The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.

The numbers are: ___ ,___ or ____,___

HELLO!!! ^-^

The answer is 1.

If √6 is the geometric mean between 6 and another number, then the number is 1.

(I had the same question and got it right using this answer so yeah) ^-^

Have an amazing day!!! ^-^

Historical Fact:

Back in the older days, the word awful was a word used to praise someone!  That is because aw in awful comes from the origin awe which is used when someone is in awe of you!!! For example: You are AWESOME!!!

The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation.

The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation. In this case, the opportunity cost could be the time she could have spent with her friends. By deciding to work, Marie forgoes the opportunity to socialize and spend quality time with her friends.

Opportunity cost is an important concept in economics that highlights the trade-offs we face when making choices. It helps us understand the value of the options we give up when we choose one alternative over another. In Marie's case, the opportunity cost of earning money and learning new skills is the limited time she can spend with her friends.

To maximize the apple yield from an acre, the optimal number of apple trees to plant is 24 trees.

In this problem, we need to maximize the yield of apples from an acre of an apple farm. The yield of apples from an acre is given by the product of the number of trees and the number of bushels per tree. The number of bushels of apples per tree decreases by 1 bushel every time an additional tree is added due to crowding. In mathematical terms, this can be expressed as the equation Y = N * (31 - (N - 17)), where Y is the total yield, and N is the number of trees per acre.

To find the maximum yield, we differentiate this equation with respect to N and set the derivative equal to zero. This gives us N = 24. Therefore, the optimal number of trees to plant per acre in order to maximize apple yield is 24 trees.

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To maximize the yield of apples per acre, plant 24 trees. This balances the number of trees and the yield per tree due to crowding.

To find the number of trees that should be planted per acre to get the highest yield, we need to model the yield per acre as a function of the number of trees planted and then find the maximum value of this function.

1. Define the variables:

  - Let ( n ) be the number of trees planted per acre.

  - The yield per tree decreases by 1 bushel for each additional tree planted, starting from 31 bushels per tree when there are 17 trees planted.

2. Model the yield per tree:

  - If ( n = 17 ), the yield per tree is 31 bushels.

  - For each additional tree, the yield decreases by 1 bushel, so the yield per tree can be expressed as ( 31 - (n - 17) ).

  Simplifying this, we get:

   Yield per tree = 31 - n + 17 = 48 - n

3. Model the total yield per acre:

  - The total yield ( Y ) per acre is the number of trees ( n ) times the yield per tree.

 Y = n × (48 - n)

4. Formulate the quadratic function:

  Y = 48n - [tex]n^2[/tex]

5. Find the maximum yield:

  - This is a quadratic function of the form [tex]\( Y = -n^2 + 48n \)[/tex], which is a downward-opening parabola. The maximum value of \( Y \) occurs at the vertex of the parabola.

  - The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] occurs at [tex]\( x = -\frac{b}{2a} \)[/tex] . In our case, ( a = -1 ) and ( b = 48 ).

 [tex]\[ n = -\frac{48}{2(-1)} = \frac{48}{2} = 24 \][/tex]

So, to get the highest yield, 24 trees should be planted per acre.

Answer:

Thus, (3,0) Rx O,90° changes to (0,-3)

Step-by-step explanation:

Given: Rx  O,90: (3,0)

To determine:

Point P (3,0) rotation about origin (0,0) of 90°

and then Reflection about x-axis.

Rotation of P(x,y) about origin of 90°

P(x,y) changes to P'(y,x)

Therefore, P(3,0) changes to P'(0,3)

Now we take reflection about x-axis

R(x,y) changes to R'(x,-y)

Therefore, P'(0,3) changes to P''(0,-3)

Please see the attachment for both rule.

Thus, (3,0) Rx O,90° changes to (0,-3)

Answer:

The domain of f(x) is all real numbers greater than or equal to -2

Step-by-step explanation:

We have been given that

[tex]f(x)=2(x)^2+5\sqrt{x+2}[/tex]

Domain is the set of x values for which the function is defined.

