The area of a rectangular plot of land is 440 m². If the length of this plot is increased by 4 m, its area would be increased to 520 m². Find the breadth of the land.​

Answer: the speed of the boat is approximately 9.43 miles per hour.

Step-by-step explanation: To find boat speed, add vectors. Boat goes east at 8 mph, with 5 mph north wind. Boat velocity is a vector eastward and current velocity is a vector northward. To combine velocities, use vector addition. Use Pythagorean theorem to find resultant velocity: resultant speed = √89 ≈ 9.43 mph.

Answer:

x=90°

Step-by-step explanation:

As in the angle, there is a box giving us info that x has to be 90°.

But to be sure that there is no mistake we have to do the following:

So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.

The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).

Therefore the answer is:

x=90°

Answer:

(x - 5)² + (y + 6)² = 16

Step-by-step explanation:

assuming you require the equation of the circle

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (5, - 6 ) and r = 4 , then

(x - 5)² + (y - (- 6) )² = 4² , that is

(x - 5)² + (y + 6)² = 16

Answer:

Step-by-step explanation:

You want the initial mass, and the mass after 7 weeks, of a sample of Palladium-100 with a half-life of 4 days and a mass of 2 mg after 16 days.

The amount of Palladium-100 remaining after t days can be modeled by ...

  a(t) = (initial amount)·(1/2)^(t/(half-life period))

  a(t) = a0·(1/2)^(t/4) . . . . . . where t is in days, and a0 is the initial amount

Using this model to find a0, we have ...

  a(16) = 2 mg = a0·(1/2)^(16/4) = a0/16

  a0 = 32 mg . . . . . . multiply by 16

The initial mass of the sample is 32 mg.

The mass after 7 weeks (49 days) will be ...

  a(49) = (32 mg)·(1/2)^(49/4) ≈ 0.0065698 mg

The mass after 7 weeks is about 6.57 µg or 0.00657 mg.

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In linear equation, Her profit is rupees 4000.

No. of purses she must sell to have neither profit nor loss is 600 nos.

She made loss of rupees 2135.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables. 

The housewife earns,

Profit on 1 purse = 25 rupees

Loss on 1 vanity bag = 20 rupees

So,

Profit on 1000 purses = 25*1000 rupees

                                   = 25000 rupees

Loss on 1050 purses = 20*1050 rupees

                                  = 21000 rupees

Here, Profit > Loss

So,

Total profit = 25000-21000 rupees

                 = 4000 rupees

i) Her profit is 4000 rupees.

If no. of vanity bags sold = 750 nos.

She made loss of = 750*20 rupees

                            = 15000 rupees

ii) No. of purses she must sell to have neither profit nor loss

= 15000/25 nos.

= 600 nos.

Profit on selling 325 purses = 325*25 rupees

                                              = 8125 rupees

Loss on selling 513 vanity bags = 513*20 rupees

                                              =10260 rupees

Here, Profit < Loss

So,

iii) She made loss of = 10260-8125 rupees

                            = 2135 rupees

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The complete question is -

A housewife along with a group of ladies sold bags of different sizes. She earns a profit of 25 on a purse and a loss of 20 on a vanity bag sold. i. She received an order of 1050 vanity bags and 1000 purses. What is her profit or loss? ii. How many purses must she sell to have neither profit nor loss, if the number of vanity bags sold is 750? iii. How much profit/loss did she make in selling 325 purses and 513 vanity bags?

The values are;

1. x = 6 ,y = 6√2

2. x = 9√2, y = 18

3. x = y = 9

4. x = 12, y = 12√2

5. x = y = 4√2

6. x = y =( 3√2)/2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

There are some special angles , in which 45 is part of them.

sin 45 = 1/√2

cos 45 = 1/√2

tan 45 = 1

1. x = 6 ( isosceles triangle)

y = 6 × √2 = 6√2

2. x = 9√2 ( isosceles triangle)

y = 9√2 × √2 = 9×2 = 18

3. x = 9√2/√2 = 9

x = y = 9 ( isosceles triangle)

4. x = 12 ( isosceles triangle)

y = 12×√2 = 12√2

5. x = 8/√2 = 8√2/2 = 4√2

x = y = 4√2( isosceles triangle)

6. x = 3/√2 = (3√2)/2

x = y =( 3√2)/2 ( isosceles triangle)

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The values of c and d that define the translation are:

c = 4

d = 0

First we know that we have a reflection over the x-axis, let's study the coordinates of the botom vertex of triangle A.

It starts at (-3, -4), after a reflection over the x-axis we change the sign of the y-coordinate.

We will get the point (-3, 4)

And the top vertex of triangle B is at (1 , 4)

Then we have a translation of:

(1, 4) - (-3, 4) = (1 + 3, 4 - 4) = (4, 0)

Then the translation (c, d) is (4, 0), that means that:

c = 4

d = 0

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The probability that both people are hopelessly romantic is 0.0025 and the probability that at least one person is hopelessly romantic is 0.0975

Let's denote the event of being hopelessly romantic as "H".

Given that 5% of the population is hopelessly romantic, we have P(H) = 0.05.

Since the events of selecting two people are independent, we can use the multiplication rule of probability to calculate the probability that both people are hopelessly romantic:

P(H and H) = P(H) x P(H) = 0.05 x 0.05 = 0.0025

To calculate the probability that at least one person is hopelessly romantic, we can use the complement rule of probability.

P(neither H nor H) = P(not H) x P(not H) = (1 - P(H)) x (1 - P(H)) = 0.95 x 0.95 = 0.9025

So, the probability that at least one person is hopelessly romantic is:

P(H or H) = 1 - P(neither H nor H) = 1 - 0.9025 = 0.0975

Therefore, the probability that at least one person is hopelessly romantic is 9.75%.

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a. i. The function f(x)/g(x) = (2x - 1)/√(3x - 5)

ii.  The domain is x > 5/3

b. i. The function f(x) - g(x) = (2x - 1) - √(3x - 5)

ii.  The domain is x > 5/3

A function is a mathematical relation ship between two variables.

Since we have the functions f and g defined as follows

f(x) = 2x-1

g(x) = √3x-5

a. i To find f/g we note that

(f/g)(x) = f(x)/g(x)

So, substituting the values of the variables into the equation, we have that

f(x)/g(x) = (2x - 1)/√(3x - 5)

ii. The domain of f(x)/g(x) = (2x - 1)/√(3x - 5) is the value for which the denominator g(x) > 0.

So,g(x) > 0

⇒ √(3x - 5) > 0

⇒ 3x - 5 > 0²

⇒ 3x > 5

⇒ x > 5/3

So, the domain is x > 5/3

b. i. to find f - g, we note that

f - g = f(x) - g(x)

So, substituting the values of the variables into the equation, we have that

f(x) - g(x) = (2x - 1) - √(3x - 5)

ii. The domain of f(x) - g(x) is the value of x at which g(x) > 0

So. g(x) > 0

⇒  √(3x - 5) > 0

⇒ [√(3x - 5)]² > 0

⇒  3x - 5 > 0

⇒ 3x > 5

⇒ x > 5/3

So, the domain is x > 5/3

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The equation of the trend line in the scatter plot is y = 5/8x + 9.

An equation is a mathematical statement that shows the equality of two expressions. Equations typically involve variables, which are symbols that represent unknown values, and constants, which are fixed values. An equation can be expressed using mathematical symbols and operators such as +, -, *, /, ^ (exponentiation), and parentheses.

Equations can take many forms, such as linear equations, quadratic equations, polynomial equations, and trigonometric equations. Linear equations are equations of the form ax + b = c, where x is the variable, and a, b, and c are constants. Quadratic equations are equations of the form ax^2 + bx + c = 0, where x is the variable, and a, b, and c are constants. Polynomial equations involve multiple terms raised to various powers, while trigonometric equations involve trigonometric functions such as sine, cosine, and tangent.

Equations can be solved by manipulating the expressions on either side of the equals sign to isolate the variable. This is done by performing the same operation on both sides of the equation in order to maintain the equality. For example, to solve the equation 2x + 3 = 7, we can subtract 3 from both sides to get 2x = 4, and then divide both sides by 2 to get x = 2.

Equations are used in many fields, such as physics, engineering, and economics, to model and solve real-world problems. For example, equations are used in physics to model the motion of objects, while in economics, equations are used to model supply and demand curves.

The equation of the trend line in the scatter plot is y = 5/8x + 9.

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[tex]\cfrac{5^7}{5^{-13}}\times\left( \cfrac{4^3}{7^{-2}} \right)^{-2}\implies 5^7\cdot 5^{13}\times \left( \cfrac{7^{-2}}{4^3} \right)^{+2}\implies 5^7\cdot 5^{13}\times\left( \cfrac{7^{-4}}{4^6} \right) \\\\\\ 5^{7+13}\times\left( \cfrac{1}{4^6\cdot 7^4} \right)\implies \cfrac{5^{20}}{4^6\cdot 7^4}\implies \cfrac{95367431640625}{9834496}[/tex]

The area of rectangle B is 64,896 square meters.

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

To find the area of rectangle B, we need to first determine the dimensions of the rectangle after it has been scaled up from rectangle A using a scale factor of 52.

To do this, we can multiply the length and width of rectangle A by the scale factor of 52:

Length of rectangle B = Length of rectangle A x Scale factor = 6m x 52 = 312m

Width of rectangle B = Width of rectangle A x Scale factor = 4m x 52 = 208m

Now that we know the dimensions of rectangle B, we can find its area by using the formula:

Area of rectangle B = Length x Width

Area of rectangle B = 312m x 208m

Area of rectangle B = 64,896 square meters

Therefore, the area of rectangle B is 64,896 square meters.

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Answer:

oh

Step-by-step explanation:

idrk i just searched it up

Therefore, we can predict that approximately 5,845,200 people left on cruises from this state in the year 2010.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

This linear equation depicts the number of passengers embarking on cruises from a certain state between 2005 and 2009.

It goes like this:

y = 117,000x + 4,919,200

For example, if x = 0, which represents the year 2005, then y = 4,919,200. If x = 1, which represents the year 2006, then y = 4,919,200 + 117,000 = 5,036,200. Similarly, if x = 2, which represents the year 2007, then y = 4,919,200 + 2(117,000) = 5,153,200.

y = 117,000(5) + 4,919,200

y = 5,845,200

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Question:

The number of people, y, leaving on cruises from a certain state from 2005 to 2009 can be approximated by y=117,000x+4,919,200, where x is the number of years after 2005.

x is 25 and the congruent angles in the kite are 25 and 155 degrees.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x.

In a kite, the two pairs of adjacent angles are congruent. Let's call the congruent angles x and y:

   x       y

 +---+   +---+

/     \ /     \

+-------+-------+

\     / \     /

 +---+   +---+

   y       x

We know that the measurements of the angles in the kite are 3x, 75, 90, and 120, so we can set up an equation based on the sum of the angles in a quadrilateral:

3x + 75 + 90 + 120 = 360

Simplifying this equation, we get:

3x + 285 = 360

Subtracting 285 from both sides, we get:

3x = 75

Dividing both sides by 3, we get:

x = 25

So x is 25. To find y, we know that the sum of x and y must be 180 (because they are congruent angles that add up to a straight line). So we can set up another equation:

x + y = 180

Substituting x = 25, we get:

25 + y = 180

Subtracting 25 from both sides, we get:

y = 155

Therefore, x is 25 and the congruent angles in the kite are 25 and 155 degrees.

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The x⁶y³ term in the expansion will be:  35 x⁶y³.

The x⁸y² term in the expansion will be: 21x⁸y².

The binomial expansion of (x + y)ⁿ is given by the binomial theorem, which states:

(x + y)ⁿ = C(n, 0) * xⁿ * y⁰ + C(n, 1) * xⁿ⁻¹ * y¹ + C(n, 2) * xⁿ⁻² * y² + ... + C(n, k) * xⁿ⁻ᵏ * yᵏ + ... + C(n, n) * x⁰ * yⁿ

where;

Given that the term 210x⁴y⁶ appears in the expansion, we can infer that it corresponds to C(n, k) * x⁴ * y⁶, where k is the number of times y appears in the term, and (n - k) is the number of times x appears in the term.

Comparing this with the given term, we can deduce the values of n, k, and x in the following way:

C(n, k) = 210

x⁴ = x⁴

y⁶ = y³ * y³

Comparing the exponents on x and y, we can set up the following equations:

n - k = 4 (1)

k = 3 (2)

Solving equation (2) for k, we get:

k = 3

Substituting this value of k into equation (1), we can solve for n:

n - 3 = 4

n = 7

So, the value of n is 7.

Now, we can use the binomial coefficient formula to calculate C(n, k):

C(n, k) = C(7, 3) = 7! / (3! * (7 - 3)!) = 35

Finally, substituting the values of n, k, and C(n, k) into the general term of the expansion, we can find the specific terms:

The x⁶y³ term in the expansion will be:

C(7, 3) * x⁶ * y³ = 35 * x⁶ * y³

The x⁸y² term in the expansion will be:

C(7, 2) * x⁸ * y² = 21 * x⁸ * y²

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Note that the shipping container that can fit the required number of cereal boxes is Option B. The volume of the container is 2,211,840 cubic feet and it can fit approximately 12,000 boxes.

First, we need to convert the dimensions of the containers from feet to inches to match the volume of the cereal boxes, which is given in cubic inches.

A) L = 15 ft = 180 inches, B = 7 ft = 84 inches, H = 8 ft = 96 inches

B) L = 20 ft = 240 inches, B = 8 ft = 96 inches, H = 8 ft = 96 inches

C) L = 18 ft = 216 inches, B = 9 ft = 108 inches, H = 6 ft = 72 inches

The volume of each container is given by V = L × B × H.

A) V = 180 × 84 × 96 = 1,288,320 cubic inches

B) V = 240 × 96 × 96 = 2,211,840 cubic inches

C) V = 216 × 108 × 72 = 1,680,384 cubic inches

To find out which container can transport at least 12,000 cereal boxes, we need to divide the total volume required by the volume of each box.

Total volume required = 12,000 × 160 = 1,920,000 cubic inches

A) 1,288,320 / 1,920,000 = 0.672

B) 2,211,840 / 1,920,000 = 1.151

C) 1,680,384 / 1,920,000 = 0.875

Therefore, the only container that can transport at least 12,000 cereal boxes is B, with a volume of 2,211,840 cubic inches.

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Answer: 2x^3y^4

Step-by-step explanation:

The expression ^4√16x^12y^16 can be simplified as follows:

^4√16 = 2, since 2^4 = 16

x^12 can be written as (x^3)^4, and ^4√(x^3)^4 = x^3

y^16 can be written as (y^4)^4, and ^4√(y^4)^4 = y^4

Therefore, ^4√16x^12y^16 simplifies to:

2x^3y^4

This expression [tex]s_{i-j}[/tex] describes the distance between two points i and j in a geometric object

In the context of symmetry and rotations, [tex]s_{i-j}[/tex] typically refers to the distance between two points i and j in a geometric object, such as a crystal lattice or a molecule.

It is a vector that points from point i to point j, and its magnitude is the distance between the two points.

The distance vector [tex]s_{i-j}[/tex] is also used to describe the position of a point in the crystal lattice relative to the rotation axis.

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Thus, the volume of composite solid made up of cone and cylinder is found as: 1099 m³.

A form with a convex surface and a round base is called a cone. We can quickly recognise a cone thanks to the following characteristics.

Given data:

Volume of composite solid = volume of cylinder + volume of cone

Volume of composite solid = πr²H + 1/3*πr²h

Put the values

Volume of composite solid = 3.14 * 5² *12  + 1/3*3.14*5²*6

Volume of composite solid =  3.14 * 25 *12  + 2*3.14*25

Volume of composite solid = 942 + 157

Volume of composite solid = 1099 m³

Thus, the volume of composite solid made up of cone and cylinder is found as: 1099 m³.

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complete question:

What is the volume of this composite solid ?

Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.

In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.

Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.

Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.

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The correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:

OB. f(x) = x³ - 5x² - 7x + 35

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

The polynomial function of lowest degree with only real coefficients and having the given zeros can be obtained by multiplying the factors (x - √7), (x + √7), and (x - 5) since the zeros are √7, -√7, and 5.

Expanding the product, we get:

(x - √7)(x + √7)(x - 5) = (x² - 7)(x - 5) = x³ - 5x² - 7x + 35

Therefore, the correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:

OB. f(x) = x³ - 5x² - 7x + 35

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Answer:

2=8m

divide both sides by 8

the 8 cancels out

and your answer is

m= 2/8

Step-by-step explanation:

hope it helped have a nice day!

The fraction that has been given illustrates that the person who ran further is Lisa and Jane.

Your information isn't complete. Therefore, an overview of the fraction will given.

Let's assume that Lisa ran 1/2 of a mile and Jane ran 3/6 of a mile. In order to know who ran more, you can convert the fraction to percentage.

This will be

[tex]\text{Lisa} = \dfrac{1}{2} \times 100 = \bold{50\%}[/tex]

[tex]\text{Jane} = \dfrac{3}{6} \times 100 = \bold{50\%}[/tex]

Therefore, both Lisa and Jane ran more.

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The original cost of a pair of gloves is 3.9

The truth table is given above for (A ⋀ B) → C.

What is the logical statement?

A logical statement, also known as a proposition or a statement of fact, is a declarative sentence that is either true or false, but not both. It is a statement that can be evaluated based on the available information or evidence to determine its truth value. In other words, a logical statement is a statement that can be either true or false, but not both.

To create a truth table for the logical statement (A ⋀ B) → C, we need to consider all possible combinations of truth values for propositions A, B, and C.

There are 2 possible truth values (true or false) for each proposition, so there are 2³ = 8 possible combinations.

We can organize these combinations into a table as follows:

| A | B | C | (A ⋀ B) | (A ⋀ B) → C |

|---|---|---|---------|-------------|

| T | T | T |    T    |      T      |

| T | T | F |    T    |      F      |

| T | F | T |    F    |      T      |

| T | F | F |    F    |      T      |

| F | T | T |    F    |      T      |

| F | T | F |    F    |      T      |

| F | F | T |    F    |      T      |

| F | F | F |    F    |      T      |

In this table, the column labeled (A ⋀ B) represents the truth value of the conjunction of A and B (i.e., A AND B), and the column labeled (A ⋀ B) → C represents the truth value of the conditional statement (A ⋀ B) → C.

The symbol "T" represents "true" and the symbol "F" represents "false".

Hence, The truth table is given above for (A ⋀ B) → C.

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Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.

If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.

(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)

Step-by-step explanation:

Answer: To calculate the probability that the shipment is rejected, we need to find the probability that at least one of the three components selected is defective.

First, we can find the probability that none of the three components selected is defective, which would mean the shipment is accepted. To do this, we use the hypergeometric distribution formula:

P(X = k) = (C(N-k,n-K) * C(K,k)) / C(N,n)

where:

N = total number of components in the shipment (160)

K = number of defective components in the shipment (4)

n = number of components selected for testing (3)

k = number of non-defective components among the selected components (i.e., all 3 components are non-defective)

Plugging in the values, we get:

P(all 3 components are non-defective) = (C(160-4-3,3-0) * C(4,0)) / C(160,3)

= (C(153,3) * C(4,0)) / C(160,3)

= (22,446 * 1) / 6,384,320

= 0.00352

Therefore, the probability that the shipment is accepted is 0.00352.

To find the probability that the shipment is rejected, we can subtract this probability from 1, since the probabilities of all possible outcomes must add up to 1:

P(at least one component is defective) = 1 - P(all 3 components are non-defective)

= 1 - 0.00352

= 0.99648

Therefore, the probability that the shipment is rejected is 0.99648, or approximately 99.65%.

Step-by-step explanation: