A contractor buys 18 yd of nylon carpet and 20 yd of wool carpet for $1922. A second purchase, at the same prices, includes 18 yd of nylon carpet and 27 yd of wool carpet for $2286. Find the cost per yard of the wool
carpet.

The probability that at least one of the seven next births in the country is a girl is 0.992, or 99.2%.

The probability of a baby being a boy is 0.538, which means that the probability of a baby being a girl is:

P(girl) = 1 - P(boy) = 1 - 0.538 = 0.462

The probability of at least one of the seven next births being a girl is the complement of the probability that all seven are boys. The probability that a single birth is a boy is 0.538, so the probability that all seven births are boys is:

P(all boys) = (0.538)^7 = 0.008

Therefore, the probability of at least one of the seven next births being a girl is:

P(at least one girl) = 1 - P(all boys) = 1 - 0.008 = 0.992 (99.2%)

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The order of the matrix is 2 x 2.

What is a matrix and what is meant by its order?

In the field of mathematics, matrices are rectangular arrangements of numerical values, symbols, or algebraic expressions, organized in rows and columns. Matrices are used in many areas of mathematics and science, as well as in engineering, physics, and computer graphics.

The term 'order' in the context of matrices refers to the dimensions of the matrix, which are determined by the number of rows and columns it contains. It is denoted by m x n, where m is the number of rows and n is the number of columns. To find the order of a matrix, we simply count the number of rows and columns. The order is usually written as a pair of numbers in the form m x n.

Determine the order of the given matrix:

In the given problem, we are asked to find the order of the matrix:

[tex]\begin{pmatrix}9 &6 \\-4 & 8\end{pmatrix}[/tex]

we count the number of rows and columns.

This matrix has 2 rows and 2 columns, so its order is 2 x 2.

Therefore, the order of the matrix is 2 x 2.

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Answer: A 48 x 24/16 = r

Step-by-step explanation:

48 x 24 = the total number of drinks

Since there are 16 drinks in each row you want divide to get the number of rows in each drink.

Ex: 48 x 24= 1,152 (total drinks)

16 drinks in a row

1,152/16 = 72

72 rows

Answer:

Step-by-step explanation:

Answer:

Yes, the manager should make changes to the current display. There should be 36 large water bottles and 36 small water bottles, which would be a 3:2 ratio. To achieve this, the manager should add 12 more large water bottles to the display.

Answer:

c

Step-by-step explanation:

because I did it in my book ‍️

Answer:

C)  2, 7, 6 can form a triangle.

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of a triangle is greater than the length of the third side.

To determine which group of given side measures will form a triangle, sum each pair of sides and compare to the third side. If all three inequalities are true, the group will form a triangle.

Given side lengths: 9, 4, 3

  ⇒ 9 + 4 > 3

  ⇒ 9 + 3 > 4

  ⇒ 4 + 3 [tex]\ngtr[/tex] 9

Therefore, this group cannot form a triangle.

Given side lengths: 8, 1, 7

  ⇒ 8 + 1 > 7

  ⇒ 8 + 7 > 1

  ⇒ 1 + 7 [tex]\ngtr[/tex] 8

Therefore, this group cannot form a triangle.

Given side lengths: 2, 7, 6

  ⇒ 2 + 7 > 6

  ⇒ 2 + 6 > 7

  ⇒ 7 + 6 > 2

Therefore, this group can form a triangle.

Given side lengths: 12, 10, 22

  ⇒ 12 + 10  [tex]\ngtr[/tex] 22

  ⇒ 12 + 22 > 10

  ⇒ 10 + 22 > 12

Therefore, this group cannot form a triangle.

Answer:

Supplementary Angles: The angles 1 & 2 are supplementary angles, as, when combined together, their total angle measurement is 180°, or a straight line. Supplementary angles, by definition, is either two angles in which, when combined, the sum is equal to 180°.

Adjacent Angles: The angles 1 & 2 are adjacent angles, as they share a common side and vertex. Vertexes, by definition is the corner point.

Why it is not:

Complementary Angles: Complementary angles suggest that, when two angles are combined together, their total angle measurements is 90°, or it creates a right angle. In this case, the total measurements of the combination of ∠1 & ∠2 is a straight line, or 180°. Therefore, complementary angles is not your answer.

Vertical Angles: Vertical angles suggest that, when there are two angles, they are directly opposite of each other. Vertical angles would share the same angle measurements.

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Answer: slope of XY is not perpendicular to YZ. Therefore, triangle XYZ is a right triangle.

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).

Using this formula, we can find the slopes of the three sides of triangle XYZ:

Slope of XY = (2h - 0) / (2h - 0) = 1

Slope of YZ = (0 - 2h) / (4h - 2h) = -h / h = -1

Slope of ZX = (0 - 0) / (4h - 0) = 0

Therefore, the slope of XY is 1, the slope of YZ is -1, and the slope of ZX is 0.

Since the product of the slopes of two perpendicular lines is -1, we can see that the slope of XY and the slope of YZ are negative reciprocals of each other, which means that they are perpendicular. Therefore, triangle XYZ is a right triangle.

The solution set of the equation x^2+3x-4=6 is {-5, 2}.

The answer of the given question are as follows :-

Para encontrar el conjunto de soluciones de la ecuación x^2+3x-4=6, debemos primero llevarla a su forma canónica. Restando 6 de ambos lados, obtenemos:

x^2+3x-10=0

Luego, podemos resolver esta ecuación utilizando la fórmula cuadrática:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

donde a = 1, b = 3, y c = -10.

Reemplazando estos valores, obtenemos:

x = (-3 ± sqrt(3^2 - 4(1)(-10))) / 2(1)

x = (-3 ± sqrt(49)) / 2

x = (-3 ± 7) / 2

x1 = 2

x2 = -5

Por lo tanto, el conjunto de soluciones de la ecuación x^2+3x-4=6 es {-5, 2}.

Translation in english :-

To find the solution set of the equation x^2+3x-4=6, we must first bring it to its standard form. Subtracting 6 from both sides, we get:

x^2+3x-10=0

Then, we can solve this equation using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 3, and c = -10.

Substituting these values, we get:

x = (-3 ± sqrt(3^2 - 4(1)(-10))) / 2(1)

x = (-3 ± sqrt(49)) / 2

x = (-3 ± 7) / 2

x1 = 2

x2 = -5

Therefore, the solution set of the equation x^2+3x-4=6 is {-5, 2}.

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1. Calculating the output when using -6 as the input, we have:

Rule 1: subtract 7  = -13

Rule 2: square the input = 36.

Rule 3: divide by 3 = 12

Rule 4: divide the input into 3 = -2

Rule 5: write π = -2π

Rule 6: volume of a cube = -216cm³

A function rule is a mathematical expression that describes how to calculate the output value of a function based on its input value. It can be thought of as a set of instructions that tell you what to do with the input value to get the output value.

2. a. True. Speed is the ratio of distance traveled to the time taken to travel that distance. In this case, the distance is fixed at 100 meters, so speed is solely dependent on time. For each value of time, there is only one corresponding value of speed, making it a function.

b. False. While time and distance are related in the formula for speed, time is not a function of distance in this case. Each student's time is independent of the distance they cover, and the same distance is covered by all students (100 meters). Therefore, for any given distance, there are multiple possible values of time, making it not a function.

c. False. The number of students racing is not related to their speed. Each student's speed depends solely on their individual time, which is not affected by the number of other students racing.

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Answer:

Brainly Plus.

Step-by-step explanation:

You have to pay money. Otherwise, I don't think you can.

Maybe you could try just installing a bunch of ad-blockers.

But pretty much the only way is Brainly Plus.

Answer:

21 feet by 15 feet

hope this helps

Answer:

m∠WUV=135°

Hope this helps.

Answer:

1. -2/7

2. 7/6

3. 53/8

4. do u mean sum? if yes then the answer is 1

5. 5/12

6. 2/5

7. -2/3

8.

9.90

10.240

11.60

12. 4/15

13.4/7

14.8/5

15.24/7

16.15/16

17.4/9

18.8/7

19.-2/5

20.-1/12

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

Step-by-step explanation:

that the answerrrrrrrrr

1 + 2i in polar form is 5√2∠63.4°.

What is a polar form ?

In mathematics, the polar form is a way of representing complex numbers using their magnitude and angle. A complex number can be represented in the form r(cos θ + i sin θ), where r is the magnitude (or modulus) of the complex number, and θ is its argument (or phase angle). Alternatively, the polar form can be represented in terms of magnitude and angle as r ∠θ, where r is the magnitude and θ is the angle in radians. This form is also known as the exponential form of a complex number. The polar form is useful in calculations involving complex numbers, especially in multiplication and division, where it is often easier to work with the polar form rather than the rectangular form (a + bi).

D. 5√2∠63.4°

To convert a complex number from rectangular form to polar form, we use the following formulas:

r = √(a^2 + b^2)

θ = tan^-1 (b/a)

Where a and b are the real and imaginary parts of the complex number, respectively.

In this case, a = 1 and b = 2, so:

r = √(1^2 + 2^2) = √5

θ = tan^-1 (2/1) = 63.4°

Therefore, 1 + 2i in polar form is 5√2∠63.4°.

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The function that expresses f(x) is f(x) = 1.99x + 3, and its graph is continuous.

A continuous function is one that doesn't have any sudden or unexpected changes in value. It means that if we make small enough changes to its input, the output will also change by a small amount.

We can express the total cost of an order as a function of the number of books sold, x, using the formula:

f(x) = 1.99x + 3

This function takes the number of books sold, multiplies it by the cost per book ($1.99), and adds a fixed fee of $3.

For example, if we sold 3 books, we can use the function to find the total cost:

f(3) = 1.99(3) + 3 = 9.97

This means that selling 3 books would cost $9.97 in total.

The graph of this function is continuous, which means that as we move along the x-axis, the y-values change smoothly and without any sudden jumps.

The term "continuous" refers to a function that can take on any value between two given points and can be broken down into infinitely many fractions and decimals.

In contrast, a discrete function can only take on specific values, usually whole numbers or integers.

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The value of x is 32.

A rectangle is a quadrilateral (a four-sided polygon) with four right angles (90-degree angles) and opposite sides that are parallel and congruent (the same length). The opposite sides of a rectangle are also perpendicular to each other, meaning they intersect at a 90-degree angle.

The rectangle is a special case of a parallelogram, where all the angles are right angles. A square is also a special type of rectangle, where all the sides are congruent.

We can use the formula for the area of a rectangle, which is:

Area = Length x Width

Substituting the given values, we get:

40 = (5/8)x + 5 x 4

Simplifying, we get:

40 = (5/8)x + 20

Subtracting 20 from both sides, we get:

20 = (5/8)x

Multiplying both sides by 8/5, we get:

x = 32

Therefore, the value of x is 32.

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Answer: Sally will earn $4,830.00 in interest over 7 years.

Step-by-step explanation:

If the interest is not compounded, then Sally will earn simple interest, which can be calculated using the formula:

I = P * r * t

where:

I = the interest earned

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the time period, in years

In this case, we have:

P = $9,000 (the initial deposit)

r = 7% = 0.07 (the annual interest rate)

t = 7 (the number of years)

So, plugging in the values:

I = $9,000 * 0.07 * 7

I = $4,830.00

Therefore, Sally will earn $4,830.00 in interest over 7 years.

Answer:

p=84

Step-by-step explanation:

p=6×14

p=84

answer: p=84

In response to the stated question, we may state that Since [tex]\theta[/tex]is in the trigonometry fourth quadrant, [tex]\theta/2[/tex] is also in the fourth quadrant.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

a) We can use the double angle formula for sine to find sin 2theta:

[tex]sin 2\theta = 2sin \theta cos \theta\\sin^2 \theta + cos^2 \theta = 1\\sin^2 \theta + (3/10)^2 = 1\\sin^2 \theta = 1 - (9/100)\\sin \theta = \sqrt(91)/10 \\sin 2\theta = 2sin \theta cos \theta\\sin 2\theta = 2(\sqrt(91)/10)(3/10)\\sin 2\theta = 3\sqrt(91)/50[/tex]

b) To find the quadrant in which [tex]\theta/2[/tex] is located, we need to find [tex]\theta/2[/tex] first:

