The graph shows the number of laps kailee ran around a track over a given number of minutes.
(a) What is the slope of the line? Use the slope formula and show your work.
(b) How many laps did Kailee run per minute?
(c) If she continued to run at the same rate, how many laps would she run in 30 min?

In this case we are multiplying the numbers and dividing them.

Fist we got to work with are numbers given the equation.

Given:

[tex]1, 5[/tex]

Therefore, the equation is:

[tex]75 / 3\\5x3[/tex]

Therefore, the correct answers are 1 = 25, 5 = 125 and 3 = 75

Answer:

take any point on the triangle and any point on the image: for now let's take point A(-3,4) A`(-0.6

Step-by-step explanation:

sf =3/4

scale factor=5

What is the unit rate for 20 pounds for $4.00? Which answer is correct?

(1): 5 pounds/$1.00

(2): 4 pounds/$1.00

(3): 1 pound/$4.00

(4): 1 pound/$5.00

The required range of the given function g(x) = -1/2 |x-6| + 1 will be g(x) ≤ 1 or in internal notation form as (-∞, 1]. which is the correct answer would be an option (A).

The function is given in the question below as:

g(x) = -1/2 |x-6| + 1

We have to determine the range of the given function.

As per the given question, we have

⇒ g(x) = -1/2 |x-6| + 1

The range of an absolute function of the form:-

c|ax+b|+k is :f (x) ≤ k

In this case k = 1

⇒ g(x) ≤ 1

[tex]\mathrm{Range\:of\:}-\frac{1}{2}\left|x-6\right|+1:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:1\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:1]\end{bmatrix}[/tex]

Therefore, the required range of the given function will be g(x) ≤ 1 or in internal notation form as (-∞, 1].

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The polynomial function over the complex numbers is,

(x + 1i) ( x - 1i) (x+ 7) ( x + 2).

What is factoring a polynomial?

Factorization of polynomials, also known as polynomial factorization, is a mathematical and computer algebraic technique that combines irreducible factors with coefficients in the same domain to produce a polynomial with coefficients in a given field or in integers.

Consider, the given polynomial

f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14

We can use a factoring "trick" here....write this as

x^4 +  9x^3 + 14x^2  + x^2  + 9x  + 14 = 0    factor by grouping

x^2 ( x^2 + 9x + 14)  +  1 ( x^2 + 9x + 14) = 0

(x^2 + 1) (x^2 + 9x + 14) = 0

(x^2 + 1) (x^2 + 9x + 14) = 0

⇒ (x^2 + 1) = 0,  (x^2 + 9x + 14) = 0

x^2 = -1,          x^2 + 7x + 2x + 14 = 0

x = ±i ,              x(x + 7) + 2(x + 7) = 0

x = ±i ,              (x + 7)(x + 2) = 0

⇒ (x + i)(x - i)(x + 7)(x - 7) = 0

(x + 1i) ( x - 1i) (x+ 7) ( x + 2) = 0

Hence, the polynomial function over the complex numbers is,

(x + 1i) ( x - 1i) (x+ 7) ( x + 2).

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The expression 0.3d = 0.95 could be used to find the number of dimes he has.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have joe who has dime and nickels in his piggy bank totaling $1.45 the number of nickels. He has is 5 more than twice the number of dimes [d].

We can write the the number of nickels as -

[n] = 2d + 5

0.1d + 0.1(2d + 5) = 1.45

0.1d + 0.2d + 0.5 = 1.45

0.3d = 0.95

Therefore, the expression 0.3d = 0.95 could be used to find the number of dimes he has.

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For first case, It is even integer. The difference of odd integers is always even integer. For second case, It is odd integer. The difference of an odd and even integers is always odd integer.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers.

Here,

a. If there is an odd pair of integers,

for example,

=3 and 5

The difference,

5-3=2

It is even integer. The difference of odd integers is always even integer.

b. If one integer is even and other is odd,

for example,

=6 and 3

The difference,

6-3=3

It is odd integer. The difference of an odd and even integers is always odd integer.

It is an even integer in the first scenario. Odd integer differences always result in even integer differences. It is an odd integer in the second case. An odd integer is always the difference between an odd and an even integer.

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Answer: y = 1.75x - 1

Step-by-step explanation: The slope of the line is 1.75

Answer:

17 degrees

Step-by-step explanation:

<ABD = 25. We know that ABD has a right triangle included. Therefore we know that 25 + 90 + <A = 180.

Therefore 115 + <A = 180.

<A = 65 degrees.

This means that part of <A = 65 degrees. The other part of <A is 44 degrees, add the two to find the whole of angle A.

65 + 44 = 109.

Angle CAD would be congruent to angle C due to alternate interior angles. meaning <C is 44 degrees. Since the angles in a triangle add up to 180 you can write the equation:

109 + 44 + <B = 180.

Combine the like terms.

163 + <B = 180.

Subtract to find angle B.

<B = 17

Answer:

24%

Step-by-step explanation:

Walmart has 152/200 employees, simplify that to a number over 100, you get 76/100. 100-76=24

Answer:

Step-by-step explanation:

152/200 = .76

100-76 = 24

=24%

Therefore, the percentage the amount of workers decrease is by 24%.

Please do tell if this helps!

The volume of the cylinder is 10,099.09 inches³.

Here we have to find the volume of the cylinder.

Given data:

Circumference = 46 inches

height(h) = 5 foot = 12 × 5 = 60 inches

Circumference = 2πr

46 = 2 ×π × r

r = 23/π

The formula for the volume of the cylinder = πr²h

Volume = π( 23/π)² 60

               = 529× 60 / π

               = 10,099.09 inches³

Therefore the volume is 10,099.09 inches³.

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{llll} \textit{"x" varies}\\ \textit{inversely with "y"} \end{array}\implies x=\cfrac{k}{y}\hspace{5em}\textit{we also know that} \begin{cases} x=32\\ y=3 \end{cases} \\\\\\ 32=\cfrac{k}{3}\implies 96=k\hspace{10em}\boxed{x=\cfrac{96}{y}} \\\\\\ \textit{when x = 11, what's "y"?}\qquad 11=\cfrac{96}{y}\implies y=\cfrac{96}{11}[/tex]

The function with the following formula is an exponential function with base b:

Given: f(x) = b^x, where b > 0, b ≠ 1 is a real number.

If r is a rational number, we can determine what b means.

An exponential function's domain is all real numbers since b^x may be defined for all real values r.

Now, all you need to know is that any positive number b^x and any real number r can be used to approximate the value of b using this approximation.

B can be any real number greater than 0 in the range.

An exponential function is always positive. And if in addition 0 < b < 1, f is a decreasing function.

Hence, f(x) decreases as x increases.

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Using simple mathematical operations, we can conclude that there are 250 sheets in a stack.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

The order of operations refers to the rules that govern how to solve an expression with several operations.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).

So, the number of sheets in the stack is represented by n.

According to the information provided, a stack of tissue paper is roughly 2.5 inches high.

The thickness of each sheet is roughly 0.01 inches. Determine the number of sheets in the stack, please.

N sheets' thickness would be.

We'll now compare the thickness of n sheets to the thickness of the stack as follows:

0.01n = 2.5

Now, solve for n as follows:

0.01n/0.01 = 2.5/0.01

n = 250

Therefore, using simple mathematical operations, we can conclude that there are 250 sheets in a stack.

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The inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let's assume that the number would be x

The sum of a number and -4 is at least 8

According to the given question, translate the phrase into an algebraic form :

x - 4 ≥ 8

Add 4 both sides of the above inequality,

x - 4 + 4 ≥ 8 + 4

x ≥ 12

Therefore, the inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

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The number of votes that each class president candidate receive is 59.2 votes and 88.8 votes respectively.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.

The number of votes gotten by each person will be:

A = Percentage × Number of votes

= 40% × 148

= 0.4 × 148.

= 59.2 votes.

B. = Percentage × Number of votes

= 60% × 148

= 0.6 × 148.

= 88.8 votes.

Therefore, A got 59.2 votes and B had 88.8 votes.

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Answer:

3

Step-by-step explanation:

75/15=

             __3_________

   15    /   75

          -    75

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

                   0

Have a great day

If a rancher has 80 feet of fencing with which to enclose two adjacent rectangular corrals, then for the maximum area the dimensions will be 10 feet and 40/3 feet

From the given figure

4x + 3y = 80 feet

3y = 80 - 4x

y = (80 - 4x) / 3

The area of the rectangle

A = length × width

A = 2x × y

= 2x × (80 - 4x) / 3

Apply distributive property

= (160/3)x - (8/3)x^2

For the maximum area differentiate the values

0 = 160/3 - 16/3x

16/3x = 160/3

x = 160/3 ÷ 16/3

x = 160/3 × 3/16

x = 10 feet

The value of y = (80 - 4x) / 3

y = (80 - 4(10))/3

y = (80-40) / 3

y = 40/3 feet

Therefore, the dimensions are 10 feet and 40/3 feet

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The required cross product of given vectors is 39k

Cross product is a parallel procedure on two vectors in three-layered space. It brings about a vector that is opposite to the two vectors. The Vector result of two vectors, an and b, is meant by a × b. Its resultant vector is opposite to an and b. Vector items are additionally called cross items.

A = 3i + 5j , B = -3i + 8j

Then, cross product of A and B,

A×B = i(5×0 - 8×0) - j(3×0 - (-3)×0) + k(3×8 - (-3)×5)

A×B = i(0) - j(0) + k(24 + 15)

A×B  = 39k

Thus, cross product of A and B is 39k

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The area of the largest rectangle is 46.47 square root.

Consider a semi-circle with a rectangle ABCD inscribed in it.

Let, O = centre of the semi-circle

A and B lies on the base of the semi-circle

OA = OB = x

D and C lie on the semi-circle

BC = AD = y

AB = CD = 2x

By Pythagorean theorem,

CB² + OB² = OC²

⇒ y² + x² = (6)²

⇒ y² = 36 - x²

⇒ y = √(36 - x²)

Now, area of rectangle in terms of x,

Area, A = 2x × y

= 2x × √(36 - x²)

Differentiating,

A' = 2 × √(36 - x²) - 2x²/(36 - x²)

When x = 0, y = 6 and when x = 6, y = 0, area = 0.

It implies that area is maximum when the value of x lies between 0 and 6.

This will occur where A’ = 0.

⇒ 2 × √(36 - x²) - 2x²/(36 - x²) = 0

⇒ 2 × √(36 - x²) = 2x²/(36 - x²)

On simplification, we get,

⇒ 2 × (36 - x²) = 2x²

⇒ 36 - x² = x²

⇒ 2x² = 36

⇒ x² = 36/2

⇒ x = √36/2

Now, y = √(36 - x²) becomes

⇒ y = √(36 - (√36/2)²)

⇒ y = √(36 - 36/2)

⇒ y = √(96 - 36)/2

⇒ y = √60/2

Maximum area = 2xy

= 2(√36/2)(√60/2)

= 46.47

Therefore, the area of the largest rectangle = 46.47 square units.

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The domain and range of the function C(t) based on the context of the problem is

The range is calculated from minima and maxima, this will be achieved using derivative

C(t) = -5t² + 10t

C'(t) = 0 = -10t + 10

t = 1

substituting t = 1

C(t) = -5(1)² + 10t = 5

so at point (1, 5) it is either minima or maxima,

The second derivative test will help to confirm if point (1, 5) is minima or maxima

C'(t) = -10t + 10

C''(t) = -10

a negative value means it is a maxima

Hence the highest value of the concentration C(t) is 5 mg/L and this is at t = 1

The concentration cannot be less than zero or negative hence the lowest concentration is 0. and the range is 0 to 5

0 ≤ C ≤ 2

The time cannot be below zero so the lowest time will be zero

The domain is controlled by the input values. considering the least concentration of the drug which will be at C = 0

C(t) = -5t² + 10t

0 = -5t(t - 2)

-5t = 0

t = 0

t - 2 = 0

t = 2

The roots of the quadratic equation gives the domain to be 0 to 2

0 ≤ t ≤ 2

The graph is attached

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For the factorial study, Dr Rhodes can use the statement  b) effect of variable A depends on variable B

In a factorial study, two intervention comparisons are undertaken side by side. As a result, in addition to behavioral treatment or standard medical care, individuals may be randomly randomized to receive either aspirin or a placebo. In factorial designs, three different sorts of outcomes are pertinent: main effects, interaction effects, and simple effects.

The primary effect is the impact of one independent variable on the dependent variable, averaged over the values of the other independent variable. Dr Rhodes can forecast the relationship between independent variables A and B using the assumption that the effect of variable A depends on variable B.

Complete question

Dr. Rhodes notices an interaction in his factorial study. In describing this, which statement might he use to explain the link between Independent Variable A and Independent Variable B in predicting the dependent variable? TRUE OR FALSE

Variable A cancels out Variable B.

The effect of Variable A depends on Variable B.

The effect of Variable A is confused by Variable B.

Variable A mainly affects Variable B.

The effect of Variable A is mediated by Variable B.

The effect of Variable A depends on Variable B.

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Answer:

The inches unit number 0.39 in converts to 1 cm, one centimeter. It is the EQUAL length value of 1 centimeter but in the inches length unit alternative.

Step-by-step explanation:

Answer:

Part B:16.5

Step-by-step explanation:

Answer

b

Step-by-step explanation:

The probability that out of four residential fires who independently reported on a single day, two are in family homes, one is in an apartment, and one is in another type of dwelling is 0.0895 or 8.95%.

The multinomial distribution deals specifically with events that have multiple discrete outcomes. The multinomial distribution is not limited to events with only discrete outcomes.

We have given that

The National Fire Incident Reporting Service stated, among all residential fires.

Let consider the number of events ,

X₁---> fires residential who are in home

X₂--> fires residential who are in appartment

X₃--> fires residential who are in another type of dwelling

The probability of ae X₁ occured (p₁)

= 73% = 0.73

The probability of event X₂ occured (p₂) = 20% =0.20

The probability of event X₃ occurred (p₃) = 7% = 0.07

Four residential fires are independently reported on a single day.

we have to calculate probability that two are in family homes, one is in an apartment, and one is in another type of dwelling?

Now, Using the Multinomial distribution,

X₁= 2 , X₂= 1, X₃ = 1 and n = 4

P( X₁, X₂,-----,Xₙ ) =( n!/(X₁! X₂! ----Xₙ!) )( p₁ˣ₁ × p₂ˣ₂ × ----× pₙˣₙ)

P( 2,1,1) = 4!/2! 1! 1! ( 0.73² × 0.2× 0.07¹)

= 12 ( 0.014 × 0.5329)

= 0.0895272

Hence, the required probability is 0.089..

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Complete question:

The National Fire Incident Reporting Service stated that, among residential fires, 73% are in family homes, 20% are in apartments, and 7% are in other types of dwellings.

a) If four residential fires are independently reported on a single day, what is the probability that two are in family homes, one is in an apartment, and one is in another type of dwelling?

It will cost his parents $187.5 to invite 15 friends to his party because it cost $12.5 to invite just one.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, may be used to calculate how many kilometers a car would go on one litre of gas if it travels 44 km on two litres of fuel.

Here,

For inviting 20 friends, The cost of party was $250.

So for 1 friend,

=250/20

=$12.5

Now he wish to invite 15 friends,

=12.5*15

=$187.5

The cost of inviting 15 friends to his party will cost $187.5 to his parents as cost of inviting 1 friend was $12.5.

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The given function is neither continuous nor differentiable at x = 1.

Given the piecewise function defined below, the function is not continuous at x = 1 because the left-hand limit is not equal to the right-hand limit. Specifically, the left-hand limit of f(x) as x approaches 1 is 3, while the right-hand limit of f(x) as x approaches 1 is 4. Furthermore, the function is not differentiable at x = 1 because the derivative does not exist at this point. This is because the derivative of the function is discontinuous at x = 1, with a derivative of 0 for x < 1 and a derivative of 1 for x > 1.

Therefore, the function f(x) is not continuous or differentiable at x = 1.

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So for the maximum area, the values of the width and length of the  rectangle will  be  2.121.

Since we know that the formula for the area of a rectangle is:

A = XY, where x and y are the width and length

since we are given the are, y=√(9-x²), so

A = √(9-x²)

taking the derivative on both sides and considering it to be zero, we get

A' = (x/√(9-x²)(-2x) + √(9-x²) = 0, after multiplying by √(9-x²)

A' = -x² + 9 -x² = 0

=>-2x² =-9

=>x² = 9/2

=> x = 3/√2

so x=2.121 so the for y = √(9-(2.121)^2) =  √(9-4.498) = 2.121

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A rectangle is bounded by a  semicircle y = radical 9 − x^2 and the x-axis. What length and width should the rectangle be to maximize the area

The equation of the ellipse with given foci (2,4) and (2,-8) and co-vertices (10, -2) and ( -6 , -2) is equal to (x - 2)²/40 + ( y + 2)²/36 = 1.

As given in the question,

Given foci of the ellipse :

( 2,4) and ( 2, -8)

Co-vertices of the ellipse :

( 10,-2) and (-6 , -2)

From the given foci and vertices ,

Centre 'c' = 2

b = 6

( h, k) = (2, -2)

a² = c² + b²

⇒a² = 4 + 36

⇒a = √40

⇒a = 2√10

Equation of the ellipse is given by:

( x - h)²/ a² + (y - k)²/b² =1

⇒( x - 2)²/ (2√10)² + (y + 2)²/6² = 1

⇒( x - 2)²/ 40 + (y + 2)²/36 = 1

Therefore, equation of the ellipse is equal to (x - 2)²/ 40 + (y +2)²/36 = 1.

The complete question is:

Determine the equation of the ellipse with foci (2,4) and (2,−8), and co-vertices (10,−2) and(−6,−2).

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A 90​% confidence interval about μ if the sample​ size, n, is 25 is (111.6, 118.4), a 90​% confidence interval about μ if the sample​ size, n, is 20 is (111.1, 118.9), a 80​% confidence interval about μ if the sample​ size, n, is 25 is (112.4, 117.6) and we need population to be normal. So we can not make intervals.

In the given question,

Sample​ mean, x​, is found to be 115.

Sample standard​ deviation, s, is found to be 10.

(a) We have to construct a 90​% confidence interval about μ if the sample​ size, n, is 25.

We need to build a 90% confidence interval. So p=0.90.

t-score for confidence interval is given by the excel code is

t=1.7109

Using these values, the margin of error is

ME = 1.7109× 10/√25

ME = 3.4

So confidence interval is

CI = (115-3.4, 115+3.4)

CI = (111.6, 118.4)

(b) We have to construct a 90​% confidence interval about μ if the sample​ size, n, is 20.

We need to build a 90% confidence interval. So p=0.90.

t-score for confidence interval is given by the excel code is

t=1.7291

Using these values, the margin of error is

ME = 1.7291× 10/√20

ME = 3.9

So confidence interval is

CI = (115-3.9, 115+3.9)

CI = (111.1, 118.9)

(c) We have to construct a 80​% confidence interval about μ if the sample​ size, n, is 25.

We need to build a 80% confidence interval. So p=0.80.

t-score for confidence interval is given by the excel code is

t=1.3178

Using these values, the margin of error is

ME = 1.3178× 10/√25

ME = 2.6

So confidence interval is

CI = (115-2.6, 115+2.6)

CI = (112.4, 117.6)

​(d) Now we have to check, could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed.

To use t-distribution, the population has to be normal.Otherwise we need a sample size of at least 30. Here sample size is less than 30.

So we need population to be normal. So we can not make intervals.

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The right question is:

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x​, is found to be 115​, and the sample standard​ deviation, s, is found to be 10.

(a) Construct a 90​% confidence interval about μ if the sample​ size, n, is 25.

​(b) Construct an 90​% confidence interval about μ if the sample​ size, n, is 20.

​(c) Construct an 80​% confidence interval about μ if the sample​ size, n, is 25.

​(d) Could we have computed the confidence intervals in parts​ (a)-(c) if the population had not been normally​ distributed.