If f(x) is a linear function, what is the value of n?
-4
-1
n
02
O
O 9
f(x)
-25
-10
20

The probability of getting a 7 is 1/13 and a black card is 1/2.

Given that

A deck of cards contains 52 cards

The total number of 7's are 4 cards

The total number of black cards is 26

A) Probability of getting a 7 = Total number of 7 / Total cards

Probability of getting a 7  = 4/52

Probability of getting a 7  = 1/13

B) Probability of getting a Black card = Total number of Black cards/ Total cards

Probability of getting a Black card = 26/52

Probability of getting a Black card = 1/2

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The probability of getting a 7  [tex]\frac{1}{13}[/tex] and a black card is [tex]\frac{1}{2}[/tex].

What is a Probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities.

A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty. It is more likely that an event will occur if its probability is higher.

Probability theory, which is widely used in fields of study like statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these ideas an axiomatic mathematical formalization.

Given that

A deck of cards contains 52 cards

The total number of 7's are 4 cards

The total number of black cards is 26

A) Probability of getting a 7 = Total number of 7 / Total cards

Probability of getting a 7  = 4/52

Probability of getting a 7  = 1/13

B) Probability of getting a Black card = Total number of Black cards/ Total cards

Probability of getting a Black card = 26/52

Probability of getting a Black card = 1/2

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The original price of the toy is p.

An easier way to understand this problem is : The original price is 1, or 100%. Now, it's reduced by 15%, so the new price is 100% - 15% = 85%.

85% can be converted to 0.85, or 85/100. Therefore, the answer is 0.85p

The length of the arc whose central angle is 50° is 10.91.

Here, we are given that a circle has a circumference of 25π.

The length of the arc of a circle is given by the following formula-

(∅/360)*2πr

where ∅ is the measure of the angle that the arc subtends at the center and r is the radius of the circle.

Here, we are already given the circumference, thus, 2πr = 25π.

And, the central angle is given to be 50. Thus, ∅ = 50

Now, substituting the values in the above formula we can calculate the length of the arc as follows-

(50/360)*25π

= 5/36 × 25π

= 125/36 × 22/7

= 2,750/ 252

= 10.91

Thus, the length of the arc whose central angle is 50° is 10.91.

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Total amount will be $1520.53(approx.)

What is Compound Interest?

Compound interest is calculated by multiplying the initial loan amount, or principal, by the one plus the annual interest rate raised to the number of compound periods minus one.The formula is,

A = P(1 + r/n)^(n*t)

Given,

principle P = $900

rate r = 6%

time t = 10 years

Put these values in formula, i.e, A = P(1 + r/n)^(n*t)

A = 900 * ( 1 + 6/100)^10

   = 900 * (106/100) ^ 10

After solving we get, A = $1520.53

Therefore, the total amount will be $1520.53(approx.)

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heared about meet, wxa szcx ewn

Tables can help to see patterns in data. Tables make the most difficult problems much easier. These are the advantage to using tables.

The reader can immediately examine the results by using tables to organize data that is too complex or detailed to be fully described in the text. By omitting numerical data from the text, they can be used to highlight trends or patterns in the data and to improve the readability of manuscripts. A table is a way to organize information or data, usually in rows and columns but sometimes with more complicated structures. In research, communication, and data analysis, tables are frequently employed. Large amounts of numerical or statistical data can be efficiently and effectively represented using scientific tables and graphs. In contrast to reading a verbose description of the information, readers are frequently drawn to tables and figures because they view them as being easier to understand.

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The area of the first and second circles is 36π m² and 9π m², respectively.

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Answer:

y = x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 1 , then

y = x + c ← is the partial equation

to find c substitute (2, - 1 ) into the partial equation

- 1 = 2 + c ⇒ c = - 1 - 2 = - 3

y = x - 3 ← equation of line

It is to be noted that the amount of cubic yards of topsoil that Helena purchased is 7 Cubic Yards. (Option D) Here is how we arrived at that answer.

Let the compost purchased be x cubic yards

And the topsoil purchased be y cubic yard

Hence

x+y = 10 .......................................1

Also

Total cost incurred = 25x+15y=180

Dividing the whole equation by 5 we get

5x+3y=36 ........................................2

Multiply 1 by 3 and subtract it from 2

5x+3y=36

-

3x+3y=30

2x      =6 Solving for x

x = 3

Plug x back into equation 1, and we have

x+y=10, this become

3+y=10 Solving for y, we have

y=10-3

=7

Hence it is correct to state that Helena purchased 7 cubic yards of topsoil.

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Answer:

86995.5

Step-by-step explanation:

86995.499184 86995.49918

Answer:

The right answer choices are B, C, and F

it D  that the fertilizer with the urea supplement is more effective than the fertilizer without it.

A histogram is the way of representation of data that is utilized to appear the frequency distribution utilizing the rectangle comparable to a bar graph. in order to decide which fertilizer is superior for plant development Farmers conducted a survey consisting of one fertilizer containing an urea supplement, whereas the other does not contain a urea supplement. in which they haphazardly chose 20 plants of the same species developing in their region. ten out of 20 on which the urea-enhanced fertilizer was applied and the rest with the non-urea fertilizer on the other 10 plants.  So After three months At just the beginning of the month, 4 plants showed normal development with the urea supplement, whereas as it were 2 plants appeared to this development when urea isn't supplied. for the second month, 7 plants showed normal development with urea supplement, whereas  4 plants appeared this growth when urea isn't supplied and in the last month of the experiment, 5 plants showed over normal development.

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Constant of proportionality  : [tex]\frac{1}{3}[/tex]

Equation: y = ka

How are the values calculated?

a: 2, 3, 10, and 12

y: 2/3, 1, 10/3, and 4

Let the constant of proportionality = k

If x and y are directly proportional ,

We know , k = [tex]\frac{y}{x}[/tex]

Here, k = [tex]\frac{y}{a}[/tex]

Considering y = 2/3 and a =2

k =   [tex]\frac{2}{3*2}[/tex] =   [tex]\frac{2}{6}[/tex]  =  [tex]\frac{1}{3}[/tex]

Thus, the constant of proportionality ( k) =  [tex]\frac{1}{3}[/tex]

The equation y is given by ,

y =  ka

Let us verify,

For k = 1/3 and a = 12

[tex]y=\frac{1}{3} *12\\\\y=4[/tex]

Thus the equation is y = ka

What is constant of proportionality?

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Answer:

6

Step-by-step explanation:

4-x/3=2

4-6/3=2

The equation of the line perpendicular to y = 6x -2 and passes through (6, -2) is y = - 1 / 6 x - 1

The equation of a linear graph can be represented in slope intercept form.

Therefore,

y = mx + b

where

Therefore,  the equation of the line is perpendicular to y = 6x -2 and passes through (6, -2).

Perpendicular lines follows the rule below:

m₁ m₂ = -1

6m₂ = -1

m₂ = - 1 / 6

Therefore, let's find the y-intercept using (6, -2)

y = - 1 / 6 x + b

-2  = - 1 / 6 (6) + b

- 2 + 1 = b

b = -1

Therefore, the equation of the line is y = - 1 / 6 x - 1

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Answer:

32 square units

Step-by-step explanation:

A plot of the points shows that PQRS is a rectangle.

The length of this is the distance of the segment PQ = distance of segment RS = 6.4 units

The width QR = width PS = 5 units

The area is 5 x 6.4 = 32 square units

Lengths are calculated as follows

Finding length of PQ using distance formula:
[tex]\overline{PQ} = \sqrt{(4-0)^2 + ((7-2)^2}\\\\= \sqrt{4^2 + 5^2}\\\\= \sqrt{16 + 25}\\\\= \sqrt{41}\\\\= 6.4\\[/tex]

Finding length of QR using distance formula:
[tex]\overline{QR} = \sqrt{8-4)^2 + (4 - 7)^2}\\\\= \sqrt{4^2 + (-3)^2}\\\\= \sqrt{16 + 9}\\\\=\sqrt{25}\\\\= 5\\[/tex]

Answer:

42

Step-by-step explanation:

We set it equal since the equations are equivalent

2x-27=x+15

2x=x+42

X=42

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Finding the numeric value of the function, the time it will take to read a book of 218 pages is given by:

196.2 minutes.

To find the numeric value of a function, we replace each instance of the variable in the function or in the expression by the desired value in which we want to find the numeric value.

In the context of this problem, the function is given by:

y = 4.5x/5

In which the meaning of the variables is given by:

For a book of 218 pages, the time is found calculating the numeric value at x = 218, that is, replacing the lone instance of x in the function by 218, hence it is given by:

y = 4.5 x 218/5 = 196.2 minutes.

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Given that g(x)=2x + 1,

therefore, the value of g(a+h) and g(a) can be written as,g(x)=2x + 1g(a+h)=2(a+h) + 1     
   = 2a + 2h + 1

g(x) = 2x + 1g(a) = 2(a) + 1   
   = 2a + 1

Now, the value of g(a+h)-g(a) will be,

g(a+h) - g(a)= (2a + 2h + 1) - (2a + 1)= 2a + 2h + 1 - 2a - 1= 2h

Hence, the value of g(a+h)-g(a) is 2h.

Answer:

6

explanation:

divide the 4.5 pounds of sunflower seeds by the 0.75 pounds of sunflower seeds

4.5/0.75= 6

Answer:

6 because 4.5 divided by 0.75 equals 6.

Step-by-step explanation:

Yes it is possible for a rectangle to have irrational sides and rational area.

What are rational numbers?

Ration numbers is an ordered pair of integers a, b written in the form a/b where b is not equal to zero.

We are given that sides of rectangle are irrational can the rectangle have rational area

Let us consider that sides of the rectangle be [tex]2\sqrt{2}[/tex] and [tex]\sqrt{2}[/tex]

Hence the area of the rectangle is the product of sides which is [tex]4[/tex] sq. units

Which is a rational number

Hence, Yes it is possible for a rectangle to have irrational sides and rational area

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Given:

A U.S. Geological Survey map has a scale of 1:24200

There are two buildings that are 3.38 miles apart.

We will find how they are inches apart on the map

First, convert from miles to inches

1 mile = 63 360 inches

So, 3.38 miles = 3.38 * 63 360 inches = 214156.8 inches

The map has a scale of 1:24200

So, using the ratio and the proportions, we will find the length on the map as follows:

Rounding to the nearest hundredth

So, the answer will be: 8.85 inches

Two angles are complementary. The measure of the larger angle is 10 greater than 9 times the smaller angle, so the measure of both angles will be 8° and 82°.

The two angles' complement and supplement are determined by the sum of their measurements. The two angles are said to be complimentary if their combined measurement equals that of a straight angle.

According to the question, the equation will form :

x = 9x + 10                      (1)

As we know that for complementary angles,

x + y = 90°

9y +10 + y = 90°

10y = 80°

y = 8°

Substitute this value in equation (1)

x = 9(8) + 10

x = 82°.

Hence, the two angles are 8° and 82° respectively.

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The total volume of water in the two jugs​ is 3.55 liters.

Given,

Jug A has 2.17 liters of water

Jug B has 0.79 liters less than jug A.

Solution:

Since jug B has 0.79 liters less than jug A.

Jug B = 2.17 - 0.79

= 1.38 litres

The total volume of water in the two jugs​ = 2.17 liters + 1.38 liters

The total volume of water in the two jugs = 3.55 liters

Therefore, the total volume of water in the two jugs​ is 3.55 liters.

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The values of the variables are :

10. x = 8 and y = 9

11.  x = 20 /9 and y = - 7/ 9  

12.  x = 3.08 and y = 4x = 12.32

10 . Given equations are ; 7x -5y = 11 ------- equation 1

and y = x + 1

On substituting this value in equation 1

we get 7x - 5 ( x + 1) = 11

7x - 5x - 5 = 11

2x = 16

x = 8 and thus y = 8 + 1 = 9

11. Given equations are : 5x - 4y = 22

x = y+ 3

On again substituting the values we get

5y + 15 - 14 y = 22

- 9 y = 7

y = - 7/ 9 and x = 20 / 9

12. Given equations are 3x + 8y = 108

and y = 4x

On again substituting equations we will get

3x + 32x = 108

35 x = 108

x = 108 / 35

x = 3.08 and y = 4x = 12.32

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Using limit definition of the derivative, The value of f'(3) is 2.

By determining the limit of a slope expression, one can get the instantaneous rate of change (derivative).

The derivative of a function f at x is the instantaneous rate of change of the function at x since the derivative is defined as the limit that determines the slope of the tangent line to a function.

Given function

f(x) = x² - 4x.

derivate with respect to x

f'(x) = 2x - 4

put x = 6

f'(x) = 2(3) - 4

= 6-4

=2

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The value of the smaller number is 5

From the question, we are to determine the value of the smaller number

Let one of the numbers be x and the other number be y

From the given information,

The difference of two numbers is 1

That is,

x - y = 1

and

Their sum is 11

That is,  

x + y = 11

Now, we will solve the equations simultaneously

From the first equation

x - y = 1

x = 1 + y     ------------- (3)

Substitute into the second equation

x + y = 11

1 + y + y = 11

1 + 2y = 11

2y = 11 - 1

2y = 10

y = 10/2

y = 5

Substitute the value of y into equation (3)

x = 1 + y

x = 1 + 5

x = 6

Hence, the number is 5

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