[tex]\theta/2 = (3\pi/2 + \theta)/2\\\theta/2 = 3\pi/4 + t\heta/2\\\theta/2 - \theta/2 = 3\pi/4\\\theta/2 = 3\pi/4\\\theta = 3\pi/2[/tex]

Since theta is in the fourth quadrant, [tex]\theta/2[/tex] is also in the fourth quadrant.

c) To find cos theta/2, we can use the half angle formula for cosine:

[tex]cos(theta/2) = \sqrt((1 + cos theta)/2)\\cos(theta/2) = \sqrt((1 + 3/10)/2)\cos(theta/2) = \sqrt(13/20)\\cos(theta/2) = \sqrt(13)/2sqrt(20)\\cos(theta/2) = \sqrt(13)/10[/tex]

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Answer:

Rushbu exchanges 300 USD at the buying rate of NRs 119.25, so she will receive:

300 x 119.25 = NRs 35775

After allowing a 10% discount, Rushbu will need to pay:

35000 - (10/100 x 35000) = NRs 31500

Including 13% VAT, Rushbu will need to pay:

31500 + (13/100 x 31500) = NRs 35655

Since Rushbu received NRs 35,775 after exchanging her 300 USD, she will have enough Nepali currency to buy the television, even after accounting for the discount and VAT.

Therefore, Rushbu will have enough money to buy the television, and she will have NRs 120 less than she received from exchanging her 300 USD, but that does not affect her buying capacity in this case.

Step-by-step explanation:

the answer will be 1272.7cm3

the formula of the volume of the cylinder is pie×radius squared×height so,

we will get the radius and the radius is half of the diameter and the diameter is 9 so 9÷2=4.5 and then it will be squared so it will be 20.25cm2 and so we will write it this way

3.14×20.25×20=1271.7cm3

hope this helped

xoxo adham

Answer:

Veronica is correct

Step-by-step explanation:

On Monday, Veronica earns 3 walks * $5.25 per walk = $15.75.

On Tuesday, Veronica earns 2 walks * $5.25 per walk = $10.50.

So far, Veronica has earned a total of $15.75 + $10.50 = $26.25.

To reach her goal of $86, Veronica needs to earn an additional $86 - $26.25 = $59.75.

Since Veronica earns $5.25 per walk, she needs to complete $59.75 ÷ $5.25 per walk = 11.38 walks.

Since Veronica cannot complete a fraction of a walk, she will need to complete 12 more walks (rounded up from 11.38) by the end of the week.

The correct answer is true

Answer:

True hope this helps!

Area of triangle= 24 cm²

Area of sector= 72.243 cm²

Total area= 96.243 cm².

A polygon with three sides and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with points A, B, and C. In Euclidean mathematics, any three points that are not collinear produce a distinct triangle and a distinct plane.

The portion of a disc enclosed by two radii and an arc is called a circular sector, also known as a circle sector or disc sector. The smaller area is referred to as the minor sector, and the bigger area as the major sector. A sector is referred to as a component of a circle made up of the circular's arc and its two radii.

In this question,

Area of triangle= 1/2 × base × height

                         = 1/2 × 6 ×8

                         = 24 cm²

Area of sector = (θ/360°) × πr²

                        = (82/360) × πr²

Here r=√6²+8²

          = 10 cm

Area of sector = (82/360) × π10²

                        = 0.23 × 314.1

                        = 72.243 cm²

Total= 24 cm²+72.243 cm²= 96.243 cm².

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The Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

Accοrding tο the Pythagοrean theοrem, the square οf a right triangIe's hypοtenuse (the side οppοsite the right angIe) equaIs the sum οf its οther twο sides' squares.

Outside waII's Iength and width are equaI if it is a square. Let's caII this Iength "x"

Using the Pythagοrean theοrem, we can find the Iength οf the diagοnaI οf the square:

diagοnaI² = height² + width²

Since the height is 9 ft and οne side οf the square is 12 ft, we can write:

diagοnaI² = 9² + 12²

diagοnaI² = 81 + 144

diagοnaI² = 225

Taking the square rοοt οf bοth sides, we get:

diagοnaI = √(225)

diagοnaI = 15 ft

Therefοre, the Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

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Answer:

50.27 ft

Step-by-step explanation: