Estimate 71.47 + 54.357 by first rounding each number to the nearest whole number.

It is to be noted that the absolute expression that shows how far the student's score is from the average is given as: "| x - 74| (Option C)

The student obtained a score of x% based on the question. As a result, x% might be larger or lower than the average score of 74%.

To establish how distant the student's score is from the average, we must subtract the student's score from the average score; i.e. (x - 74)

This difference, however, might be negative: as a result, the absolute value of (x - 78) must be calculated, yielding |x - 74|.

As a result, the phrase that may be used to assess how distant the student's score is from the average is as follows: |x - 74| which is the same as option c - An Absolute expression.

Absolute expressions are or modulus of a real number x, abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.

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ANSWERS

a) 58

b) 62.2

EXPLANATION

a) The median is the middle value. It separates the data set in two. To find the median we have to put the data in order, from least to greatest:

The number of data is odd, this means that the median will be one of the values of the data set and not a mean between two of them. If there are 9 values, the median is the 5th value - so we have 4 values to the left and 4 values to the right.

The first 4 values are 44,49,53,54, so the median is 58.

b) The mean is the sum of all values of the data set divided by the amount of data:

Rounded to one decimal place, the mean is 62.2

Step-by-step explanation:

Meow island get's their population multiplied by 3 per year

Purr island get's and additional 4 cats per year

The population of cats on each island in the mathematical form is:

Meow island:

f(0) = 2

And,

f(x) = 3f(x - 1)

Where x is the number of years from x = 1, 2, 3 ,,,,

Purr island:

y = 4x + 2

Where x is the number of years from x = 0, 1, 2, 3 ,,,,

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,

We will make ordered pair of number of years x and number of cats y as

(x, y).

Meow island:

We see that the number of cats is increasing 3 times the previous number of cats.

So,

f(0) = 2

And,

f(x) = 3f(x - 1)

Where x is the number of years from x = 1, 2, 3 ,,,,

Purr island:

(0, 2), (1, 6), (2, 10), (3, 14) ....

The equation for the table.

y = mx + c

m = (6 - 2) / (2 - 1) = 4/1 = 4

(0, 2) = (x, y)

2 = 4 x 0 + c

c = 2

Now,

y = 4x + 2

Thus,

The population of cats on each island in mathematical form is given above.

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Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to x³ -11x² +41x -51.

As given,

Standard form of the polynomial function:

f(x) = r(x-a)(x-b)(x -c)

r : leading coefficient

a, b, c are zeros

Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is given by

f(x) = 1(x -3) (x -(4+i))(x - (4-i))

⇒ f(x) = (x -3) (x-4 -i)(x -4 +i)

⇒ f(x) = (x-3) [(x-4)² -i²]

⇒f(x) = (x-3)(x² -8x +16+1)

⇒f(x) =(x-3)(x² -8x+17)

⇒f(x) = x³-11x² +41x-51

Therefore, polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to

x³ -11x² +41x -51.

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The Conditional Probability that the coin is weighted towards heads is 0.25/0.75 . Conditional probability is the result of Bayes’ Theorem .

A coin is tossed twice . So, total outcomes are { HH , TH , HT, TT} that is 4 .

Probability= favourable outcomes / total outcomes

Probability of getting two heads = ¼ = 0.25

Favourable outcomes are { HH , HT, TH}

Probability of getting at least one head = ¾ = 0.75

Conditional probability is measure of the probability of an event occurring, given that another event has already occurred.

Formula , P(A|B) = P(A and B)/ P(B)

Here, p(A|B) is conditional probability of A given B

P(B) is probability of event B occur

P(A and B) is probability of both events A and B occur

We have to find conditional probability that coin is weighted towards heads and it is = Probability of getting both heads / probability of getting at least one head

= ¼ / ¾ = 0.25 / 0.75

Which is required result .

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Let the magazine be m and the eraser be e. Then the total cost is 25.

The equation can now be shown as follows;

Therefore each eraser cost $5

Given

different choices

Find

Which of the following is not a condition necessary to create a valid probability distribution?

Explanation

Each discrete outcome can have different probability of occuring

Hence the option stating each discrete outcome hsould have equal probability of occuring is not necessary

Final Answer

option (a) is correct option

Answer: 1.4 or just 1

Step-by-step explanation:

But we are going to a decimal point then go to 1.4, cause the 9 makes the 3 round-up. :)

Answer: 1.4

Step-by-step explanation:

I believe you're asking what 1.39 rounded to the nearest tenths place is, in that case it is 1.4

Answer:

Every number that is greater than 6

The possible coordinates of the other points are (1, -1) and (5, 1)

From the question, we have

Where (1, y) represents the other points

The distance between the points is then calculated using the following distance formula

d = √[(x₁ - x₂)²+ (y₁ - y₂)²]

Where x and y are the coordinates of the two points

Substitute the known values in the above equation

So, we have

d = √[(-3 - 1)²+ (-2 - y)²]

Evaluate

d = √[16+ (-2 - y)²]

The distance is 5 units

So, we have

√[16+ (-2 - y)²] = 5

Square both sides

16+ (-2 - y)² = 25

This gives

(-2 - y)² = 9

Square root of both sides

-2 - y = +/-3

So, we have

y = -2+/-3

Evaluate

y = -1 and y = 5

Hence, the coordinates are (1, -1) and (5, 1)

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To construct the graph of the hyperbola, the procedure is as follows:

The equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:

(y - y*)²/a² - (x - x*)²/b² = 1.

A vertical hyperbola opens up and down.

In this problem, the equation is:

(y + 2)²/36 - (x + 5)²/64 = 1.

Hence the center is:

(-5, 2).

The value of coefficient a is:

a² = 36 -> a = 6.

Then the vertices of the hyperbola are:

The slopes of the asymptotes of the parabola are given as follows:

±a/b.

Hence:

Since the asymptotes pass through the center, the equation is:

y - 2 = ± 3/4(x + 5).

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Answer:

2 hours

Step-by-step explanation:

10+10= 20, so $20 fee

2+2= 4, so a fee for every hour she has the bike.

20+4= $24, so 2 hours maximum

If you tried adding another hour (which would be $12) that would equal $36 which is over her budget.

Answer:

u = 24

Step-by-step explanation:

-7/8u = -21

Solve for u

Multiply each side by -8/7

-8/7 *-7/8u = -21 *-8/7

u =3*8

u = 24

Answer:

u = 1/24

Write the equation:

–7/8u = –21

Get rid of fraction:

–7/2^3 • u = –21

–7 = ( – (8u) ) 21

Solve:

–7 = –8u + 21

–7 + 8u = –8u + 8u + 21

–7 + 8u = 21

–7 + 7 + 8u = 21 + 7

8u = 21 + 7

8u = 28

u = 1/24

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Question:

Solution:

The definition of parallel lines tells us that if two lines are parallel, they have the same slope. On the other hand, the slope-intercept form of a line is given by the following formula:

y = mx+b

where m is the slope of a line. In this case, the slope of the given line would be m = -2/3. Then the correct answer would be:

Answer:

  3.97%

Step-by-step explanation:

You want to know the annual interest rate, compounded daily, that will result in $43,000 growing to $75,000 in 14 years.

The formula for the account value is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested at annual rate r compounded n times per year for t years.

Filling in the given values, we can solve for r.

  75000 = 43000(1 +r/365)^(365·14)

  75/43 = (1 +r/365)^5110 . . . . . divide by 43000 and reduce the fraction

Taking the 1/5110 power gives ...

  (75/43)^(1/5110) = 1 +r/365 ≈ 1.00010886855

  r/365 = 0.0010886855 . . . . subtract 1

  r = 0.001086855·365 . . . . . multiply by 365

  r ≈ 0.039737 = 3.9737%

The required interest rate is about 3.97%.

Answer:

y= x/(n-9)

Step-by-step explanation:

Move 9 to the right side to get n-9

Take y over to get x=y(n-9)

Then shift n-9 over to other side to get y= x/(n-9)

The increase in the selling price is 1.818.

Test statistic:

A test statistic is a statistic used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.

The given values are:

a = 0.1

x = 94

μ = 90

The formula for test statistic will be:

t = ((x- μ) / ([tex]\frac{s}{vn}[/tex])

Now put the values in the given equation we have:

t = (94-90) / ([tex]\frac{22}{10}[/tex])

 = 4/2.2

  = 1.818

Therefore the increase in the selling price is 1.818.

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The triangle have shorter sides of 12.9 and 14.9 cm, respectively

From the question, the given parameters are:

Also, from the question, we have:

Two shaded sides of the triangle differ by 2

In this case, the shaded sides of the triangle are

Opposite and Adjacent

This can also be interpreted as

Base and Height

So, we have

Base - Height = 2

The area is calculated as

Area = 0.5 * Base * Height

So, we have

0.5 * Base * Height = 96

This gives

0.5 * (Height + 2) * Height = 96

Divide by 0.5

(h + 2) * h = 192

Using a graphing calculator, we have

h = 12.9

Substitute h = 12.9 in Base - Height = 2

Base - 12.9 = 2

Evaluate

Base = 14.9

Recall that the Opposite and Adjacent are the shorter sides of a right triangle

Hence, the shorter sides are 12.9 and 14.9 cm

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Answer:12:30,2:5 and 18:45

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the green graph be G and the blue graph, be B:

1) Be cognate of the fact that the function in blue is completely negative, while the upper green graph is positive

Note: First, we should note that the blue function must therefore be a transformation of the Green function.

This means B takes the form:

y = (s)*a*|X+b|

We are required to find a, b, and s, where s is the sign.

2) From (1), we can deduce that, if graph G was transformed into B, then the first transformation begins by reflecting G along the X-axis (multiplying by -1).

Therefore, s = -1

3) From (2), it follows that the first transformation produces the following effect:

y = |X| transformed to y = -|X|

and B now takes the form y = -a*|X+b|

4) We notice again that the apexes of both functions do not touch. This means G was not only reflected along the X-axis but was also shifted or translated along the X-axis.

5) Building from (4), we notice that the Blue function takes a value of 0 when x is 1. If we put this in the general equation for B;

y = -a*|X+b| implies;

0= -a*|1+b|      

|1+b| = 0/-a

|1+b| = 0

1+b = 0

and y becomes:

Notice also that when the x is 5, the Blue function now takes a value of -1. If we put this in a general equation for B;

y = -a*|X-1|

-1 = -a*|5-1|

-1 = -a*|4|

-4a = -1

Blaise M.

The amount that Jane would earn for working for 60 hours is $630.

The given function is a linear function. A linear function is a function that changes at a constant rate. When a linear graph is drawn on a coordinate graph, it can slope either upward or downward.

The linear function that represents the total amount she earns is:

Total earnings = cost per hour x total number of hours worked

Total earnings = $10.50 x h  

Total earnings = $10.50 x 60 = $630

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The most appropriate choice for function will be given by -

g(x) = -|x| is the correct function

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

f(x) = |x| is the given function.

f(x) has been transformed to g(x) according to  the graph given in the figure

In the figure, the range is negative real number.

So the transformation g(x) = - |x|

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SOLUTION:

Step 1:

In this question, we are given the following:

The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury​ (mm Hg), find the volume when the pressure is 200 mm Hg.

Step 2:

This is an application of Boyle's law which states that:

Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.

Next:

CONCLUSION:

The volume when the pressure is 200 mm Hg is:

The answer of the linear equation for Y=2x+5 is x = (y-5)/2.

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0.  Now in this equation, x is a variable, A is a coefficient, and B is constant.

The given linear equation is,

Y=2x+5

Now, solve this linear equation for x

Take 5 to LHS it will change sign to -ve

y-5 = 2x

Next, take coefficient of x below to LHS

(y-5)/2 = x

Now, swap the sides

x = (y-5)/2

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The equation of u when it is the subject is u = 9/t - 12at

From the question, the original equation is given as

9 = 12at2 + ut

Next, we rewrite the equation to show the exponents

This is represented as

9 = 12at² + ut

To solve further, we simply isolate the variable term ut

This is done by subtracting 12at²  from both sides of the equation

So, we have the following equation

9 - 12at² = 12at² - 12at² ut

Evaluate the like terms in the equation

So, we have

9 - 12at² = ut

Lastly, divide both sides of the equation by t

So, we have

(9 - 12at²)/t = ut/t

Evaluate the quotients

9/t - 12at = u

Make us the subject

u = 9/t - 12at

Hence, the solution for the equation for u is u = 9/t - 12at

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Solution;

y=5x

Explanation;

Answer:

x = - 5;

y = 5;

Step-by-step explanation:

Identify the equation.

y = ( 2 / 3 )x + c;

Substitute a point.

5 = ( 2 / 3 )( - 2 ) + c;

5 = ( - 4 / 3 ) + c;

5 - ( - 4 / 3 ) = c;

5 + ( 4 / 3 ) = c;

19 / 3 = c;

y = ( 2 / 3 )x + ( 19 / 3 );

Substitute point A.

3 = ( 2 / 3 )x + ( 19 / 3 );

3 - ( 19 / 3 ) = ( 2 / 3 )x;

( 9 / 3 ) - ( 19 / 3 ) = ( 2 / 3 )x;

- ( 10 / 3 ) = ( 2 / 3 )x;

- ( 10 / 3 )( 3 / 2 ) = x;

( - 30 / 6 ) = x;

- 5 = x;

x = - 5;

Substitute point B. Use common sense and notice that point B is actually the same as the first point.

y = 5;

Answer:

x =  -5

y = 5

Step-by-step explanation:

You could write the equation in the point slope form of a line

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])

Use the slope they gave us 2/3.  Use the point they gave us for [tex]x_{1}[/tex] ( -2 ) and [tex]y_{1}[/tex] ( 5)

y -5 = 2/3(x - -2)

y - 5 = 2/3(x + 2)  Plug in 3 for y to solve for x

3-5 = 2/3(x + 2)

-2 = 2/3x + 4/3  subtract 4/3 from both sides of the equation

-2 - 4/3 = 2/3x

[tex]\frac{-6}{3}[/tex] - [tex]\frac{4}{3}[/tex] = 2/3x

[tex]\frac{-10}{3}[/tex] = 2/3 x  Multiply both sides by [tex]\frac{3}{2}[/tex]

([tex]\frac{3}{2}[/tex])[tex]\frac{-10}{3}[/tex] = ([tex]\frac{3}{2}[/tex])([tex]\frac{2}{3}[/tex]) x

-5 = x

substitute in -2 for x to solve for y

y - 5 = 2/3(x + 2)

y - 5 = 2/3(-2+2)

y - 5 = 2/3(0)

y - 5 = 0  Add 5 to both sides

y = 5

Answer:5760

Step-by-step explanation:

48 beats per min and its 120 min in 2 hours so multiply 120×48=5760