match the vocabulary to the proper definition. 1 . improper fraction a number that divides evenly into a given number 2 . coefficient expressions, equations, and operations involving variables 3 . algebraic the bottom part of a fraction; represents the whole 4 . denominator a fraction with a numerator that is larger than or equal to the denominator 5 . factor the number in an algebraic term

The exact value of all six trigonometric functions from the given below point (-4,5) on the terminal side of an angle θ in standard position are as follow:

sinθ = (-4/√41) ,   cosecθ = ( -√41/4)

cosθ =(5/√41) ,    secθ = ( √41 /5)

tanθ =(-4/5) ,        cotθ = ( -5/4)

As given in the question,

Given point ( x, y) = (-4,5)  which is below on the terminal side of an angle θ in standard form.

Coordinate y represents the perpendicular side

Coordinate x represents the base

Using Pythagoras theorem ,

Let 'r' represents the hypotenuse .

r = √x² + y²

 = √(-4)² + 5²

 = √16 + 25

 = √41

Exact value of all the trigonometric functions are as follow:

sinθ = (x/r)

        = (-4 /√41)

cosθ = ( y /r)

       = ( 5/ √41 )

tanθ = ( x/y)

       = ( -4 /5)

cosecθ = ( r / x)

            = ( -√41 /4)

secθ = ( r/y)

        = ( √41/ 5)

cotθ = ( y/x)

        =( -5/4)

Therefore, the exact value of all six trigonometric functions from the given below point (-4,5) on the terminal side of an angle θ in standard position are as follow:

sinθ = (-4/√41) ,   cosecθ = ( -√41/4)

cosθ =(5/√41) ,    secθ = ( √41 /5)

tanθ =(-4/5) ,        cotθ = ( -5/4)

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The range of f(x) = 3/4ˣ - 4 is all real numbers greater than -4. I.e. (-4, ∞).

Given,

The function, f(x) = 3/4ˣ - 4

We have to find the range of the function;

Function;-

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Domain and Range of a Function;-

It is the collection of all potential function inputs. For instance: F(x) = x2 in the illustration below. The domain is the set of all the inputs, and the range is the set of all the outputs.

Here,

The function, f(x) = 3/4ˣ - 4

That is,

The range of f(x) = 3/4ˣ - 4 is all real numbers greater than -4. I.e. (-4, ∞).

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The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

Given that

In a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal. Calculate a 90% confidence interval for the percentage of all U.S. adults who support the proposal based on the results of this poll (at the time of the poll). Complete the table below after that. Carry your calculations to a minimum of three decimal places.

We have to find the lower limit of 90%.

We know that

In a poll of 200 randomly selected U.S. Among adults, 104 expressed support for the novel idea.

p-hat = 104/200 = 0.52

ME = z×√[pq/n] = 2.5758×√[0.52*0.48/200] = 0.091

Now, the lower limit of the 90% confidence interval well be

p-hat-ME = 0.52-0.091 = 0.429

Therefore, The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

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The values of mean and standard deviation of the total passenger baggage weight in respected cases of commuter airline is given below:

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are the probability that something happens divided by the probability that it doesn't happen.

Relative Frequency Definition.

Subjective Probability.

a.) If there are only two passengers on the plane, the mean of the total passenger baggage weight would be 76 pounds and their standard deviation would be10 pounds.

b.) The probability would be 0.1611 that the total passenger baggage weight from two passengers exceeds 90 pounds.

c.) If the plane has ten passengers, the mean of the total passenger baggage weight would be 380 pounds and their standard deviation would be 30 pounds.

d.) The probability would be 0.1515 that the pilot will not take off.

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The function whose graph is a straight line ; slope is constant and highest degree is one then that function is known as linear function.

Linear function:-

Thus, an function whose graph is a straight line ; slope is constant and highest degree is one then that function is known as linear function.

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The flux of the given function f = x³i + y³j + z³k is given by f',

f' = 3(x²i + y²j + z²k)

Given, f = x³i + y³j + z³k

we have to find the flux of the given function f = x³i + y³j + z³k

On partial differentiating the function, we get

f' = 3x²i + 3y²j + 3z²k

f' = 3(x²i + y²j + z²k)

So, the flux of the given function f = x³i + y³j + z³k is given by f',

f' = 3(x²i + y²j + z²k)

Hence, the flux of the given function f = x³i + y³j + z³k is given by f',

f' = 3(x²i + y²j + z²k)

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We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. Hence, it is TRUE

The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do. The ANOVA test is used by analysts to ascertain how independent factors in a regression analysis affect the dependent variable.

ANOVA basically stands for analysis of the variance.

Hence, according to above statements, given fact is true.

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Answer:

12

Step-by-step explanation:

Use 5 for m

Use -3 for x

Use 7 for y

y =mx + b

7 = (5)(-3) + b

7 = -5 +b

12 = b

The  both hypotheses in statistical symbols and in everyday language is:

Null Hypothesis: H₀:μ=15 micrograms

Alternative Hypothesis: H₁:μ>15 micrograms.

The null hypothesis in inferential statistics is that two possibilities are the same. The null hypothesis states that the observed difference is attributable solely to chance. The likelihood of the null hypothesis being true can be calculated using statistical testing.

Given,

The federal government has established 15 micrograms per liter as the maximum safe level of lead in drinking water. The Linois state department of health samples water from a large sample of residents' homes because it suspects that the water in the city of Steel is unsafe.

Null Hypothesis:

The federal government has established that  the maximum safe level of lead in drinking water is 15 micrograms.

H₀:μ=15 micrograms

Alternative Hypothesis:

The federal government has established that  the maximum safe level of lead in drinking water is more than 15 micrograms.

H₁:μ>15 micrograms.

Null Hypothesis: H₀:μ=15 micrograms

Alternative Hypothesis: H₁:μ>15 micrograms

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The equation of the graphed parabola is y=a (x + 3) ^2 -4.

Given that parabola is plotted, concave upwards, with vertex located at coordinates (-3, -4).

   According to the question, we need to find the equation of the graphed parabola.

The equation of a quadratic function of vertex (h, k) is given by y=a + k

In the above equation the leading coefficient is "a"

We are given point (-3, -4).

We need to put the value of h=-3 and k=-4 and the required equation, and we will get the equation as: -

y=a (x + 3) ^2 -4

    Therefore, the equation of the parabola that is plotted, concave up, with vertex located at coordinates (-3, -4) is y=a (x + 3) ^2 -4.

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A linear function table  is a table having a constant rate of  change between  its datapoints  

A linear equation is is an equation that consists of each variable raised with a maximum of one degree. the linear equation in terms of variables x and y can be written in the form  of  y = mx + c, where m is the slope and x is the independent variable, and y is the dependent variable when the data points of the given  table are potted in   a graph, we get a straight  line for a linear function table, a such function must  have a constant  slope in between its points

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The speed of rocket when it is very far away from the the rocket is 9990 m/s.

In the given question, a rocket is launched straight up from the earth's surface at a speed of 15000 m/s.

v = 15000m/s = 1.5×10^{4} m/s

We have to find the speed of rocket when it is very far away from the the rocket.

As we know,

Mass of Earth(M) = 5.972×10^{24} kg

Radius of Earth(R) = 6.371×10^{6} m

The value of G = 6.67×10^{-11}

Applying law of conservation of energy,

-GMm/R + 1/2 mv^2 = 0+1/2 mV^2

Taking common m on both side, we get

-GM/R + v^2/2 = V^2/2

Substituting the value

-(6.67×10^{-11})(5.972×10^{24})/ 6.371×10^{6} + (1.5×10^{4})^2/2 = V^2/2

V^2/2 = -6.67×5.972×10^{-11+24}/ 6.371×10^{6} + 2.25×10^{8}/2

V^2/2 = -6.252×10^{13-6} + 1.125×10^{8}

V^2/2 = -6.252×10^{7} + 11.25×10^{7}

V^2/2 = 4.998×10^{7}

Multiply by 2 on both side we get

V^2 = 9.996×10^{7}

V^2 = 99.96×10^{6}

Taking square root on both side, we get

V = 9.99×10^{3}

V = 9990 m/s

Hence, the speed of rocket when it is very far away from the the rocket is 9990 m/s.

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Answer:

414.69

Step-by-step explanation:

2*pi*r

The number of small cups is 10, and the number of large cups is 50.

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form y=mx+c.

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

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p = the number of small cups sold,

q = the number of large cups sold,

Salma sold 60 cups then the equation becomes:

p + q = 60                     ---------------(1)

Salma sold 60 cups of lemonade total of 920 ounces then the equation becomes:

12p + 16q = 920            ---------------(2)

Multiplying the equation 1 by 12 then substracted from equation 2, we get:

12p + 16q = 920

12p + 12q = 720

4q = 200

q = 50

Substituting q = 50 into equation (1) we get,

p + 50 = 60

p = 10

Hence, the number of small cups is 10, and the number of large cups is 50.

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The equation given is linear, not proportional, and thus, there is no constant of proportionality.

Here we have the following linear equation:

y = 5*x - 1/3

The general linear equation is:

y = m*X + b

Where m is the slope and b is the y-intercept, so in this case we have:

slope = 5

y-intercept = -1/3

Partocularly, when the y-intercept is 0 we have a proportional relation:

y = m*x

And then m is called the "constant of proportionality"

In this case the y-intercept is not zero, thus, there is no constant of proportionality, just a slope.

