Which of the following represents a true statement

The  percentage of each types of s. aureus

Total number of individuals = 1000

Number of individuals susceptible (fs) to methicillin = 900

The percentage = (Number of individuals susceptible (fs) to methicillin / Total number of individuals) × 100

= (900/1000) × 100

= 90%

90 are somewhat susceptible (ss) to methicillin

The percentage = (90 /1000) × 100

= 9%

10 are killed only by a full treatment with methicillin (ft)

The percentage = (10/1000) × 100

= 1%

Therefore, the percentage of each types of s. aureus are 90%, 9% and 1%

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Answer:

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Total hours worked is x + y.

Earning from the part time job is 24x, from the internship is 12y.

Inequality for the number of hours:

Inequality for the earning:

This can be simplified by dividing all terms by 12:

Answer:

[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]

[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]

Step-by-step explanation:

Part-time job

Internship

The student needs to work less than 15 hours a week:

[tex]\implies x+y < 15[/tex]

The student needs to earn at least $240 a week:

[tex]\implies 24x+12y \geq 240[/tex]

Therefore, the system of inequalities is:

[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]

The second inequality can be simplified by dividing each term by 12:

[tex]\implies \dfrac{24x}{12}+\dfrac{12y}{12} \geq \dfrac{240}{12}[/tex]

[tex]\implies 2x+y \geq 20[/tex]

Therefore, a second system of inequalities is:

[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]

To solve the system of equalities, graph both inequalities and shade the overlapping region.  

Any (x, y) point in the overlapping region is a solution to the system of inequalities.

So, it will take the rider 5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.

The circumference of the ferris wheel is equal to the diameter times pi, or 50*pi=157.08 ft. Since the ferris wheel makes one revolution every 40 seconds, the speed of the ferris wheel is 157.08/40=3.92 ft/sec.

Since the rider starts at a height of 30 ft above the ground and ends up 50 ft above the ground, the total change in height is 50-30=20 ft. Since the speed of the ferris wheel is 3.92 ft/sec, it will take the rider 20/3.92=5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.

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Answer:

x = -58

Step-by-step explanation:

18 + x = -40

-18 -18

x = -58

The total number of books completed by 2:45 pm will be 42.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that when the librarian starts downloading new books at 11:00 am, there are 15 already loaded. When she checks at noon, there are 25 books completely loaded.

The number of books loaded in 1 hour is calculated as,

N = 25 - 15

N = 10 books

Now from 12 noon to 2:45 pm, the time in hours will be,

T = 165 minutes or 165 / 60 = 2.75 hours

The equation for the number of books loaded will be written as,

y = 15 + 10T

y = 15 + ( 10 x 2.75)

y = 15 + 27.5

y = 42.5 or 42

The completely loaded books are 42 in number.

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If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.

What is bisector of an angle?

In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..

Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.

Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.

AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.

Consider △ABD and △DBC:

∠ABD = ∠DBC

∠ADB = ∠BDC

Therefore, △ABD ≅ △DBC

According to CPCT, AD ≅ CD.

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Answer:

The answer is 140

Step-by-step explanation:

The first step is simple L x W which will give us.

L being 5 and W being 3.5 The equation is 5 × 3.5 = 17.5.

With that being said I just need to multiply that answer by 8 which gives us 140.

This means that he will need 140 ft of light in order to put light around each window.

Hope this helped :)

Answer: One gallon of gas in Toronto would cost approximately $3.43. To find this, first convert the price of gasoline in Buffalo to liters. Since there are 3.8 liters in one gallon, one gallon of gas in Buffalo costs $2.29 * 3.8 liters = $8.69. Next, divide the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.91 / 3.8 liters/gallon = $0.24/liter. Finally, multiply the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.24/liter * 3.8 liters/gallon = $0.91/gallon. Round this to the nearest cent to find that one gallon of gas in Toronto costs $0.91/gallon = $<<0.91/gallon=0.91>>0.91.

The translation from the parent function is defined according to the following option:

A translation of 5 units to the right.

The four possible translations are defined as follows:

The parent function in this problem is defined as follows:

f(x) = x².

The translated function is given as follows:

g(x) = (x - 5)².

Meaning that the translated function can be written as follows:

g(x) = f(x - 5).

Thus the transformation to the parent function is given as follows:

x -> x - 5.

Thus it was a translation right of five units, and the third option is the correct option.

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The number 40 represents the one-time charge which is the y-intercept. And the number 20 presents the fee for gym per month. The x-intercept represents that you need to pay 14 monthly fees for a year.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' represents the number of months and 'y' be the total cost. Then the equation is given as,

y = 20x + 40

The number 40 addresses the one-time charge which is the y-capture. Also, number 20 presents the charge for the exercise center each month. The x-block addresses that you really want to pay 14 month-to-month charges for a year.

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Answer:

Step-by-step explanation:To find the zeros of the quadratic function f(x) = 2x² + 3x - 2, we can use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

We can write the function as follows:

f(x) = 2x² + 3x - 2 = 0

We can then factor the quadratic as follows:

f(x) = 2(x-1)(x+1) = 0

Since the product of the factors is zero, at least one of the factors must be zero. Therefore, the zeros of the quadratic are x = 1 and x = -1.

Answer:We may rewrite f(x) = (x-1)^2

We stretch by having 3(x-1)^2

We reflect about the y axis by changing x to -x:   3(-x-1)^2 = 3(x+1)^2

We  move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2

Step-by-step explanation:A way to verify this:  Consider y = x^2 to be the unit parabola.  f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1;  moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2

We may write g(x) = 3x^2 + 18x + 27, also.

The expression which represents the correctly rewritten form of the given expression; 20x⁴y³ - 30x³y⁴ is; 5x³y³ ( 4x - 6y ).

It follows from the task content that the expression which correctly represents the rewritten form of the given expression be determined.

On this note, since the given expression is;

20x⁴y³ - 30x³y⁴

The greatest common factor of both terms in the expression is; 10x³y³ .

On this note, the expression can be factorised completely as follows;

10x³y³ ( 2x - 3y )

However, the expression which is equivalent to the expression above among the answer choices is;

5x³y³ ( 4x - 6y )

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Answer: ( -56 - 45t ) / 72t

Step-by-step explanation:

attached a picture for explaination.

hope that helps...

Answer:

41° and 49°

Step-by-step explanation:

Two angles are said to be complements if the sum of their measures is 90 degrees. Since one angle is eight more than twice the other, we can set up the following equation to represent the situation:

2x + 8 = 90

Solving for x, we get:

2x = 82

 x = 41

Since the two angles are complements, their measures must add up to 90 degrees. Therefore, the measure of the other angle is 90 - 41 = 49 degrees.

Therefore, the two angles have measures of 41 and 49 degrees.

The domain of the relation is {4,8} and the range of the relation is {n,q,m}.

A function or relation's domain is the set of all potential independent values that it can have.

Suppose that the relation S is defined as follows.

S= {(4,n), (8,q), (4,m)}

The first term at the point represents the input and the second term at the point represents the output.

So,

the input values are 4,8 and 4 and their respective outputs are n, q and m,

The collection of all conceivable independent values that a function or relation may take is known as its domain.

So, the domain is {4,8}.

The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.

So, the range is {n,q,m}

Therefore, the domain is {4,8} and the range is {n,q,m}.

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Answer:

A,D,E

Step-by-step explanation:

A:

14/4 = 3.5

D:

7/2 = 3.5

E: 14/4 = 3.5

The constant of proportionality for the table is 3.5. Any other table that satisfies the equations x/y = 3.5 will have the same constant of proportionality.

To find the constant of proportionality, we can divide the y-values by the corresponding x-values and see if they are the same for all given points. In this case, if we divide 24.5 by 7, we get approximately 3.5. If we divide 31.5 by 9, we also get approximately 3.5. Therefore, the constant of proportionality is 3.5 for this table.

Now, we need to find the relationships that have the same constant of proportionality.

For example, if we have a table with the following values:

x1 y1

x2 y2

x3 y3

and the constant of proportionality is k, then we have the following equations:

x1/ y1 = k

x2/ y2 = k

x3/ y3 = k

So, any other table that satisfies these equations will have the same constant of proportionality as the given table.

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Answer: B

Step-by-step explanation:

vertical angles are =

The graph of the equation, y = -19x + 10 is shown below.

If the equation of a line is expressed in slope-intercept form as y = mx + b, it means that:

Given a line has the equation, y = -19x + 10, therefore;

the slope (m) = -19.

the y-intercept (b) = 10.

Therefore, the graph of the line is shown in the attachment below and it cuts the y-axis at 10.

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In the given relation, 1 is not a domain.

The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.

All the values that go into a function. The output values are called the range.

The domain of a function is the set of all possible inputs for the function.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.

Given that, a function,

{(5, 1), (4, -3), (3, -1)}

We know, a domain is the set of all "x" values.

Therefore, domain of the function are, 5, 4 and 3

But, if we see, 1 is one of the values of y.

Hence, 1 is not a domain.

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A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.

As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.

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The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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Answer:

n=1

Step-by-step explanation:

(-y + 3) + (2y - 4) = (ny - 1)

-y + 3 + 2y - 4 = ny - 1

-y + 2y + 3 - 4 = ny - 1  -> combine like terms on the left side of the equation

y - 1 = ny - 1 ==> simplify

y - 1 + 1 = ny - 1 + 1  

y = ny  ==> solve for n

y/y = ny/y

1 = n ==> n=1

The domain of the function is { (x, y) ∈ R² | x² + y² ≥ 1 }

What is Domain of function?

A function's domain is the collection of all potential inputs. For instance, all real numbers are in the domain of f(x)=x², and all real numbers are in the domain of g(x)=1/x, with the exception of x=0. Special functions with more constrained domains can also be defined.

According to question

⇒ [tex]z = e^{\sqrt{x^{2}+ y^{2} -1 } }[/tex]

⇒ x² + y² - 1 ≥ 0

 ⇒ x² + y² ≥ 1

Hence, the Domain of f(x, y) is  { (x, y) ∈ R² | x² + y² ≥ 1 }

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The depth of the submarine after 8 minutes is -123.6 feet below sea level.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Depth of the submarine after y minutes.

= -270 + 18.3y

The depth of the submarine after 8 minutes.

= -270 + 18.3 x 8

= -270 + 146.4

= -123.6

Thus,

The submarine is at -123.6 feet below sea level.

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Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.

A crucial periodic function in trigonometry is the cosine function.

Utilizing the unit circle will make understanding the cosine function the simplest.

Draw a unit circle on the coordinate plane, center the angle at the origin, and label one side as the positive x-axis for the supplied angle measure.

The point where the other side of the angle intersects the circle has an x-coordinate of cos(), and a y-coordinate of sin().

According to our answer-

B = 2pi/T, where T is the period and T = 1/f is the frequency; T is the period

Determines horizontal phase shift by using

C =determines vertical shift.

When solving the given issue, D = midline = 5

A = amplitude = 2.

B = 2pi/T = 2pi/(2/3) = 3pi since frequency = 3/2 means that the period is T = 2/3, which is the reciprocal of the frequency.

C = 0.

The result of adding everything up is A = 2, B = 3pi, C = 0, and D = 5.

so,

A*cos(B(x-C)) + D = y

y = 2*cos(3pi(x-0)), plus 5.

y = cos(3pi*x) * 2 * + 5

Hence, Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.

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The number which can be raised by 3 to give the value of 11 is 2.224.

The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.

Given:

The exponent to which 3 must be raised to obtain 11,

Assume the number is x then, According to the statement,

x³ = 11

x  = ∛11

x = 2.224

Thus, the number is 2.224.

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