slope)

7 is the starting value (y-intercept).

Answer:

y = 8x + 7

Step-by-step explanation:

m = y2-y1 / x2-x1

m = 31-23 / 3-2

m = 8/1

m = 8

y=8x+b

(0,7)

7=8(0) + b

7=0+b

b = 7

y = 8x + 7

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Therefore ,we  reject H₀   Percentage of type A blood  donations differs from 40% (percentage of population having type A blood)

According to the scientific method, a theory cannot be regarded as scientific unless it has been tested. The majority of scientific hypotheses are based on observations from the past that cannot be adequately explained by the state of knowledge at the time.

Here,

We are going to develop a proportion test.

Information we have:

Proportion   P₀   =  40 %      P₀   =  0,4  (percentage of population having type A blood)

Sample size    n   =   150

Sample  mean   P  =  82/ 150      P  = 0,5466

As  P₀  =   0,4      Q₀  =  0,6     P₀*Q₀   =  0,24

1.-Test Hypothesis:

H₀    null hypothesis                            P₀   =   0.4

Hₐ   alternative hypothesis                 P₀   ≠   0.4

2.- signficance level

    a  )   α  =  0.01    we have a two tail-test      α/2    =   0.005  

    b  )   α  =  0.05                                               α/2    =   0.025

Then  from t-student table we get t(c)   n  = 150    df =  149

    a  )   α/2    =   0.005             t(c)    =  2.581

    b  )   α/2    =   0.025             t(c)    =  1.962

3.-Compute t(s)

t(s)   =   (  P  -  P₀ )  / √P₀Q₀/n  

Plugging  in known values  

t(s)   =[ ( 0.5466 -  0,4  )*√150 ] / √0.24

t(s)   = 0,1466 * 12.25 / 0.4899

t(s)   =  3.6657

Compare t(s)  and  t(c)

t(s)  >  t(c)       3.6657  >  2.581      

Then  t(s) is out of the acceptance region  we reject  H₀.

Simple inspection led us see that for

α/2    =   0.025             t(c)    =  1.962

The situation is the same

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To find rank of mark

From the given options 1st option is correct

both 1 and 2 need

Given statements are

1. there are 45 students in class.

2. 12 students scored less than mark.

we need both 1 and 2 statements to find the rank of mark

without knowing the class strength we cannot find the rank of marks

and we should also know that how many students have scored less than mark in 2nd statement it is given that 12 students scored less than mark.

from the given options 1st option is correct

both 1 and 2 need

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Answer: 8

Step-by-step explanation:

fifty-two divided by six rounded down is eight.

Answer:

b. Write the equation/inequality:

I think I'm not sure

Answer:

y = [tex]\frac{1}{2}[/tex]x + 2

Step-by-step explanation:

Parallel lines have the same gradient, so

y = [tex]\frac{1}{2}[/tex]x + c

Put in your point (2,3):

(3) = [tex]\frac{1}{2}[/tex](2) + c

3 = 1 + c

3 - 1 = c

2 = c

So

y = [tex]\frac{1}{2}[/tex]x + 2

It is false, that the margin of error of a confidence interval is the error from biased sampling methods.

The margin of error of a confidence interval is the amount of accuracy in a sample with respect to the population. It is calculated by taking the sample standard deviation and dividing it by the square root of the sample size. The margin of error helps to quantify the reliability of estimates and provides a range within which the population parameter is likely to fall. It does not refer to errors in sampling methods, which are typically a result of bias. Bias is a systematic error that arises from the sampling procedure, resulting in estimates that are not an accurate representation of the population.

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Answer:

2/10

Step-by-step explanation:
0.2 is 2 tenths. and 2/10 is also two out of ten. two out of ten is two tenths. therefor it is 2/10

The equation of a line passes through the given point and the slope is y -3 = 1/2(x +2).

Here we have to find the equation of the line that passes through (-2, 3).

Data given:

Line passes through the point = (-2,3)

Slope of the line = 1/3

The formula for the equation of the line:

y - y1 = m(x -x1)

m = slope of the line

(x1, y1) = point on the line

Now put the values in the formula, we have:

y -3 = 1/3(x -(-2))

y - 3 = 1/3( x +2)

Therefore the equation of the line is y -3 = 1/3(x +2).

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240240 many different possible rankings are there.

What is combination?

In mathematics, a choice is made from a set of various elements whenever the order of a choices is unimportant (unlike permutations). For instance, there really are three possible combinations of the two fruits, an apple and a pear, if three fruits are provided, like an apple, a tangerine, and a pear. Formally speaking, a set S's k distinctive components make up a subset known as a k-combination. In other words, 2 combinations are identical only if all of their members are the same. (How the people are arranged in each set is irrelevant.) how many k-combinations there are for a set of n components

The formula below calculates how many ways there are to make an ordered list of "unique components chosen from a set of 'n' elements, in accordance with the arrangement principle:

P(N,R)=  [tex]\frac{n!}{n-r!}[/tex]

p(14,5)= 14!/9!

=14*13*12*11*10

=240240

Hence, 240240  many different possible rankings are there.

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the vallue of k is 25,  positive integers 6^6 and 8^8.

What is LCM?

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers. Consider the integers 2 and 5. There will be different multiples for each. Least Common Multiple is the meaning of the abbreviation LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

Only the primes 2 or/and 3 are present in LCM, hence k cannot have any other primes.

In light of the fact that the power of 3 in LCM is greater than the powers of either the first or second number, k must have 312 as its multiple (otherwise, how would 312 appear in LCM?).

Because at least one of the numbers must have the words (224) and (312) as its factors in order for (224) * (312) to be a common multiple, b must now equal 12. (maybe other numbers).

As can be seen, the 224 component is already taken care of by 88.

As a result, k must handle the LCM's 312 component.

Since a can take on any value between 0 and 24 (inclusive) without modifying the LCM's value, the value of k is therefore (2a) * (312).

Hence the vallue of k is 25.

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The equation of a vertical line is x = c, where c is a constant. So, in this case, x = -5, since the point (-5, -2) is on the line.

The equation of a vertical line is x = c, where c is a constant. A vertical line is a line with all points having the same x-coordinate. This means that all points on the line will have the same x-value, and the y-value will be different. In this case, the point (-5, -2) has an x-value of -5. This means that all points on the line will have an x-value of -5. This gives us the equation x = -5, which is the equation of the vertical line passing through the point (-5, -2).

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The probability of surviving for 3 years will be 54.8.

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

one hundred eighty patients were treated for disease x from 2007 to 2009.

The probability of surviving for 3 years=P 2007*P 2009*P 2010.

According to given information,

The probability of surviving for 3 years will be 54.8.

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Step-by-step explanation:

Simulteanous Equations are multiple equations with corresponding number of unknown variables.

They can be solved by 2 methods: Substitution and Elimination Method.

x = 4

y = 8

We will use the Elimination Method since the question specify as so.

4x - 3y = -8 (Equation 1)

9x - 3y = 12 (Equation 2)

By using Equation 1 - Equation 2,

4x - 9x - 3y - (-3y) = - 8 - 12

-5x - 3y + 3y = - 20

-5x = - 20

x = - 20 ÷ - 5 = 4

Now we substitute x = 4 into Equation 1.

4(4) - 3y = - 8

16 - 3y = - 8

-3y = - 8 - 16

-3y = - 24

y = - 24 ÷ - 3

= 8

Therefore the varables are:

x = 4

y = 8

When taking the square root of both sides of this equation, the square roots may depend upon equation.

Let, the equation be:

x² = 4

May be the Equation has two solutions:

x = ±√4 = ±2

Equations involving distances, such as those obtained when using the Pythagorean theorem, have solutions. Negative solutions are irrelevant because there are no negative distances.

    c² = a² + b²

⇒ c = √(a² + b²) .

Generally these are considered irrelevant as they are useless. Mathematically, negative time values ​​work in the equation, but have no real interpretation.

Expressions such as:

x⁶ = 4

This, has 2 real and 4 complex solutions.

Again,

x³ = ±2 . after rooting both sides

The two real solutions are :

x = ±∛2

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Answer:

The length is 33.37 yards of the hypotenuse.

What is Congruence of triangles ?

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In congruent triangle, corresponding sides are equal.

We know, Pythagorean theorem is

Hypotenuse ² = perpendicular² + base²

Let x = be the measure of length of two legs of a right triangle

H² = x² + x²

H² = 2x²

We know, x = 23.6 yards

H² = 2(23.6)²

H² = 1113.92

H = 33.37 yards

Hence, the length is 33.37 yards of the hypotenuse.

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The slope of a line perpendicular to the line y = -4x + 12 is 4.

Slope is calculated by taking the difference in the y-coordinates divided by the difference in the x-coordinates of two points on a line. Since we only have one point, we cannot calculate the slope. The slope of the original line is -4.

To find the slope of the line perpendicular to it, we take the negative reciprocal of the original slope.

Therefore, the slope of the perpendicular line is 4.

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The solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Solve as shown below,

(a) 8 × 3 = 24

(b) –7 × 5 = -35

(c) –6 × (–9) = -(-54) = 54

(d) 8 ÷ (–2) = 8 × 1 / (-2) = - 4

(e) –24 ÷ (–3) = -24 ×  1 / (-3) = 8

(f) –36 ÷ 6 = -36 × 1 \ 6 = -6

Therefore, the solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.

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The greatest number of servings that can be made from this package is 11.

This can be illustrated through an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Since the unopened package of cream cheese contains 8 1/4 ounces of cream cheese and a serving is 3/4 of an ounce.

The greatest number of servings that can be made from this package will be simply be gotten by dividing the fractions that are given in the question. In this case this implies that we have to divide 8 1/4 by 3/4. This will be illustrated as:

= 8 1/4 ÷ 3/4.

= 11

The above calculation simply shows that the greatest number of serving will be 11.

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The inverse of a conditional statement is when both the hypothesis and conclusion are negated.

What is hypothesis and conclusion?

A conditional statement's first clause, or "if," contains the hypothesis.

A conditional statement's second, or "then," component is the conclusion. A hypothesis produced the conclusion.

You can enroll in a reputable college if you earn good grades.

You will get into a good college if you get good grades, and the part that comes after the "if" is known as a hypothesis.

The part that comes after the "then" is known as a conclusion. An "If-then" or "conditional statement" is a series of hypotheses followed by a conclusion.

The opposite of a conditional statement is when the hypothesis and conclusion are both negated.

This is done by negating both the "If" part (p) and the "then" part (q).

The conditional statement is known as p q in geometry. The inverse is written as pq, where q stands for the negation of the statement or not.

Hence, the inverse of a conditional statement is when both the hypothesis and conclusion are negated.

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Answer: Inverse

Step-by-step explanation: Inverse Statements: The inverse of a conditional statement is found by negating the hypothesis and the conclusion. That means you will write the opposite for both parts of the conditional statement.

Example: statement: If two angles are vertical angles, then they are congruent.

Inverse: If two angles are not vertical angles, then they are not congruent. This is not valid.

The original size of the bag is given by the equation A = 14 ounces

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the original size of the bag be = A

Now , the equation will be

The increased size of the bag = 16.8 ounces

The percentage increase in the size of the bag = 20 %

So , the equation for the percentage increase in the size of the bag is

Original size of the bag + ( 20/100 ) x percentage increase in the size of the bag = increased size of the bag

Substituting the values in the equation , we get

A + ( 20/100 ) x A = 16.8

( 120 / 100 ) A = 16.8

On simplifying the equation , we get

Multiply by 100 on both sides of the equation , we get

120A = 1680

Divide by 120 on both sides of the equation , we get

A = 14 ounces

Therefore , the value of A is 14 ounces

Hence , The original size of the bag is 14 ounces

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The 2x2 linear system can be solved by the method of substitution .

In the question ,

it is given that ,

a 2x2 linear system is the system in which there are 2 equations with two unknown ,

Step (1) : we take the value of 1 variable from 1 equation ,

Step(2) : we substitute the value of that variable in equation(2) and solve to get the solutions .

let us understand the method of substitution with the help of example .

Let the 2x2 linear system be 2x + 3y = 14   and x + y = 12

From , x+y=12 , we get

x = 12 - y ,

Substituting the value of x in 2x + 3y = 14 ,

we get ,

2(12 - y) + 3y = 14

So , y = -10  

putting in x = 12 - y ,

we get ,

x = 12-(-10) = 22 .

Therefore , the method to solve the 2x2 linear system is explained .

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The equation of the line L is y = 4 - x

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

y = x/20(x² - 10)

Resulting equation: x³ + 10x - 80 = 0 for 0 ≤ x ≤ 5

Represent the equation of the line L with y = L

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

L = x/20(x² - 10)

Multiply both sides by the denominator of x/20(x² - 10)

So, we have

20L = x(x² - 10)

Open the  brackets

20L = x³ - 10x

Set to 0

x³ - 10x - 20L = 0

Recall that

x³ + 10x - 80 = 0

So, we have

x³ + 10x - 80 = x³ - 10x - 20L

Evaluate the like terms

20x - 80 = - 20L

Divide through by -20

L = 4 - x

Substitute L = 4 - x in y = L

y = 4 - x

Hence, the equation is y = 4 - x

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The periodic table is useful for understanding atomic properties that show periodic trends. Periodic trends are specific patterns that are present in the periodic table that illustrate different aspects of a certain element, including its size and its electronic properties.

Percent 20.5% of 78 is 16 rounded to the nearest tenth.

How to calculate percentage?

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Let x% of 78 is 16

⇒ [tex]\frac{x}{100}\times 78=16[/tex]

⇒ x = [tex]\frac{16\times 100}{78 }=\frac{1600}{78}=20.5[/tex]

Therefore, 20.5% of 78 is 16.

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By Midsegment theorem we find the length of KL is 8.

A triangle is a three-sided polygon that consists of three edges and three vertices.

We know by midsegment theorem, the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

The length of midsegment KL =1/2 of the length of the third segment FH.

KL = 1/2(FH)

KL = 1/2(16)

KL is sixteen divided by 2.

KL = 8

Hence, the length of KL is 8.

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Answer: $18.50

Step-by-step explanation:

Take 277.50 divided by 15 = $18.50

The required price of each tube for rent is given as $18.6.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Renting 15 tubes for a float down the Ichetucknee River costs $277.50 for a group.
So,
Let the rent of each tube be x,
According to the question,
15x = 277.50
x = 277.50 / 15
x = 18.6

Thus, the required price of each tube for rent is given as $18.6.

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