The sum of two numbers is 9 If one number is 3 subtracted from the​ other, the result is Find the numbers.

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

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Answer:

13

Step-by-step explanation:

The box plot ends at 13.

Box plots show the average score of the data. It shows the minimum, median and maximum. The line inside the box is the median. The minimum, in this case is 0 and the max is 13.

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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The responses to the linear optimization questions are;

Question 1

The optimal daily profit is $380

Question 2

The combination of x and y that yield the optimal value is the option;

x = 0, y = 3

Linear programming is a method by which the optimal solution can be obtained from a model represented mathematically and in which the constraints of the model have linear relationships.

Question 1

Let B represent the number of bear claws, C the almond-filled croissant, F represent the flour, Y represent the amount of yeast and A represent the number of almonds.

The amount of ingredient per each produce is therefore;

B = 6·F + 1·Y + 2·A

C = 3·F + 1·Y + 4A

The amount of ingredient available for the days production is as follows;

Ingredient available; 6600·F + 1400·Y + 4800·A

The constraints are therefore

6·B + 3·C ≤ 6,600

B + C ≤ 1,400

2·B + 4·C ≤ 4800

The maximizing function is therefore;

Profit = 0.2·B + 0.3·F

The equations of the lines are therefore;

B = 1,100 - 0.5·C

B = 1400 - C

B = 2400 - 2·C

The vertices of the feasible region are;

(0, 1100), (600, 800), (1000, 400), 1200, 0)

The values of the maximizing function at the vertices of the feasible region are;

Profit, P = 0.2×1100 + 3×0 = 220

At point (600, 800), P = 0.2×800 + 0.3×600 = 340

At point (1000, 400), P = 0.2×400 + 0.3×1000 = 380

At point (1200, 0), P = 0.2×0 + 0.3×1200 = 360

Question 2

Maximize $3·x + $15·y

Subject to the following constraints;

2·x + 4·y ≤ 12

5·x + 2·y ≤ 10

x, y ≥ 10

The equations are therefore;

4·y ≤ 12 - 2·x

y ≤ 3 - 0.5·x...(1)

5·x + 2·y ≤ 10

2·y ≤ 10 - 5·x

y ≤ 5 - 2.5·x...(2)

x ≥ 10, y ≥ 10

The coordinates of the vertices of the feasible region are;

(0, 3), (1, 2.5), and (2, 0)

The values of the maximizing function are therefore;

At (0, 3), M = $3 × 0 + $15 × 3 = $45

At (1, 2.5), M = $3 × 1 + $15 × 2.5 = $40.5

At (2, 0), M = $3 × 2 + $15 × 0 = $6

The combination of x and y that yield the optimum is therefore;

(x, y) = (0, 3)

x = 0, and y = 3

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A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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\({ \bf{ \underbrace{Given :}}}\)

Radius of the circle "\(r\)" = 9 in.

\({ \bf{ \underbrace{To\:find:}}}\)

The circumference of the circle.

\({ \bf{ \underbrace{Solution :}}}\)

\(\sf\orange{The\:circumference \:of\:the\:circle\:is\:56.52\:in.}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

We know that,

\(\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }\)

\( = 2 \times 3.14 \times 9 \: in \\ \\ = 56.52 \: in\)

Therefore, the circumference of the circle is 56.52 in.

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Answer:

30 inches

Step-by-step explanation:

A = L * W * H

A = 5 * 3 * 2

A = 15 * 2

A = 30

13/51 hours per pound

EXPLANATION

= 2 3/5 hours : 10 1/5 pound

= 13/5 hours : 51/5 pound

= 13/5 × 5/51 hours per pound

= 65/255 hours per pound

= 13/51 hours per pound

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Answer:

x = 45

Step-by-step explanation:

Straight line has 180 degrees; so if you add all the angles up:

2x + x + x = 180

4x = 180

x = 45 degrees

Answer:

45°

Step-by-step explanation:

2x + x + x = 180°

4x = 180°

x = 180°/4

x = 45°

The triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.

Given that:

The diagram is shown.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The ratio of the corresponding sides of the triangle ΔFGH and ΔLJK is given as,

FG / JL = HF / LK = GH / JK

32/8 = 36/9 = 48/12

4 = 4 = 4

The ratio of the corresponding side will be equal. Then the triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.

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Door:80( actual height) 44( height on set)

Table 28( actual height) 15.4 ( height on set)

Stool 18 ( actual height) 9.9 ( height on set)

Step-by-step explanation:

Times the actual height inches by 0.55 and you get your height on set.

