Suppose that the relation S is defined as follows. S={(-2, 6), (1,2), (-2, -4)}Give the domain and range of S. Write your answers using set notation.

Answer: Y = 6  1/2

Step-by-step explanation: Let's begin,

step 1) Isolate the variable by dividing each side by factors that don't contain the variable.

Then, Exact Form:

y = 13/2

Decimal Form:

y = 6.5

Mixed Number Form:

y = 6  1/2

Answer:

The answer is 6.72 x 10⁷

Step-by-step explanation:

The answer is 6.72 x 10⁷ because I solved it and I got this answer.

Answer:

1,2,3,4,6,9,12,18,36

Step-by-step explanation:

Answer:

1/19

Step-by-step explanation:

There are a total of 36+2 = 38 spaces

2 are green

P(green) = green / total

             = 2/38

            =1/19

            .052631579

Answer:

The answer is (1,-1)

Step-by-step explanation:

The best approach for this problem is to plug in the coordinates into the given inequality.

\(7x-3y\geq 10\\\)

(3,4) ------> \(7(3)-3(4)=9\)

9 is less than 10 so, we can rule this one out.

(1,0) -------> \(7(1)-3(0)=7\)

7 is less than 10 so, we can rule this one out.

(1,2) -------> \(7(1)-3(2)=1\)

1 is less than 10 so, we can rule this one out.

(1,-1) -------> \(7(1)-3(-1)=10\)

10 is equal to 10, so this is the answer.

Hope this helps!

As mentioned by Mark there are an unlimited number of pairs that satisfy your equation. So let us see how you can characterize these solutions

if 7x - 3y > 10 then

7x > 10 +3y

Now we can substitute any value for y and get the appropriate value for x. For example I can choose y to be 6

then by substitution

7  must be > 10+ 3*6

or 7x must be > 28

or x must be > 4

So all pairs such that x is > 4 and y = 6 are solutions.

I can create an infinite number of pairs choosing any number for y. Likewise I could have chosen x and solved the problem for y. In the above example I chose 6 for y to make the division easy. I could have chosen any number(real or integer) for y and solved the equation for x  to derive appropriate  pairs

Answer:

Product = \(\dfrac{64}{135}\)

Step-by-step explanation:

The expression is as follows :

\(\dfrac{4}{7}\times \dfrac{8}{9}\times \dfrac{14}{15}\)

We need to find the product of the above expression

As 7 × 2 = 14

So, it will become :

\(4\times \dfrac{8}{9}\times \dfrac{2}{15}\\\\=\dfrac{4\times 8\times 2}{9\times 15}\\\\=\dfrac{64}{135}\)

So, the product of the given fractions is \(\dfrac{64}{135}\).

Answer:

64/135

Step-by-step explanation:

Answer:

Point A:  (2, 10)

Point B:  (-3, 0)

Point C:  (-5, -4)

Point D:  (-5, -32)

Step-by-step explanation:

Points A and B are the points of intersection between the two graphs.

Therefore, to find the x-values of the points of intersection, substitute one equation into the other and solve for x:

\(\implies 2x+6=-2x^2+18\)

\(\implies 2x^2+2x-12=0\)

\(\implies 2(x^2+x-6)=0\)

\(\implies x^2+x-6=0\)

\(\implies x^2+3x-2x-6=0\)

\(\implies x(x+3)-2(x+3)=0\)

\(\implies (x-2)(x+3)=0\)

\(\implies x=2, -3\)

From inspection of the graph:

To find the y-values, substitute the found x-values into either of the equations:

\(\begin{aligned} \textsf{Point A}: \quad 2x+6 & =y\\2(2)+6 & =10\\ \implies & (2, 10)\end{aligned}\)

\(\begin{aligned} \textsf{Point B}: \quad -2x^2+18 & =y\\-2(-3)^2+18 & =0\\ \implies & (-3,0)\end{aligned}\)

Therefore, point A is (2, 10) and point B is (-3, 0).

If the distance between points C and D is 28 units, the y-value of point D will be 28 less than the y-value of point C.  The x-values of the two points are the same.

Therefore:

\(\textsf{Equation 1}: \quad y=2x+6\)

\(\textsf{Equation 2}: \quad y-28=-2x^2+18\)

As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:

\(\implies 2x+6-28=-2x^2+18\)

\(\implies 2x^2+2x-40=0\)

\(\implies 2(x^2+x-20)=0\)

\(\implies x^2+x-20=0\)

\(\implies x^2+5x-4x-20=0\)

\(\implies x(x+5)-4(x+5)=0\)

\(\implies (x-4)(x+5)=0\)

\(\implies x=4,-5\)

From inspection of the given graph, the x-value of points C and D is negative, therefore x = -5.

To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:

\(\begin{aligned} \textsf{Point C}: \quad 2x+6 & =y\\2(-5)+6 & =-4\\ \implies & (-5,-4)\end{aligned}\)

\(\begin{aligned} \textsf{Point D}: \quad -2x^2+18 & = y \\ -2(-5)^2+18 & =-32\\ \implies & (-5, -32)\end{aligned}\)

Therefore, point C is (-5, -4) and point D is (-5, -32).

Answer:

a) A = (2, 10) and B = (-3, 0)

b) C = (-5, -4) and D = (-5, -32)

Explanation:

a) To determine the coordinates of A and B, find the intersection points of  the line "y = 2x + 6" and curve "y = -2x² + 18".

Solve the equation's simultaneously:

y = y

⇒ 2x + 6 =  -2x² + 18

⇒ 2x² + 2x + 6 - 18 = 0

⇒ 2x² + 2x - 12= 0

⇒ 2x² + 6x - 4x - 12 = 0

⇒ 2x(x + 3) - 4(x + 3) = 0

⇒ (2x - 4)(x + 3) = 0

⇒ 2x - 4 = 0, x + 3 = 0

⇒ x = 2, x = -3

Then find value of y at this x points,

at x = 2, y = 2(2) + 6 = 10

at x = -3, y = 2(-3) + 6 = 0

Intersection points: A(2, 10) and B(-3, 0)

b) Given that CD = 28 units. Also stated parallel to y axis so x coordinates for both will be same but differ in y coordinate.

\(2x + 6 = -2x^2 + 18 + 28\)

\(-2x^2 + 18 + 28-2x - 6 = 0\)

\(-2x^2-2x+40=0\)

\(-2x^2-10x+8x+40=0\)

\(-2(x+5)+8(x+5)=0\)

\((-2x+8)(x+5)=0\)

\(x = -5, 4\)

\(\leftrightarrow \sf C(-5, y_2), \ D(-5, y_2)\)

Find y value for Point C : 2x + 6 = 2(-5) + 6 = -4

Find y value for Point D :  -2x² + 18 =  -2(-5)² + 18 = -32

\(\sf \rightarrow Point \ C = (-5, -4)\\ \\\rightarrow Point \ D = (-5, -32)\)

A total of 8 workers are required for a building time of 15 days.

In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:

n ∝ 1 / t

n = k / t

Where k is the proportionality ratio, which can be eliminated by building the following formula:

n₁ · t₁ = n₂ · t₂

If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:

n₂ = n₁ · (t₁ / t₂)

n₂ = 10 · (12 / 15)

n₂ = 10 · (4 / 5)

n₂ = 8

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Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

Answer:

y = -x + 7

Step-by-step explanation:

y = x + 5 works for the first row, but fails for the rest.

y = x + 3 fails for the first row

y = -x + 7 works for the first row ( -1 + 7 = 6)

It works for the second row ( -2 + 7 = 5)

It works for the third row ( -3 + 7 = 4)

And it works for the final row ( -4 + 7 = 3)

Answer:

Step-by-step explanation:

u=㏑ x

x=e^u

v=㏑ y

y=e^v\(x^{2} y^5 =(e^u)^{2} (e^v)^5=e^{2u}e^{5v}=e^{2u+5v}\)

Answer:

D. 2u + 5v

Step-by-step explanation:

answer on edge

Answer:

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Step-by-step explanation:

I used a scientific calculator, 2² is 4 and when I take 4.7 × 10-³ minus 4 the answer is negative, so I'm guessing that it's a number less than 4.

Again, I haven't learned this yet since I'm 12 so it might be wrong.

Answer:

10 [units].

Step-by-step explanation:

1) the x-coordinates have the same value, then

2) the required distance can be calculated as distance between '-5' and '5':

5--5=10 [units].

The probability that an animal has stripes will be 0.86.

The probability that an animal has stripes will be:

= Orange stripes + Brown stripes + Grey stripes

= 0.16 + 0.3 + 0.4

= 0.86

The probability that an animal doesn't have stripes will be:

= 1 - 0.86

= 0.14

Therefore, the probability that an animal doesn't have stripes is 0.14.

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The angled relationship is the Same-side interior angle where x is 6 and ∠EFG is 102°

For the parallel lines ED and FG, where EF is the transversal,

The angle DEF and the angle EFG are same-side interior angles.

By the same-side interior angle theorem, we can say that the interior angles on the same side of the transversal are supplementary (the sum of the angles is 180°).

∠DEF = 13x°

∠EFG = 17x°

∠DEF + ∠EFG = 180°

13x + 17x = 180

30x = 180

x = 6

∠DEF = 13x = 13*6 = 78°

∠EFG = 17x = 17*6 = 102°

Therefore, the angles follow the same-side interior angles relationship, x = 6 and ∠EFG = 102°

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The value of z is 8633/137 or 63.01, approximately.

\(\frac{x}{y} =\frac{z}{100}\)

\(\frac{x}{y}*100 =\frac{z}{100}*100\\ \\100\frac{x}{y} =z\\ \\z=100\frac{x}{y}\)

\(z=100\frac{(86.33)}{(137)}\\ \\z=\frac{8633}{137}=63.01\)

If the calculated value of "z" is correct, then the original equation should return the same value on both sides of the equal symbol (=) when substiting all the variables by their respective value.

\(\frac{86.33}{137} =\frac{\frac{8633}{137}}{100}\\ \\0.63=0.63\)

That's correct!

Hence, the value of z is 8633/137 or 63.01.

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Answer:

(Amount for 1 inch of red ribbon) x (240) = total cost

Step-by-step explanation:

Answer:

htrtrheherh

Step-by-step explanation:

Answer:

YES

Step-by-step explanation:

A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.

Answer:

-------------------------

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

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Answer:

D. 4 units

Step-by-step explanation:

Similar figures have corresponding lengths in proportion.

\(\frac{4x}{2x}=\frac{x+1}{x} \\ \\ 2=1+\frac{1}{x} \\ \\ 1=\frac{1}{x} \\ \\ x=1\)

Therefore, the height of Figure 1 is 4.

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Answer:

7X+7=2(X+1)

7X+7=2X+2

7x-2X =2-7

5X/5 =-5/5

. X =-1

Considering the definition of scale, the length of the Mississippi River on the map is 96.667 cm.

The scale of a cartographic representation, or map scale, is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map.

Scale is the relationship between a real object (for example, the surface of the Earth or a portion of it) and the representation that is made of it.

The scale is represented as a fraction as follows: measured on the map/measured in reality

In this case, you know that:

Considering the definition of scale, you can calculate the length of the Mississippi River on the map as follow:

5 cm/ 120 miles= measured on the map/2320 miles

(5 cm/ 120 miles)× 2320 miles= measured on the map

96.667 cm= measured on the map

Finally, the length of the Mississippi River on the map is 96.667 cm.

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Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.

Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.

The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.

To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.

Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.

The payment for raw materials purchases in July (35% of X pounds) will be:

0.35 * X pounds

The payment for raw materials purchases in August (65% of X pounds) will be:

0.65 * X pounds

Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

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The value of p pennies, n nickels and twice as many quarters as pennies is (51p + 5n) cents or  $(51p + 5n)/100.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).

Given that you have p number of coins of pennies, n number of coins of nickels and  twice as many quarters as pennies.

Thus the number of coins of quarters is 2p.

The value of penny, nickel, and quarter are

1 penny = 1 cent

1 nickel = 5 cents

1 quarter = 25 cents

The value of p number of pennies is p cents.

The value of n number of nickels is (n×5) =5n cents.

The value of 2p number of quarter is (2p × 25) = 50p cent.

The total value is p + 5n + 50p = (51p + 5n) cents

Divide 51p + 5n by 100 to convert it into dollar:

(51p + 5n) cents = $(51p + 5n)/100

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Answer:

3/65 = 0.046 = 4.6%

Step-by-step explanation:

Notice that the total number of marbles is:

6 + 14 + 8 + 12 = 40

Then , the probability of getting a black marble first is 6/40 = 3/20

Now, since the experiment is without replacing, he is left with a total of 39 marbles in the bag, and the probability of getting a clear one is now 12/39

The total probability is the product of these two:

(3/20) x (12/39) = 3/65 = 0.046 = 4.6%

Answer:

25.2

Step-by-step explanation:

168 x .15 = 25.2

\(\large\text{Hey there!}\)

\(\rm{15\%\ of\ 168}\\\\\rm{= 15\% \times 168} \\\\\rm{= \dfrac{15}{100}\times 168}\\\\\rm{= \dfrac{15}{100}\times \dfrac{168}{1}}\\\\\rm{=\dfrac{15\times168}{100\times1}}\\\\\rm{= \dfrac{2,520}{100}}\\\\\rm{= 25.2}\)

\(\huge\text{Therefore, your answer should be: }\)

\(\huge\boxed{\frak{25.2}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)