Translate the statement five times the difference of a number and 3 is 17

Answer:

6

Step-by-step explanation:

Simplifying the expression (2+1)2, we can first perform the operation within the parentheses, which gives us:

(2+1)2 = 3 x 2

Then, we can multiply 3 by 2, which gives us:

3 x 2 = 6

Therefore, the simplified expression for (2+1)2 is 6

The price of one square meter of the coffee and plantain farm is $0.05.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

1 hectare of the farm = $500

Now,

To determine the price per square meter of a coffee and plantain farm.

We would need to divide the cost of 1 hectare = $500 by the number of square meters in a hectare.

So,

One hectare is 10,000 square meters.

This means,

= $500 ÷ 10,000 sq m

= $0.05 per square meter

Therefore,

The price of one square meter of the coffee and plantain farm is $0.05.

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The complete question.

What is the price of a square meter of coffee and plantain farms?

If 1 hectare of the farm is $500.

a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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The probability of a rejected part, knowing that it came from a known shift can be calculated as follows:

Shift 1: (51/600) x 100% = 8.5%

Shift 2: (72/850) x 100% = 8.5%

Shift 3: (50/650) x 100% = 7.7%

Shift 4: (57/510) x 100% = 11.2%

The probability that a randomly selected part is defective is (1287/19500) x 100% = 6.6% (rounded to one decimal place).

The probability that a randomly selected part is not defective is (18213/19500) x 100% = 93.4% (rounded to one decimal place).

The probability that a part came from Factory A is (3500/19500) x 100% = 17.9% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory A is (120/3500) x 100% = 3.4% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory B is (125/2700) x 100% = 4.6% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory C is (210/5000) x 100% = 4.2% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory D is (712/4700) x 100% = 15.1% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory E is (120/3600) x 100% = 3.3% (rounded to one decimal place).

Based upon these probabilities, Factory D should be investigated more as it has the highest probability of a defective part among all the factories.

The probability of a defect for the flagged factory is (230/2610) x 100% = 8.8% (rounded to one decimal place).

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Answer:

A

Step-by-step explanation:

hope this helps

It is found that the distance between the two memorials is of 1,42 miles.

The distance between two points (x1 , y1) and (x2 , y2) is of:

Distance formula = [tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]

One memorial is at point (3,-1).

The other is at point (7, -5).

Thus, in the coordinate grid, the distance is of:

D = 5.66

In the coordinate, the distance is of 5.66 units. Each unit is worth 0.25 miles, thus:

D = 5.66 units

The distance between the two parks is of 1.42 miles.

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Answer:

2.8

Step-by-step explanation:

To calculate the GPA of the student, we first need to calculate the total number of grade points earned by the student. We can do this by multiplying the number of credits for each course by the corresponding grade point value and then adding up the results:

A in a 3-credit course: 4 x 3 = 12 grade points

B in each of three 4-credit courses: 3 x 4 = 12 grade points each, for a total of 3 x 12 = 36 grade points

C in a 2-credit course: 2 x 2 = 4 grade points

D in a 3-credit course: 1 x 3 = 3 grade points

Total grade points earned = 12 + 36 + 4 + 3 = 55

Next, we need to calculate the total number of credits earned by the student:

A in a 3-credit course = 3 credits

B in each of three 4-credit courses = 3 x 4 = 12 credits

C in a 2-credit course = 2 credits

D in a 3-credit course = 3 credits

Total credits earned = 3 + 12 + 2 + 3 = 20

To find the GPA, we divide the total grade points earned by the total credits earned:

GPA = Total grade points earned / Total credits earned

GPA = 55 / 20

GPA = 2.75

Therefore, the GPA of the student is 2.75.

To calculate the GPA, convert each grade into points, multiply each point value by the number of credits for that course, and add the total. Then divide the total by the total credits. Using this calculation, the student's GPA is 2.75.

The grade point average (GPA) is calculated on the basis of the grades earned in each course and the course's credit value. First, each grade is converted into points. Then, each point value is multiplied by the number of credits for that course. Finally, the total points are added together, and the sum is divided by total credits to yield GPA.

The total credits are 3 (for A) + 12 (for Bs) + 2 (for C) + 3 (for D) = 20. The total points are 12 (for A) + 36 (for Bs) + 4 (for C) + 3 (for D) = 55. Hence, the GPA is 55 total points ÷ 20 total credits = 2.75.

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The proof that at least three of any 25 days chosen must fall in the same month of the year holds true because; there are twelve months in a year.

This proof required for the statement in the task content follows from the fact that, there are 12 months in a year.

here, we have,

Hence, the proof that at least three of any twenty-five, 25 days chosen must fall in the same month of the year is because, there are 12 months in a years and after choosing two days from each month, amounting to 24 days, the 25th day would fall into a month and hence, such month has 3 days already.

Ultimately, the statement that at least three of any 25 days chosen must fall in the same month of the year holds true because there are 12 months in a year.

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The solution is, x²-14x+24

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Given:

x=12, x=2

Solution:  In order to determine the quadratic equation we need to move the integers onto the side where x is and then distribute.

Move the integers

Solution #1

x-12 = 0

Solution #2

x-2=0

Create and expression and distribute

(x-12)(x-2)=0

solving we get,

x²-14x+24 = 0

Therefore, after completing the steps we were able to determine that the quadratic equation that will have solutions of x = 12 and x = 2 is x^2 - 14x + 24.

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The exponential equation that passes through these two points is:

y = 26.678*(14/11)^x

A general exponential equation is:

y = A*(b)^x

If we know the two points (3, 55) and (4, 70), then we can write  two equations:

55 = A*(b)^3

70 = A*(b)^4

If we take the quotient between the second equation and the first one, then we get:

70/55 = (A*(b)^4)/(A*(b)^3)

70/55 = b

14/11 = b

Then we can write:

55 = A*(14/11)^3

(11/14)^3*55 = A

26.678 = A

Then the exponential equation is:

y = 26.678*(14/11)^x

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a. The proportion of adults who took zinc are 17/100.

b. The proportion of adults who took vitamin C reported NOT having a cold in the last 30 days are 41/56.

c. The proportion of adults who reported having a cold took Echinacea are 3/13.

The solution has been obtained by using proportions.

What is proportion?

The comparison of two numbers in mathematics, is known as a proportion. According to the law of proportion, two sets of provided numbers are deemed to be directly proportionate to one another if they increase or decrease in the same ratio. They are inversely proportional if not.

We are given a table showing the results of the survey.

a. Out of 200, 34 adults took zinc. So, the proportion comes out to be

34/200 = 17/100

b. From the table, we can see that 82 adults out of 112, were reported of not having cold in the last 30 days. So, the proportion comes out to be

82/112 = 41/56

c. It is given that total 52 people were reported of having cold. Out of this, 12 adults took Echinacea. So, the proportion comes out to be

12/52 = 3/13

Hence, the required proportions have been obtained.

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The solution of the system of equations is:

x = 12, y = 11, z = 2

We can rewrite our system of equations as:

x + y + z = 25

5x + y + 9z = 89

-7x + 6y + 6z = -6

First, if we subtract the first equation and the second one, we will get:

(5x + y + 9z) - (x + y + z) = 89 - 25

4x + 8z = 64

And if we subtract 6 times the first equation from the third one, we will get:

-7x + 6y + 6z - 6*(x + y + z) = -6 - 6*25

-13x = -156

We can solve this for x:

x = -156/-13 = 12

Now we know the value of x, replacing it in:

4x + 8z = 64

Will give:

4*12 + 8z = 64

8z = 64 - 4*12 = 16

z = 16/8 = 2

And the value of y will be given by:

x + y + z = 25

12 + y + 2 = 25

14 + y = 25

y = 25 - 14 = 11

Then the solution is:

x = 12, y = 11, z = 2

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The evaluation of the limits of the piecewise function at the specified intervals are as follows;

[tex]\lim\limits_{x\to2^+}\frac{f(x) -1}{f(x + 4)} = -2[/tex]

[tex]\lim \limits_{x\to 1^-}f(f(x) + 1) = 11[/tex]

[tex]\lim\limits_{h\to 0}\frac{f(6+h) - f(6)}{h} = 2[/tex]

A piecewise function is a function with rules or definition of the function based on the interval of the function.

The equation representing the piece wise function at x → 2⁺, can be found as follows;

Points on the graph of the function are; (3, 2), and (4, 1)

Slope of the graph of the function = (1 - 2)/(4 - 3) = -1

Equation of the function is; y - 2 = -1·(x - 3) = 3 - x

y = 3 - x + 2 = 5 - x

y = 5 - x

y = f(x) = 5 - x

f(x) - 1 = 5 - x - 1 = 4 - x

f(x) - 1 = 4 - x

f(x + 4) = 5 - (x + 4) = 5 - x - 4 = 1 - x

f(x - 4) = 1 - x

[tex]\frac{f(x) - 1}{f(x + 4)} = \frac{4 - x}{1 - x}[/tex]

The coordinate points on the piecewise function at x → 1⁻ are; (0, 3), and (1, 4)

The slope of the graph is; (4 - 3)/(1 - 0) = 1

The equation is; y - 3 = x

y = f(x) = x + 3

f(f(x) + 1) = f((x + 3) + 1) = f((x + 3) + 3 + 1) = f(x + 7)

f(x + 7)  = (x + 7 + 3) = x + 10

The points on the piecewise function at x = 6 are; (5, 2), and (7, 6)

The slope is; (6 - 2)/(7 - 5) = 2

The equation is; y - 2 = 2·(x - 5) = 2·x - 10

y = 2·x - 10 + 2 = 2·x - 8

y = f(x) = 2·x - 8

f(6 + h) = 2·(6 + h) - 8 = 12 + 2·h - 8 = 4 + 2·h

f(6) = 2 × 6 - 8 = 4

f(6 + h) - f(6) = 4 + 2·h - 4 = 2·h

[tex]\frac{f(6 + h) - f(6)}{h} = \frac{2\cdot h}{h}= 2[/tex]

The limits of the function is therefore;

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The value of the transformed function after a vertical stretch in the y direction is h ( x ) = k ( | x | - 3 ) , where k is the scale factor

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = ( | x | - 3 )   be equation (1)

Now , when the function is stretched in the y direction , we get

Vertical stretch by a factor k: y = k × f(x)

On simplifying , we get

Let the transformed function be represented as h ( x )

where the value of h ( x ) is

Let the scale factor of stretching be k

h ( x ) = k ( | x | - 3 )

Hence , the transformed function is h ( x ) = k ( | x | - 3 )

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The values of x are 3 or 0. 3 and 0 will satisfy the equation |2x-3| +7 =10.

What is an absolute function?

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The parent function with an absolute value is defined as f(x)=| x |.

Given equation is

|2x-3| +7 =10

Subtract 7 from both sides:

|2x-3| +7 - 7 = 10 - 7

|2x-3| = 3

Applying absolute function:

Either, 2x-3 = 3         or, 2x-3 = -3

Add 3 on both sides:

2x = 6                         2x = 0

Divide both sides by 2:

x = 3      or     x = 0

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Answer:

-195

Step-by-step explanation:

1+1+1+1-200+1

1+1+1+1-4x50+1

-195

Hopes this helps!!

I don't know if you have this answer!!

Answer: The answer is  (A)

Step-by-step explanation:

The arc length of PR: 16/3π unit. This can be solved by using the formulas of circle.

A circle is a form made up of all points on a plane that are at a specific distance from the centre point. In other words, it is the path a moving point in a plane takes to travel around a curve while maintaining a constant distance from another point. The group of points in a plane that are all equally far from one another is known as a circle. The radius and the centre both refer to the distance from the centre. The diameter is defined as the radius divided by two. A circle's angle of subtraction from its centre is a complete angle, which is equal to or radians.

In circle Z, m∠PZR = 2/3π

radius = 8 unit

length of the arc PR:

= 2/3π × 8

= 16/3 π unit

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Answer:

3. Initial cost = 99 dollars.  Each hour (h) is 19 dollars. The total value will be initial cost + hours*(cost per hour)=> t=99+19h.

4. She will be using the car for 3 days. Each day costs 29.99. There is no initial cost, so her total cost will be 29.99*3=89.97 dollars.

The value of y is given as follows:

y = 4.3 cm.

The value of y is obtained applying the two secant segment theorem, which means that the following equation will hold true:

3(3 + y) = 2(2 + 9).

(a secant is a segment that crosses the circumference of the circle twice, and the product has to be equal for each).

Then we apply the distributive property to each side of the equality, and then isolate the variable y, as follows:

9 + 3y = 22

3y = 13

y = 13/3

y = 4.3.

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Answer:

x = [tex]\frac{7}{12}[/tex]

Step-by-step explanation:

[tex]7-2(3-8x)=7-6-16x[/tex]

Add/subtract like terms

[tex]5(3-8x)=1-16x[/tex]

Distribute 5

[tex]15-40x=1-16x[/tex]

Simplify

[tex]-40x+15=-16x+1[/tex]

Add -16x to both sides

[tex]-24x+15=1[/tex]

Subtract 15 on both sides

[tex]-24x=-14[/tex]

Divide by -24

[tex]x=\frac{7}{12}[/tex]

Answer:

Step-by-step explanation:

If the generation time of bacteria is 30 minutes, it means that in every 30 minutes, the number of cells will double. Let No = 100 be the initial number of cells, and n be the number of generations at that point.

Using the given formula N1 = N x 2^n, we can find the number of cells at any given time t, in minutes.

For t = 30 minutes:

The number of generations in 30 minutes is 1 (since generation time is also 30 minutes)

N1 = 100 x 2^1 = 200 cells

For t = 60 minutes:

The number of generations in 60 minutes is 2 (since generation time is 30 minutes)

N1 = 100 x 2^2 = 400 cells

For t = 90 minutes:

The number of generations in 90 minutes is 3 (since generation time is 30 minutes)

N1 = 100 x 2^3 = 800 cells

For t = 120 minutes:

The number of generations in 120 minutes is 4 (since generation time is 30 minutes)

N1 = 100 x 2^4 = 1600 cells

Therefore, after 30 minutes, the number of cells will be 200, after 60 minutes it will be 400, after 90 minutes it will be 800, and after 120 minutes it will be 1600.

Using the given restrictions we can see that there are 37 balls on the box.

Let's assume that the total number of balls is B.

We know that in the box there are more than 25 and fewer than 40 tennis balls, so we have the inequality.

25 < B < 40

If we count in 3's, then there is one left over, so we can write:

B = 3*n + 1   (where n is an integer number)

And if we count in 5's there are 2 leftovers:

B = 5*m + 2  (where m is an integer, from this we conclude that the number ends in a 2 or a 7)

Then we have 3 restrictions:

25 < B < 40

B = 3*n + 1

B = 5*m + 2

notice that if n = 12

B = 3*12 + 1 = 37

if m = 7

B = 5*7 + 2 = 37

and 37 is a solution of the inequality, then we conclude that there are 37 balls on the box.

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The real GDP per capita increased by 28% from 2012 to 2013.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

The table with GDP deflator and population

Now,

i. The percentage change in nominal GDP from 2012 to 2013 can be calculated as follows:

[(Nominal GDP in 2013 - Nominal GDP in 2012) / Nominal GDP in 2012] x 100

= [(112 - 75) / 75] x 100

= 49.33%

Therefore, nominal GDP grew by 49.33% from 2012 to 2013.

ii. Real GDP is nominal GDP adjusted for inflation. To find real GDP, we need to use the GDP deflator:

Real GDP (in billions) = Nominal GDP (in billions) / (GDP Deflator / 100)

In 2012: Real GDP = 75 / (50 / 100) = £150 billion

In 2013: Real GDP = 112 / (54 / 100) = £207.41 billion

iii. The percentage change in real GDP from 2012 to 2013 can be calculated as follows:

[(Real GDP in 2013 - Real GDP in 2012) / Real GDP in 2012] x 100

= [(207.41 - 150) / 150] x 100

= 38.27%

Therefore, real GDP grew by 38.27% from 2012 to 2013.

iv. To determine if the growth in nominal and real GDP increased the standard of living, we need to look at the change in real GDP per capita. Real GDP per capita is calculated by dividing real GDP by the population:

Real GDP per capita in 2012 = 150 / 50 = £3 billion

Real GDP per capita in 2013 = 207.41 / 54 = £3.84 billion

The percentage change in real GDP per capita can be calculated as follows:

[(Real GDP per capita in 2013 - Real GDP per capita in 2012) / Real GDP per capita in 2012] x 100

= [(3.84 - 3) / 3] x 100

= 28%

Therefore, by the percentage the answer will be 28% from 2012 to 2013.

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The solution to the system of equation 2x - 3y = 4 and -2x + 6y = -10 is (-1,-2).

Given the system of equation in the question;

2x - 3y = 4

-2x + 6y = -10

First, solve for y in equation one.

2x - 3y = 4

2x - 4 = 3y

3y = 2x - 4

Divide each term by 3

y = (2/3)x - 4/3

Now, solve the system of equation, plug y = (2/3) - 4/3 into equation two and solve for x.

-2x + 6y =-10

Plug in y = (2/3) - 4/3

-2x + 6( (2/3)x - 4/3 ) = -10

Simplify

-2x + 4x - 8  = -10

2x - 8 = - 10

2x = -10 + 8

2x = -2

x = -2/2

x = -1

Now, plug x = -1 into equation two and solve for y.

-2x + 6y = -10

Plug in x = -1

-2( -1 ) + 6y = -10

2 + 6y = -10

6y = -10 - 2

6y = -12

y = -12/6

y = -2

Therefore, the value of x is -1 and y is -2.

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This graph shows how far Han is from his house as he drives. (0, 10) is the Y Vertical intercept. Han is therefore originally located 10 miles from his house.Horizontal intercept of X (10,0) It indicates that it takes 10 minutes to reach.

The point where the graphs of a function and relation meets the y-axis of the coordinate system is known as a y-intercept, also referred to as a vertical intercept. Analytic geometry is used for this, with the widely accepted standard that the variable y is represented by the vertical axis and the variable x by the horizontal axis.

Anything straight to the horizon is said to as horizontal. Since the vertical is the polar opposite of the horizontal, everything that intersects it at a right angle of 90 degrees is known as vertical. Hence, the line that runs form left to center is seen as being horizontal.

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Answer:

11° 33'

Step-by-step explanation:

[tex]21' = \left(\dfrac{21}{60}\right)^\circ = \left(\dfrac{7}{20}\right)^\circ \\50^\circ 21' = 50 \dfrac{21}{60}\; degrees\\\\38^\circ 48' = 38 \dfrac{48}{60} \;degrees[/tex]

Break
[tex]50 \dfrac{21}{60} = 49 + 1 \dfrac{21}{60}\\[/tex]

[tex]1 \dfrac{21}{60} = \dfrac{1 \times 60 + 21}{60} = \dfrac{81}{60}[/tex]

Therefore
[tex]50^\circ21' - 38^\circ48' = 49\dfrac{81}{60} - 38\dfrac{48}{60}[/tex]

Subtract the whole numbers:
49 - 38 = 11

Subtract the fractions:
[tex]\dfrac{81}{60} - \dfrac{48}{60} = \dfrac{33}{60} = 33'[/tex]

So

50°21' - 38°48' = 11° 33'

Answer:

Step-by-step explanation:

Answer:

$29.34.

Step-by-step explanation:

To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:

Current balance = previous balance + new charge

Current balance = $319 + $170

Current balance = $489

The minimum payment is 6% of the current balance:

Minimum payment = 6% x current balance

Minimum payment = 6% x $489

Minimum payment = $29.34

Therefore, the minimum payment on the credit card would be $29.34.

Answer:

$29.34.

Step-by-step explanation:

To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:

Current balance = $319 + $170 = $489

Minimum payment = 6% x $489 = $29.34

The minimum payment on the credit card would be $29.34.

Hope this helped, have a GOOD DAY!!!!!

The Standard deviation of the given data is 989.615.

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

We have data as

$54,410, $51,991, $51,730, $51,300, $51,196, $51,190, $51,122, $51,115, $51,037 and $50,875.

Also we have

Count, N: 10

Sum, Σx: 515966

Mean, μ: 51596.6

Now, using the formula of Standard Deviation

= √1/ N[tex]\sum_{i=1}^n (x_i- \mu)[/tex]²

= (54410 - 51596.6)² + (51991 - 51596.6)² +(51730 - 51596.6)² + (51300 - 51596.6)²+ (51122- 51596.6)² + (51115- 51596.6)² + (51037- 51596.6)² + (50875 - 51596.6)² / 10

= √9793384.4 /10

= √979338.44

= 989.615

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