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Answer:

b = -2

Step-by-step explanation:

y = mx + b

use -2 for m

use 1 for x

use -4 for y

-4 = (-2)(1) = B

-4 = -2 + b  Add two to each side

-2 = b

[tex]\huge \boxed{\sf -2}\\\\\\\displaystyle \sf Line\ equation\ y=mx+b \\\\Substituting \ m=-2 \ and\ (1,-4) \\\\-4=-2(1)+b\\\\-4=-2+b\\\\Adding\ 2\ to\ each\ side \\\\-4+2=-2+b+2\\\\-2=b[/tex]

P-values means in this problem is that to reject a null hypothesis it should be smaller . If p-value is large , means the alternate hypothesis is weak, so you do not reject the null.

In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.

The p-value serves as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected.

A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis .The p-value approach to hypothesis testing uses the calculated probability to determine whether there is evidence to reject the null hypothesis.

According to the question,

If h₀ ( null hypothesis ) is true then there is a chance equal to the p-value that the average number of hours women work each week is 83 hours

It means if our p-value is bigger that it couldn't get any evidence to reject null hypothesis But if h₁ (alternative hypothesis ) is true then there is chance to the p-value that the average number of hours women work is not more 83 hours or more means the to p-value is smaller and stronger to reject null hypothesis.

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The Fundamental Theorem of Algebra states that a polynomial of fifth degree will have five roots, which is the case with this particular polynomial.

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The correct statement is: 'A standard normal distribution has a mean of 0 and a standard deviation of 1 '

The correct answer is an option (b)

In this question, we need to complete given statement.

We know that the normal distribution is a symmetrical and bell-shaped distribution.

In standard normal distribution the mean, median and mode are all equal. Also, it always has a mean of zero and a standard deviation of one.

So,  A standard normal distribution has a mean of 0 and a standard deviation of 1 .

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It's always true that a reflection on the x-axis followed by a reflection on the y-axis leaves a point in its original location.

What is a coordinate axis?

A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space.

When a reflection in the x-axis followed by a reflection in the y-axis leaves a point in its original location. Is it always true?

The answer is true.

Reason: For example, piece of graph paper into 4 pieces, draw this same thing on all four:  

In this condition reflection in the x-axis followed by a reflection in the y-axis leaves a point in its original location of different color is yes.

Hence, it's always true that a reflection on the x-axis followed by a reflection on the y-axis leaves a point in its original location.

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The polynomial for the given zeros is p(x) = x⁴ + 4x³ - 3x² - 12x. The correct answer is option (B).

The factor theorem for a polynomial p(x) states that for some real number a if p(a) = 0, then (x - a) is one of the factors of p(x).

Given that,

The zeros for a polynomial are 0, -4 and√3.

As per the factor theorem the polynomial for zeros a, b, c  and d can be written as,

p(x) = (x - a)(x - b)(x - c)(x - d)

Thus the polynomial for the given zeros is,

(x - 0)(x - (-4))(x - √3)(x + √3)

= x(x + 4)( x² - 3)

= x(x³ + 4x² - 3x - 12)

= x⁴ + 4x³ - 3x² - 12x

Hence, the required polynomial is p(x) = x⁴ + 4x³ - 3x² - 12x.

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According to reserch about 18 percent people worldwide having sprinter gene.

In the given question, we have to find how many people have the sprinter gene.

As we know that;

The ACTN3 gene is the recently identified "sprinters gene."

A gene, as we already stated, codes for a protein. Alpha-actinin-3 is designated by ACTN3. This protein, which can only be found in fast twitch muscle fibres, gives muscles their explosive ability.

In order to summarise the genetic component, an individual has the ACTN3 gene if alpha-actinin-3 is present in muscle cells. They are therefore better suited for quick movements.

According to reserch about 18 percent people worldwide having sprinter gene.

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The graph of the solution set of the given inequality can be seen in the image at the end.

Here we have the following inequality:

-0.96 ≥ x*0.3

To solve this, we need to isolate the variable x in one of the sides of the inequality.

To do that, we need to divide both sides by 0.3

-0.96/0.3  ≥ x*0.3/0.3

-3.2 ≥ x

So our variable x is smaller than or equal to -3.2

Then the graph will be a closed circle at x = -3.2 and a line that extends to the left side.

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The correct option is option (d). The utility will be maximum on indifference curve below I.

Indifference curve:

An indifference curve is a graph that shows the combination of two products that provide consumers with equal satisfaction and utility. Each point on the indifference curve indicates that the consumer is indifferent to his two points, all delivering equal utility.

The equation of a typical indifference curve is, U(x,y)=c

where the constant c stands for the utility level achieved on the curve

Since consumer has an income of $48 which means consumer budget line initially was,. 4x+4y=48 ---(1)

And final budget line after price change is 12x+4y=48 ---(2)

With the above budget line it is impossible to have any of the indifference curve. Because for equilibrium Budget line should be tangent to Indifference curve and thus equilibrium will be below point D.

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Complete question :

Refer to the following indifference map for a consumer who has a income of $48 to spend on goods x and y and the market price of x and y are both $4.now suppose the price of good x increases to $12 while the price of good y remains $4. utility will be maximized on which indifference curve?

a) I

b) II

c) III

d) on an indifference curve below I

The four parent functions are Linear Functions, Parabolas and Quadratic Functions, Polynomial Functions - Cubic Functions and Absolute Value Functions.

In the given question we have to write the four parent function.

As we know that;

The simplest function in a family of functions, a parent function maintains the definition of the entire family.

There are several basic functions that we run with frequently in math. These fundamental functions include the square root function, basic polynomials, absolute values, and rational and exponential functions.

The 4 parent functions are;

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Answer:

Ways to choose a set two balls of the same color:

[0.5 * (b) * (b - 1)] + [0.5* (r) * (r - 1)]

Different colors:

0.5 * [(b) * (r) + (r) * (b)] = 0.5 * (2 * b * r)  

= b * r

Any two balls

0.5 * (b + r) * (b + r - 1)

= 0.5 * [b * (b + r - 1) + r * (b + r - 1)]

= 0.5 * [b^2 + b * r - b  + b * r + r^2 - r]

= 0.5 * [b^2 - b + r^2 - r + b * r + b * r]

= 0.5 * [b * (b - 1) + r * (r - 1) + 2 * b * r]

= 0.5 * (b * (b - 1)) + 0.5 * (r * (r - 1)) + 0.5 * (2 * b * r)

= [0.5 * (b * (b - 1)) + 0.5 * (r * (r - 1))] + [b * r]

= Number of ways of choosing two balls of the same color + number of ways of choosing two balls with different colors

Step-by-step explanation:

A  water bottle would have 600 milimeters.

What is multiplication?

In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product. In the multiplication problem, 6 9 = 54, the numbers 6 and 9 are factors, and 54 is the product.

If one fluid ounce has approximately 30mm.

then 20 fluid ounce will have = 30 * 20

                                                 = 600 millimeters.

Hence, a water bottle would have 600 milimeters.

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the probability of drawing a green marble, putting it aside, and then drawing another green marble is 3/68

Total 17 marbles

4 - blue marbles

6 - green marbles

2 - red marbles

The rest - yellow marbles

Probability of drawing red first:

P(red) = number of red / total number = 2/17

Probability of drawing green second, without replacement:

P(green) = number of green / number left in the bag = 6/16 = 3/8

Probability of red and green in order:

P = P(red)*P(green) = 2/17*3/8 = 3/68

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The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .

In the question ,

it is given that ,

Option(a) ,  

R is a relation on set of all people where (a,b) is in R if a is taller than b .

Reflexive : NO , because "a" cannot be taller than "a" itself .

Symmetric : NO , because if "a" is taller than "b" , then "b" will be shorter than "a" .

Transitive : YES , because if "a" is taller than "b" and "b" is taller than "c" , then "a" is taller than "c" .

Option(b)

R is a relation on set of integers > 0 where (a,b) is in R if a divides b .

Reflexive : YES , because every number divides itself .

Symmetric : NO , because if "a" divided "b" , then "b" may not divide "a" .

Transitive : YES , because if "a" divided "b" and "b" divides "c" , then "a" must divide "c" .

Option(c)

R is a relation on set of all people where (a,b) is in R if a is married to b .

Reflexive : NO , because marriage is between two people , and "a" cannot marry "a" .

Symmetric : YES , because if "a" is married to "b" , then "b" is married to "a" .

Transitive : NO , because if "a" is married to "b" and "b" is married to "c" , then "a" is not married to  "c" .

Therefore , The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .

The given question is incomplete , the complete question is

Write in the space provided the property or properties that each relation possesses (reflexive, symmetric, transitive).

(a) R is a relation on the set of all people, (a,b) is in R if a is taller than b .

(b) R is a relation on the set of integers > 0 , (a,b) is in R if a divides b .

(c) R is a relation on the set of all people , (a,b) is in R if a is married to b .

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Substitution is one method for solving linear equation systems.

First, arrange the equations so that the variables are vertically arranged.

Step 2: Pick the variable that is most straightforward to take out, and multiply it by a different value in each equation so that its coefficients are the same.

Subtract the two equations in step three.

Solve the one variable system in step four.

Step 5: To find the other equation, re-enter that number into either equation.

Step 6: Reread the question and re-enter your responses to double-check.

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