Answer:

Step-by-step explanation:

The rule says that to find the number of years required to double your money at a given interest rate, you just divide the interest rate into 72. For example, if you want to know how long it will take to double your money at eight percent interest, divide 8 into 72 and get 9 years.

Answer:

Step-by-step explanation:

To find the tip, we first need to calculate 11% of the bill amount, which is:

0.11 x $65 = $7.15

Therefore, the tip is $7.15.

Answer:

$7.15

Step-by-step explanation:

Syep by step picture attached

Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Answer:

13/200

Step-by-step explanation:

so we grab the fraction:

6 1/2%

make it a decimal instead of a fraction

6.5%

divide it by 100 to get

6.5/100

and multiply it by 2 because decimals have no place inside fractions lol

13/200

Given:

The radius of smaller cylinder is 2 m.

The radius of larger cylinder is 8 m.

The height of smaller cylinder is 14 m.

Both cylinders are similar.

To find:

The height of larger cylinder.

Solution:

It is given that the both cylinders are similar to each other.

We know that the corresponding sides of similar figure are proportional.

Let height of the larger cylinder is \(h_2\).

\(\dfrac{r_1}{r_2}=\dfrac{h_1}{h_2}\)

\(\dfrac{2}{8}=\dfrac{14}{h_2}\)

\(\dfrac{1}{4}=\dfrac{14}{h_2}\)

On cross multiplication, we get

\(1\times h_2=14\times 4\)

\(h_2=56\)

Therefore, the height of the larger cylinder is 56 m.

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

Step-by-step explanation:

The problem here is that the question is not clear.  In particular, what does "2)" mean?

Reflecting across the x axis is easy.  Think of the x axis as a mirror.  when you look in a mirror, your image is behind the mirror the same distance you are in front of the mirror.  So, to reflect across the x axis, just multiply all the y values of the points by -1.  For the reflection part

(-3,4) becomes (-3,-4)

(1,2) becomes (1,-2)

(-2,1) becomes (-2,-1)

Step 2 probably is a translation, but it is not clear what it is - so I cannot help you further.

If you get step 2 straight, the dilation by 3 is achieved by multiplying all the x and y values by 3.

An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).

The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.

In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.

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Answer:

17. no 18. yes 19. no 20. yes 21. yes 22. no

Missy will need a minimum of 570 square inches of wrapping paper to completely cover the box.

To calculate the minimum amount of wrapping paper needed to cover the box, we need to find the surface area of the box.

A rectangular box has six sides: a top, a bottom, two sides, and two ends.

The top and bottom sides have the same dimensions, which are 17.5 inches by 10 inches. So each of these sides has an area of 17.5 in × 10 in = 175 square inches.

The two side surfaces also have the same dimensions, which are 17.5 inches by 4 inches.

Each of these sides has an area of 17.5 in × 4 in = 70 square inches.

The two end surfaces have the same dimensions, which are 10 inches by 4 inches. Each of these sides has an area of 10 in × 4 in = 40 square inches.

To find the total surface area of the box, we add up the areas of all six sides:

175 in² (top) + 175 in² (bottom) + 70 in² (side 1) + 70 in² (side 2) + 40 in² (end 1) + 40 in² (end 2)

Total surface area = 570 in².

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Step 1: Probability of flipping a coin two times

Probability = number of required outcome/number of possible outcome

Step 2 : Probability of rolling a 3 on a die

Probability = number of required outcome/number of possible outcome

Therefore

Probability of flipping a coin two times,

with the coin landing on heads all two times, and

rolling a 3 on a die =

To find the solution to the system of equations represented by the two lines based on the given tables of ordered pairs, you can follow these steps:

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Answer:

3x

Step-by-step explanation:

39*x / 13

39/13 * x

3*x

3x

Answer:

3x

Step-by-step explanation:

We are given the expression:

39*x /13

We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.

(39*x /13) / (13/13)

(39x/13) / 1

3x / 1

When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.

3x

The expression 39*x/13 can be simplified to 3x

The length of the base of the triangle is 8 yards whose height is half of 28 yards.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

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Answer:

6/5

Step-by-step explanation:

The scale factor can be obtained by simply finding the ratio of the lenght of the side of one shape to the length of the same side of the other shape.

Thus, we can obtain the scale factor that will take us from △ABC to △MNO as illustrated below:

Original Length BC = 15 in

New Length NO = 18 in

Scale factor =?

Scale factor = New lenght NO / Original length BC

Scale factor = 18 / 15

Scale factor = 6/5

Therefore, the scale factor that will take us from △ABC to △MNO is 6/5.

Answer:

y^2

Step-by-step explanation:

See the image for solution

Hope it helps

Have a great day

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses