Explain how to find the constant of proportionality for the ratio of robins to cardinals.


Not really sure how this works!! Thank you for all help

Answer:

The answer is D.

Step-by-step explanation:

Key:

1 dime = $0.10

1 nickel = $0.05

Solve:

A. 70+10=80

B. 60+10=70

C. 50+15=65

D. 60+15=75, so D is correct.

Answer:

(-1, 0) and (8, 9)

Step-by-step explanation:

x² - 6x-7 = x + 1

x² - 7x - 8 = 0

(x - 8)(x + 1) = 0

x = -1, 8.

When x = - 1, y = 0

and x = 8, y = 9

A .The canoe left the campsite did the motorboat catch up with it 3 hrs and 40 minutes

B . The motorboat travel at 1 hr 40 minutes

A group of campers and one group leader left a campsite in a canoe.

They traveled at an average rate of 10 km/h.

1st Group DATA:

rate = 10 km/h ; distance = x km ; time = d/r = x/10 hrs

Two hours later, the other group leader left the campsite in a motorboat.

He traveled at an average rate of 22 km/h.

Group Leader DATA:

rate = 22 km/h ; distance = x km ; time = d/r = x/22 hrs

A. How long after the canoe left the campsite did the motorboat catch up with it?

Group time - Leader time = 2 hr

x/10 - x/22 = 2

Multiply thru by 110 to get:

11x - 5x = 220

6x = 220

x = 110/3 = km

canoe total time = x/10 = (110/3)/(10) = 11/3 = 3 hrs and 40 minutes

B. How long did the motorboat travel?

motorboat time = x/22 = (110/3)/22 = 1 hr 40 minutes

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Answer:

22 students per class

Step-by-step explanation:

hope this helps :)

The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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Answer:

$

180

Step-by-step explanation:

The original price is the quotient between $120 and 2/3, we get:

P = $180

We know that 2/3 of the original price is $120, then to get the original price, we need to take the quotient between $120 and 2/3.

\(P = \frac{\$120}{2/3} = (3/2)*\$ 120\)

By taking that quotient we will see that the original price of the coat is:

\(P = (3/2)*\$120 = $180\)

We conclude that the original price of the coat is $120.

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a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

What is inequality?

An inequality is a mathematical statement that shows the relationship between two values where one value is either greater than or less than the other value. It is represented by symbols such as >, <, ≥, or ≤. For example, if x is a variable and we want to express that x is greater than 5, the inequality would be written as x > 5.

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) To graph the region, we can plot the lines that define the inequalities and shade the area that satisfies all of them.

c) Solving the system of inequalities graphically, we find the maximum number of machines that can be installed is 11 (6 small and 5 large).

d) To find the maximum profit, we need to substitute the number of machines into the profit equation. P = 250,000X + 300,000Y. Plugging in X = 6 and Y = 5, we find the maximum profit to be 2,500,000.

Hence,

a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72

b) We have drawn the graph.

c) The maximum number of machines that can be installed is 11.

d) The maximum profit is 2,500,000.

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Answer: 7 and 17

Step-by-step explanation:

Since the area of a rectangle is the product of the two sides, the product of these two numbers must be 119.

The factors pairs of 119 are 1 and 119, and 7 and 17.

x+7 and x-3 have a difference of 10. The difference of 7 and 17 is also 10. Hope this helped!

In the future, please take a less blurry photo because I had to guess the part where I think it said x-3.

1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.

2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.

3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.

1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.

2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.

3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.

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The values of the variables in the expression are as follows:

a = 3

b = 4

c = 3

d = -4

Here, we have,

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Let's find the value of the variables in the expression.

(ax + b)(cx - d) = 9x² - 16

acx² - adx + bcx - bd = 9x² - 16

Therefore,

9x² - 16 = (3x + 4) (3x - 4)

Hence,

(ax + b) = (3x + 4)

Therefore,

a = 3

b = 4

(cx - d) = (3x - 4)

cx = 3x

d = -4

Therefore,

c = 3

d = -4

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cmplete question:

What is the value of a ?

What is the value of b ?

What is the value of c ?

What is the value of d ?

1)  the break-even quantities for each profit function are,

x = - 14920

x = 25680

2) the break-even quantities for each profit function are,

x = 5000

x = 4000

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equations are,

1) p(x) = -2x² + 22x - 17

2) p(x) = -2x² + 18x - 40

Now, To determine the break-even quantities for each profit function, where x is the number sold, in thousands, we can put p(x) = 0 in both equation and solve for x;

1) p(x) = -2x² + 22x - 17

-2x² + 22x - 17 = 0

x = - 22 ± √22² - 4×- 2×- 17 / (2×- 2)

x = - 22 ± √484 - 136 / - 4

x = - 22 ± √348 / - 4

x = - 22 ± 81.7 / - 4

x = (- 22 + 81.7) / - 4

x = - 59.7 / 4

x = - 14.92

x = (- 22 - 81.7) / - 4

x = 102.7 / 4

x = 25.68

Thus, the break-even quantities for each profit function are,

x = - 14920

x = 25680

2) p(x) = -2x² + 18x - 40

-2x² + 18x - 40 = 0

x² - 9x + 20 = 0

x = - (- 9) ± √81 - 4×1×20 / 2

x = 9 ± √1 / 2

x = (9 ± 1) / 2

x = (9 + 1) / 2

x = 10/2

x = 5

x = (9 - 1) / 2

x = 8/2

x = 4

Hence, the break-even quantities for each profit function are,

x = 5000

x = 4000

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Answer:

Step-by-step explanation:

Answer:

He had $200 to begin with.

Answer:

x=29

Step-by-step explanation:

because the two sides of the acute triangle are the same length, the ones at the bottom are the same as well. the total of the angles of a triangle is 180, and we know that one of the angles are 64 so we subtract that from 180 and get 116 which we divide by two to get the other two angles: 58 and 58. at the bottom of the image, two angles are connected and make a straight 180 line so we can take 58 out of that 180 and get 122 in the obtuse angle and divide by two to get 29 in the acute angles of the obtuse triangle.

Answer:

C. 1 and 2

Step-by-step explantation:

First, i would order them as U>T, T>R, R>Q, S>T

we can rewrite them as

U>T>R>Q,

now adding S, we get U>S>T>R>Q,

so U>S

We can also rewrite all of them as inequalities:

U-T>0

T-R>0

R-Q>0

S-T>0

Add R-Q and T-R

(R-Q)+(T-R)>0

-Q+T>0

T>Q, but because S>T we can say S>Q

The vertex of the graphed function f(x) = [x - 4] + 3 is (4, 3).

The function f(x) = [x - 4] + 3 is in the form of an absolute value function, where the expression inside the absolute value brackets represents the input value shifted horizontally by 4 units to the right.

The constant term of 3 represents a vertical shift upwards by 3 units.

To find the vertex of this function, we need to determine the x-coordinate that corresponds to the minimum value of the absolute value function.

In this case, since the absolute value function is within brackets and not being multiplied or divided by a coefficient, the minimum value occurs at the point where the expression inside the brackets equals zero.

Therefore, setting x - 4 = 0, we find x = 4.

Substituting this x-value into the function, we find f(4) = [4 - 4] + 3 = 3. So the vertex of the graphed function is located at the point (4, 3), where x = 4 and y = 3. This means that the graph is shifted 4 units to the right and 3 units upward from the origin.

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Using matrices the simultaneous equation is solved to get x = 3 and y = 5

This method required finding determinants in three occasions then dividing

The given equation

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]= \left[\begin{array}{c}19\\8\\\end{array}\right]\)

the determinant is

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right]\)

3 * 1 - 2 * 1 = 3 - 2 = 1

Solving for x

determinant while replacing x values

\(\left[\begin{array}{cc}19&2&\\8&1\\\end{array}\right]\)

19 * 1 - 2 * 8 = 19 - 16 = 3

solving for x = 3/1 = 3

Solving for y

determinant while replacing y values

\(\left[\begin{array}{cc}3&19&\\1&8\\\end{array}\right]\)

3 * 8 - 19 * 1 = 24 - 19 = 5

solving for y = 5/1 = 5

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Answer:

Step-by-step explanation:

a-b=(-7)-(-16)=-7+16=9

Answer: B  :)

Step-by-step explanation:

you need to find the number of containers for all the juice so add all of them together and then divide by 1.4 or the volume of the containers to get to amount you need

When \(n=0\), we have

\(5^{3^0} + 1 = 5^1 + 1 = 6\)

\(3^{0 + 1} = 3^1 = 3\)

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for \(n=k\), that

\(3^{k + 1} \mid 5^{3^k} + 1\)

Now for \(n=k+1\), we have

\(5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)\)

so we know the left side is at least divisible by \(3^{k+1}\) by our assumption.

It remains to show that

\(3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1\)

which is easily done with Fermat's little theorem. It says

\(a^p \equiv a \pmod p\)

where \(p\) is prime and \(a\) is any integer. Then for any positive integer \(x\),

\(5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3\)

Furthermore,

\(5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3\)

which goes all the way down to

\(5^{3^k} \equiv 5 \pmod 3\)

So, we find that

\(\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3\)

QED

Answer:

2.12in

Step-by-step explanation:

Pizza is circular in nature

Area of a circle = πr²

r is the radius

Given

A = 14.13in²

14.12 = 3.14r²

r² = 14.12/3.14

r²= 4.49

r = 2,12in

Hence the radius of the pizza is 2.12in

Answer:

false

Step-by-step explanation:

mmmmmmmmmmmmmmmm

Answer:

False

Step-by-step explanation:

If you do the equation, the first answer is equal to 2.1230842e-28 and the second answer is equal to 3.1866355e-11. Therefore they are not the same.

Answer:

15x+25 ; 70

Step-by-step explanation:

Given that,

Fernando cleans pools for the summer for $25 an hour plus a supply fee of $15.

Here, $25 is constant and $15 increases as the number of hour increase. For x hours, the cost for Fernando to clean a pool is given by :

y = 15x+25

For 3 hours,

y = 15(3)+25

= 45 + 25

= 70

So, the required option is (c) " 15x+25 ; 70 ".

Answer:

Plan 2

Step-by-step explanation:

Plan 2 has an initial cost of $50 plus $5 for each hour thereafter.

Plan 1 has a steady cost of $29 per hour.

As an example, if a student is tutored for 5 hours, Plan 2's cost would be $50 + $5(5) = $75.

Plan 1's cost would be $29(5) = $145.

The set of values that we are permitted to enter into our function is referred to as the domain of a function. The x values for a function f make up this collection (x). A function's range is the range of values that it can accept as input. When we enter an x value, the function outputs this set of outcomes.

(a) f - {1 2 3 4 5} -> {1 2 1 2 1}

This function is neither injective nor surjective. It is not injective because f(1) = f(3) = f(5) = 1, and it is not surjective because 2 is not in the range.

(b) f - {1 2 3 4 5} -> {1 2 3 1 2}

This function is neither injective nor surjective. It is not injective because f(1) = f(4) and it is not surjective because 3 is not in the range.

(c) f(x) = { x if x < 3, x - 3 if x > 3}

This function is both injective and surjective, and hence bijective. It is injective because each element in the domain maps to a unique element in the codomain, and it is surjective because every element in the codomain is mapped to by at least one element in the domain. Hence, this function is bijective.

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Tο summarize, here are the classificatiοns fοr each functiοn:

(a) f(x) = {1 2 1 2 1} is neither injective nοr surjective.

(b) f(x) = {1 2 3 1 2} is neither injective nοr surjective.

(c) f(x) = { x if x < 3 x -3 if x > 3 } is neither injective nοr surjective.

In mathematics, a functiοn definitiοn is a statement that defines a relatiοnship between input values (called the dοmain) and οutput values (called the cοdοmain οr range). A functiοn takes an input value and prοduces a unique οutput value based οn a certain rule οr algοrithm.

(a) The functiοn is neither injective nοr surjective. It is nοt injective because bοth 1 and 2 are mapped tο 1, sο there are multiple inputs that map tο the same οutput. It is nοt surjective because the οutput 3 is never used.

(b) The functiοn is neither injective nοr surjective. It is nοt injective because bοth 1 and 2 are mapped tο the οutput 1, sο there are multiple inputs that map tο the same οutput. It is nοt surjective because the οutput 3 is never used.

(c) The functiοn is neither injective nοr surjective. It is nοt injective because bοth 3 and 4 are mapped tο the οutput 0, sο there are multiple inputs that map tο the same οutput. It is nοt surjective because the οutput 1 is never used.

Hence,

Tο summarize, here are the classificatiοns fοr each functiοn:

(a) f(x) = {1 2 1 2 1} is neither injective nοr surjective.

(b) f(x) = {1 2 3 1 2} is neither injective nοr surjective.

(c) f(x) = { x if x < 3 x -3 if x > 3 } is neither injective nοr surjective.

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Answer:

the product of the decimal equivalents of all discount in the series

Answer:

Option 1, Option 2, Option 4

Step-by-step explanation:

A function represents a set of ordered pairs with the domain/x-value being different for every set. These include sets 1, 2, and 4.

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The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.

We have,

Cylinder and prism.

Here we have to find the equivalent ratio to 8/2.

First simplifying the given ratio as

8/2

= (4 x 2)/2

= 4 /1

Now, some more ratios equivalent to 8/2.

1. 8/2 x 3/3 = 24/ 6

2. 8/2 x 4/4 = 32/8

3. 8/2 x 6/6= 48/12

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Answer:

I believe it might be d but I'm not sure, sorry hope I could help

We are given the following complex fraction

8/1 is divided by 3/5

Recall that dividing is the same as multiplying by the reciprocal.

The reciprocal of 3/5 is 5/3 (simply invert the fraction)

Now simply multiply the fractions

Therefore, the simplified fraction is 40/3