The given function is the combination of a square and square root function.

Square function is defined for all real values. Whereas, the square root function is defined for only positive values.

Therefore, the function is defined when

[tex]x + 2\geq0[/tex]

Subtract 2 to both sides

[tex]x\geq-2[/tex]

Hence, the domain of f(x) is all real numbers greater than or equal to -2

Answer:

1. option D is correct;  [tex](x+2)^2+(y+7)^2=36[/tex]  

2. option C is correct; center: (-4, 5) and radius = 11 unit

Step-by-step explanation:

The general equation of the circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]                .....[1]

where,

(h, k) is the center of the circle and r is the radius of the circle.

1.

As per the statement:

The center of a circle is at (−2, −7) and its radius is 6.

⇒(h, k) = (-2, -7) and r = 6 units

Substitute these in [1] we have;

[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]  

⇒[tex](x+2)^2+(y+7)^2=36[/tex]  

Therefore, the equation of circle is, [tex](x+2)^2+(y+7)^2=36[/tex]  

2.

As per the statement:

The equation of a circle is:

[tex](x+4)^2+(y-5)^2 = 121[/tex]

We can write this as:

[tex](x-(-4))^2+(y-5)^2 = 11^2[/tex]

On comparing with equation [1] we have;

(h, k) = (-4, 5) and r = 11 units

Therefore, the center and radius of the circle is,

center: (-4, 5) and radius = 11 unit

The approximate percent change is:

55%

It is given that:

The new number, 550, is 200 more than the original number.

Let the original number be: x

That means:

550=200+x

x=550-200

x=350

Now, the percent change is calculated as:

[(New number-Original number)/original number]×100

= [tex]\dfrac{550-350}{350}\times 100\\\\=\dfrac{200}{350}\times 100\\\\=57.14\%[/tex]

which is approximately equal to :

55%

In this exercise we have to use the knowledge of sine to be able to calculate the triangle values, in this way we can say that:

[tex]h= 8.3[/tex]

So from the values ​​initially given we can describe that the calculation for this triangle will be:

[tex]x / 48 = sin(10)\\ x = 48* .1736\\ x = 8.3335\\ sin 10^0 = h/48\\ h = 48 sin 10^0\\ h = 8.3 inches[/tex]

See more about triangles at brainly.com/question/25813512

Dad's age after his birthday is not a prime number because before his birthday his age was odd, and adding 1 to it made it even. All even numbers greater than 2 are not prime as they are divisible by 2. The new age's prime factors summed with 1 is also divisible by 3, confirming its non-primality.

Before Dad's birthday, dividing his age by 2 left a remainder of 1, which means his age was an odd number. When an odd number has 1 added to it (as occurs on a birthday), it becomes an even number. Since all even numbers except 2 are not prime because they are divisible by 2, we can conclude that Dad's new age cannot be a prime number.

Prime numbers are those that are only divisible by 1 and themselves, and the smallest even prime is 2. Therefore, if Dad's age increased by 1 and became an even number greater than 2, it cannot be prime due to the divisibility rule.

Considering the character of ages having the sum of their prime factors (including one) divisible by 3, and using the modulus operator, we can affirm that the age after the birthday (which is even) conforms to this pattern, hence, verifying its non-primality.

[tex] |\Omega|=6^2=36\\
|A|=\underbrace{2}_{\text{the sum is 3}}+\underbrace{4}_{\text{the sum is 9}}=6\\\\
P(A)=\dfrac{6}{36}=\dfrac{1}{6}\approx17\% [/tex]

d.........................

Answer:  The correct probability is (D) [tex]P(C/A)=\dfrac{13}{17}.[/tex]

Step-by-step explanation:  We are given to select the option that gives the correct probability statements using the Venn-diagram in the figure.

From the figure, we can see that there are three events, A, B and C.

And,

[tex]n(A)=1+6+7+3=17,\\\\n(B)=1+6+4+9=20,\\\\n(C)=6+4+6+7=23,\\\\n(A\cap B)=1+6=7,\\\\n(A\cap C)=6+7=13,\\\\n(B\cap C)=6+4=10,\\\\n(A\cap B\cap C)=6.[/tex]

By the law of SET THEORY, we have

[tex]n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\\\\\Rightarrow n(A\cup B\cup C)=17+20+23-7-13-10+6\\\\\Rightarrow n(A\cup B\cup C)=36.[/tex]

So, the total number of elements in the sample space 'S' will be

n(S) = 36 + 8 = 44.

Therefore,

[tex]P(A/B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{\dfrac{n(A\cap B)}{n(S)}}{\dfrac{n(B)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{20}=\dfrac{7}{20},\\\\\\\\P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\dfrac{n(B\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{7}{44}\times \dfrac{44}{17}=\dfrac{7}{17},\\\\\\\\P(A/C)=\dfrac{P(A\cap C)}{P(C)}=\dfrac{\dfrac{n(A\cap C)}{n(S)}}{\dfrac{n(C)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{23}=\dfrac{13}{23},\\\\\\\\P(C/A)=\dfrac{P(C\cap A)}{P(A)}=\dfrac{\dfrac{n(C\cap A)}{n(S)}}{\dfrac{n(A)}{n(S)}}=\dfrac{13}{44}\times \dfrac{44}{17}=\dfrac{13}{17}.[/tex]

Thus, the correct probability is [tex]P(C/A)=\dfrac{13}{17}.[/tex]

Option (D) is correct.

The probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

For the value of probability P(A|B):

We know that:

[tex]\rm P(A/B)=\frac{P(A\cap B)}{P(B)} \Rightarrow \frac{\frac{n(A\cap B)}{n(T)} }{\frac{n(B)}{n(T)} }[/tex]

From the Venn diagram:

n(A∩B) = 7, n(B) = 20, n(T) = 44

P(A/B) = (7/44)×44/20)

P(A/B) = 7/20

For P(B|A):

[tex]\rm P(B/A)=\frac{P(B\cap A)}{P(A)} \Rightarrow \frac{\frac{n(B\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]

The values of n(B∩A) = 7, n(A) =17

P(B/A) = (7/44)×(44/17)

P(B/A) = 7/17

For P(A|C):

[tex]\rm P(A/C)=\frac{P(A\cap C)}{P(C)} \Rightarrow \frac{\frac{n(A\cap C)}{n(T)} }{\frac{n(C)}{n(T)} }[/tex]

The value of n(A∩C) = 13, n(C) = 23

P(A/C) = (13/44)×(44/23)

P(A/C) = 13/23

For P(C|A):

[tex]\rm P(C/A)=\frac{P(C\cap A)}{P(A)} \Rightarrow \frac{\frac{n(C\cap A)}{n(T)} }{\frac{n(A)}{n(T)} }[/tex]

The values of n(C∩A) = 13, n(A) = 17

P(C|A) = (13/44)×(44/17)

P(C|A) =13/17

Thus, the probability P(A/B) is 7/20, the probability P(B/A) is 7/17, the probability P(A/C) is 13/23, and the probability is P(C|A) is 13/17 option fourth is correct.

Learn more about the Venn diagram here:

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The answer is:

y = -x + 13

Work/explanation:

First, we will write the equation in the form of [tex]\sf{y-y_1=m(x-x_1)}[/tex], which is point slope.

Plug in the data

[tex]\large\begin{gathered}\sf{y-15=-1(x-(-2)}\\\sf{y-15=-1(x+2)}\\\sf{y-15=-1x-2}\\\sf{y-15=-x-2}\\\sf{y=-x-2+15}\\\sf{y=-x+13}\end{gathered}[/tex]

Hence, the slope intercept is y = -x + 13.