Round to the closest whole number. 32% of the animals were males. If the herd had 112 animals how many were female?

Answer:Il y a 2 configurations de Thalès La première donne BC/CE = AC/CD = 1/2

la seconde donne BC/CE = CF/CA => CF = CA/2 = 3/2

Step-by-step explanation:

Answer: the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.

Step-by-step explanation:

(-2, 5) and (-4,-5) are two points in the coordinate plane.

The first point (-2, 5) has an x-coordinate of -2 and a y-coordinate of 5. This point is 2 units to the left of the y-axis and 5 units above the x-axis.

The second point (-4, -5) has an x-coordinate of -4 and a y-coordinate of -5. This point is 4 units to the left of the y-axis and 5 units below the x-axis.

To find the distance between these two points, we can use the distance formula:

distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Plugging in the coordinates of the two points, we get:

distance = sqrt[(-4 - (-2))^2 + (-5 - 5)^2] = sqrt[(-2)^2 + (-10)^2] = sqrt[104]

So the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.

Answer:

See below

Step-by-step explanation:

The roots aka solutions to a quadratic equation in standard form:
[tex]ax^2 + bx + c = 0[/tex]
are given by

[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

The term under the square root sign, [tex]b^2 - 4ac[/tex] is called the discriminant

The type and number of roots are determined by the sign of the discriminant

When [tex]b^2 - 4ac = 0[/tex]  there is one real root.
When [tex]b^2 - 4ac > 0[/tex]  there are two real roots.
When [tex]b^2 - 4ac < 0[/tex]  there are two complex(imaginary) roots.

Answer:

13.5

Step-by-step explanation:

If y and x have a proportional relationship, we can write this relationship as:

y = kx

where k is the proportionality constant.

To find the value of k, we can use the information that "y = 9 when x = 2":

9 = k(2)

Solving for k, we get:

k = 9/2

Now we can use this value of k to find the value of y when x = 3:

y = (9/2)(3) = 27/2 = 13.5

Therefore, the value of y when x = 3 is 13.5.

In a case whereby volume of this sphere is 904.32 cubic inches the surface area of this sphere can be expressed as 452.16 in^2

The concept here is using the surface area formula which is

A = Area = (4 π r^2 )  

V= Volume =( 4/3 π r^3)

Then A / V = 3 / r

Also, r = [(3 * V / 4 *  π)^1/3 ]

Then we can substitue the values as

π = 3.14

volume = 904.32 cubic inches

=[ (3 * 904.32 / (4 *  π))^1/3]

= 6 inch

Hence ,  A =( 3 / 6 * V )

= (1/2 * 904.32)

= 452.16 in^2

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Complete question:

The volume of this sphere is 904.32 cubic inches. What is the surface area of this sphere?

Use a 3.14 and round your answer to the nearest hundredth.

Answer:3x+5x

Step-by-step explanation:

3x÷5 +x

3x+5x(multiply each term by 5)

The tens digit is 8, and the units digit is 9 (since y = x + 1). Therefore, the original number is 89.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation contains one or more variables, which are unknown values that can vary or change. The variables are usually represented by letters such as x, y, or z. The expressions on either side of the equals sign can be constants, variables, or functions of variables.

The simplest form of an equation is a linear equation, which can be represented as ax + b = c, where a, b, and c are constants and x is a variable. To solve a linear equation, we need to find the value of the variable that makes the equation true. This is done by performing arithmetic operations on both sides of the equals sign to isolate the variable.

Equations can also be more complex, involving multiple variables, powers, and functions. In such cases, algebraic techniques such as factoring, substitution, and solving systems of equations may be required to find the solution.

Equations are used to describe relationships between variables in many fields of study, including physics, chemistry, economics, and engineering. They are also used in everyday life, such as in calculating the cost of a purchase after applying a discount, or determining the amount of time it takes to travel a certain distance

Let's represent the tens and units digits with x and y, respectively. According to the problem statement, we have two equations:

y = x + 1 (the units digit is one more than the tens digit)

10x + y + 10y + x = 187 (the sum of the original number and the reversed number is 187)

Simplifying the second equation, we get:

11x + 11y = 187

x + y = 17 (dividing both sides by 11)

Substituting y = x + 1 into the second equation, we get:

x + (x + 1) = 17

2x + 1 = 17

2x = 16

x = 8

So the tens digit is 8, and the units digit is 9 (since y = x + 1). Therefore, the original number is 89.

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The solution of the given problem of area comes out to be the regular decagon is approximately 324.16 cm².

Its surface area is a reliable indicator of its overall size. When figuring out the right triangle squared, the environment is taken into account. The surface area of everything determines its overall size. The total of the volumes from each of the twelve vertical sides makes up the water volume inside a cuboid. Utilize the following formula to get the box's dimensions: The region is represented by 2lh, 2lw, & 2hW. (SA). The area is represented by the flexible shape's entire surface area.

Here,

The area of ​​a regular decagon can be calculated using the formula:

Area = (perimeter x apothem) / 2

For a regular decagon with a side of 6.8 cm and an apothem of 9.52 cm, the perimeter can be calculated as 10 times the length of the side, that is:

Perimeter = 10 x 6.8 cm = 68 cm

Therefore, the area of ​​the decagon is:

Area = (68 cm x 9.52 cm) / 2 = 324.16 cm²

So, the area of ​​the regular decagon is approximately 324.16 cm².

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The coterminal angle is 304°, which lies in the fourth quadrant with a reference angle of 44°.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

To find the coterminal angle of 664°, we can add or subtract any multiple of 360° to it.

664° - 360° = 304°

The coterminal angle of 664° is 304°.

To determine the quadrant that 664° lies in, we can divide it by 90° and take the quotient:

664° ÷ 90° = 7 with remainder 34

As remainder is 34 and it is less than 90, the angle lies in the fourth quadrant.

To find the reference angle of 664°

we can subtract the nearest multiple of 90°:

664° - 6(90°) = 44°

The reference angle of 664° is 44°.

Therefore, the coterminal angle is 304°, which lies in the fourth quadrant with a reference angle of 44°.

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Answer:

deprication a/c Dr. 30,00,000

To land a/c 30,00,000

Step-by-step explanation:

deprication is an expense so, according to modern rules of accounts Dr. debit all assets & expenses and cr. credit all income, capital, all liability

(assets ) land value is deprecating so, deprication is an expense so, we Dr. deprication a/c expense is an increase (name the expense) and the value of land (assets) is diminishing Or depricating so, cr. land a/c

When the triangle's vertices are (2, 2), (4, 2), and (2, 2), its circumference is 28. (4,6).

An closed path that surrounds, distinguishes, or comprises a multiple shape or a three-dimensional length is spoken to as a boundary. The perimeter of either an ellipse or circle refers from its outermost area. The perimeter calculation had several practical uses. Discover how to determine the perimeter by adding the measurements of the vertices of various forms. You can still find the perimeter of a shape by multiplying its side lengths. The peripheral of an object is the space around it. At your house, a covered garden is one illustration. The circumference of anything is all area encircling it. For a 50 feet x 50 feet yard, a 200 yard fence is required.

given

d=√(x2−x1)2+(y2−y1)2

d1=√(4+1)2+(−5−6)2=√146≅12

For the second two;

d2=√(−2−4)2+(−4+5)2=√37≅6

And for the last pair;

d3=√(−2+1)2+(−4−6)2=√109≅10

So the sum of the three sides is roughly;

12+6+10=28

When the triangle's vertices are (2, 2), (4, 2), and (2, 2), its circumference is 28. (4,6).

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The sample space lists all possible outcomes of rolling a number cube twice, where W represents a roll with a value of 6 or higher, and L represents a roll with a value of 5 or lower.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

The answer to Question 3 is List 2, which gives the sample space for pulling 2 marbles from the bag with replacement.

The answer to Question 4 is two ninths. Since there are three cards with one D each, the probability of selecting a D on the first draw is 1/3. Since the cards are replaced, the probability of selecting a D on the second draw is also 1/3. Therefore, the probability of selecting D and D in that order is (1/3) * (1/3) = 1/9. However, since the order of selection does not matter, we must also consider the probability of selecting D and D in the reverse order, which is also 1/9. Therefore, the total probability is 1/9 + 1/9 = 2/9.

The answer to Question 5 is four thirty sixths or one ninth. The only ways to get a sum of 5 are by rolling a 1 and a 4, a 2 and a 3, or a 3 and a 2. Each of these outcomes has a probability of 1/6 * 1/6 = 1/36, so the total probability is 3 * 1/36 = 1/12 = 4/36.

The answer to Question 6 is Rolling a number cube twice.  For example, WW represents rolling a 6 or higher on both rolls, and LL represents rolling a 5 or lower on both rolls.

Therefore, The sample space lists all possible outcomes of rolling a number cube twice, where W represents a roll with a value of 6 or higher, and L represents a roll with a value of 5 or lower.

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Answer:

Step-by-step explanation:

list 4

Answer:

3

Step-by-step explanation:

∠LMN = ∠BMN + ∠LMB (linear angles)

59x + 3 = 160 + (-1 + 7x)

59x - 7x = 160 - 1 - 3

52x = 156

x = 156/52 = 3

Answer:

The volume of the rectangular prism is 96.

Step-by-step explanation:

Use the formula L × W × H to get your answer. Plug in the givem measurements. 8 × 4 × 3 = 96.

Therefore, Sam wrote a total of 38,789 digits. Therefore, the probability that Sam chooses a 0 is approximately 0.026. So the sum of all the digits in the numbers from 1000 to 9999 is: 4500.

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability is calculated by dividing the number of outcomes that satisfy a certain condition (such as rolling a six) by the total number of possible outcomes. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.

Here,

(a) Sam writes down all the positive integers from 1 to 9999, inclusive. To find the total number of digits Sam wrote, we can count the number of digits in each number and add them up.

Numbers from 1 to 9 have one digit each, so there are 9 numbers with one digit, for a total of 9 digits.

Numbers from 10 to 99 have two digits each, so there are 90 numbers with two digits, for a total of 180 digits.

Numbers from 100 to 999 have three digits each, so there are 900 numbers with three digits, for a total of 2700 digits.

Numbers from 1000 to 9999 have four digits each, so there are 9000 numbers with four digits, for a total of 36000 digits.

Adding up these totals gives:

9 + 180 + 2700 + 36000 = 38789

Therefore, Sam wrote a total of 38,789 digits.

(b) Since Sam chose the digits 1 to 9999, there are 4 digits (0, 1, 2, and 3) that can appear in the thousands place, and 10 digits (0 to 9) that can appear in each of the other three places.

Therefore, the probability of choosing a 0 at random is the number of times 0 appears in the numbers divided by the total number of digits written down.

0 appears as the last digit in 1000 numbers (from 10 to 9990), and as the first digit in 9 numbers (1000, 10000, 2000, 20000, 3000, 30000, 4000, 40000, and 5000). So the total number of times 0 appears is 1000 + 9 = 1009.

The total number of digits Sam wrote is 38,789, so the probability of choosing a 0 at random is:

1009/38789 ≈ 0.026

Therefore, the probability that Sam chooses a 0 is approximately 0.026.

(c) We can find the sum of all the digits Sam wrote by adding up the sum of the digits in each number from 1 to 9999.

The sum of the digits in the numbers from 1 to 9 is 1+2+3+4+5+6+7+8+9=45.

The sum of the digits in the numbers from 10 to 99 can be found by observing that each of the digits from 0 to 9 appears in the tens place the same number of times (that is, 10 times each). Since there are 90 two-digit numbers, each digit appears a total of 10 x 90 = 900 times in the tens place. So the sum of the digits in the tens place is:

900(0+1+2+3+4+5+6+7+8+9) = 45,000

Similarly, each of the digits from 0 to 9 appears in the hundreds place the same number of times (that is, 100 times each). So the sum of the digits in the hundreds place is:

100(0+1+2+3+4+5+6+7+8+9) = 4500

Finally, each of the digits from 0 to 9 appears in each of the four places (thousands, hundreds, tens, and ones) the same number of times (that is, 1000 times each). So the sum of all the digits in the numbers from 1000 to 9999 is: 4500.

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a) Note that  the probability that the 10th transistor  produced is the first with a defect is: ≈ 0.0171

b) The probability that the machine produces no defective transistors in a batch of 100 is: ≈ 0.1338

c) The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:  = 50

d) The expected value and standard deviation for the number of transistors produced before the first with a defect is ≈ 18.71

e)  Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.

(a) Since each transistor is independent, the probability that the 10th transistor produced is the first with a defect is the same as the probability that the first 9 transistors are not defective and the 10th one is defective. The probability that a transistor is not defective is 1 - 0.02 = 0.98. Therefore, the probability is:

P(1st defective on 10th) = (0.98)⁹ x 0.02 ≈ 0.0171

(b) The probability that the machine produces no defective transistors in a batch of 100 is:

P(no defects in 100) = (0.98)¹⁰⁰ ≈ 0.1338

(c) The number of transistors produced before the first with a defect follows a geometric distribution with parameter p = 0.02. The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:

E(X) = 1/p = 1/0.02 = 50

The variance of a geometric distribution is (1-p)/p², so the standard deviation is:

σ = √((1-p)/p²)

= √(0.98/0.0004)

≈ 22.36

(d) The expected value and standard deviation for the number of transistors produced before the first with a defect are calculated in the same way as in (c), but with a different value of p:

E(X) = 1/p = 1/0.05 = 20

σ = √((1-p)/p₂)

= √(0.95/0.0025)

≈ 18.71

(e) Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.

As the probability of an event increases, the expected wait time until success decreases. In other words, the mean becomes smaller. However, as the probability of an event increases, the variability in the wait time until success also increases.

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Answer:

(a) 0.0167

(b) 0.1326

(c) The expected value, mean, μ = 50        SD, σ = 49.4975

(d) The expected value, mean, μ = 20        SD, σ = 19.4936

(e) Increasing the probability of an event decreases the mean and standard deviation of the wait time until success.

Step-by-step explanation:

The correct answers are

1)  2x^2 + 12

2) Option C.

3) Option B.

1. You must apply the Distributive property as following:

(-5x^2 - 2x +4) + (8x^2 -x -1) - (x^2 -5x + 2x -10)

2. Now, you must distribute the negative sign, then you have:

3. Finally, you must add the like terms. Then you obtain the polynomial:

2x^2 + 13

4. By definition, a polynomial that has two terms is classified as a binomial. Therefore, the answer is the option C.

5. The degree of a polynomial is determined by highest exponent of the variable. So, it is a polynomial of degree 2 (option B).

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The three vertices will give us the dilated figure.

First we find the slope of the line that would pass through the point of dilation, (-3, 0), and each vertex.

From (-3, 0) to (5, 4), the slope would be

m = (4-0)/(5--3) = 4/8

Since the scale factor is 1/2, this means each part of the slope would be multiplied by this scale factor:

(4(1/2))/(8(1/2)) = 2/4

This means from our point of dilation we count up 2 and over 4; this puts the new point at (-3+4, 0+2) = (1, 2).

From (-3, 0) to (3, 8) the slope is

m = (8-0)/(3--3) = 8/6

Multiplying the rise and run by 1/2, we have

(8(1/2))/(6(1/2)) = 4/3

This means the dilated point would be up 4 and over 3 from (-3, 0), putting it at (-3+3, 0+4) = (0, 4).

From (-3, 0) to (-5, 4), the slope is

m = (4-0)/(-5--3) = 4/-2.

Multiplying the rise and run by 1/2, we have

(4(1/2))/(-2(1/2)) = 2/-1

This means the dilated point would be up 2 and over -1 from (-3, 0), putting it at (-3+-1, 0+2) = (-4, 2).

These three vertices give us the dilated figure.

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Answer:

Step-by-step explanation:

Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square. Therefore, the diagonal of the square is twice the radius of the circle, or 10 mm.

To find the area of the square, we can use the formula A = s^2, where s is the side length of the square. The diagonal of the square is √2 times the side length, so we have:

10 mm = √2 x s

s = 10 mm / √2

The area of the square is:

A = s^2 = (10 mm / √2)^2 = 100 mm^2 / 2 = 50 mm^2

To find the area of the circle, we can use the formula A = πr^2, where r is the radius of the circle. We are given that the radius is 5 mm, so:

A = π(5 mm)^2 = 25π mm^2

To find the shaded section, we need to subtract the area of the circle from the area of the square. The shaded section is the remaining area of the square after the circle has been inscribed. Therefore, the shaded section is:

Shaded Section = Square Area - Circle Area

Shaded Section = 50 mm^2 - 25π mm^2

Shaded Section ≈ 10.79 mm^2 (rounded to two decimal places)

Answer: 464

Step-by-step explanation: First you multiply by 580 times .20 and subtract the answer of that by 580

The probability of selected exactly three girls is A 0.022

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

In this case, the probability of an event us usually represented as a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

In this situation, the probability of selected exactly three girls is 0.022. This can easily be seen in the table.

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The quadratic formula can be used to resolve the equation x2 - 2x - 3 = 0.

x=(-b sqrt(b2 - 4ac)) / 2a

x = (2 ± sqrt(4 + 12)) / 2

If we simplify, we get:

x = (2 ± 2sqrt(4)) / 2

x = 1 ± sqrt (4)

As a result, x = 1 + 2 and x = 1 - 2 are the solutions.

The following are the answers, separated by commas:

3, -1

[tex]x^2 + 5x + 6 = 0[/tex]

[tex]x^2 + 5x + 6 = 0[/tex]

We can factor this equation into: to find its solution.

(x + 2)(x + 3) = 0

The following answers can therefore be determined using the zero product attribute: x + 2 = 0 or x + 3 = 0.

x = -2 or x = -3

The following are the solutions, each separated by a comma:

-2, -3

36. We can factor the equation to find the solution to x2 + 3x - 4 = 0.

(x + 4)(x - 1) = 0

We can calculate x + 4 = 0 or x - 1 = 0 using the zero product property.

We obtain the following results when we solve for x: x = -4 or x = 1.

Hence, the answers are x = -4 and x = 1.

Solution: -4, 1.

37. We can factor the equation to find the solution to x2 - 6x + 5 = 0.

(x - 5)(x - 1) = 0

We can calculate x - 5 = 0 or x - 1 = 0 using the zero product condition.

We obtain x = 5 or x = 1 when we solve for x.

Hence, the answers are x = 5 and x = 1.

Respondents: 5

38. We can apply the quadratic formula x = (-b (b2 - 4ac)) / 2 to solve 6x2 + 5x + 1 = 0. (2a)

We obtain the following equation by plugging in the variables a = 6, b = 5, and c = 1: x = (-5 (25 - 24)) / 12 x = (-5 1) / 12

We obtain x = -2/3 or x = -1/2 by simplifying.

The answers are therefore x = -2/3 and x = -1/2.

Solution: -2/3, -1/2

39. The equation 4x2 + 15x + 9 = 0 can be factored as follows:

(4x + 3)(x + 3) = 0

In response to the zero product property, we get either 4x + 3 = 0 or x + 3 = 0.

When we solve for x, we have x = -3/4 or -3.

Hence, x = -3/4 and x = -3 are the answers.

Response: -3/4, -3

[tex]40. x^2 - 36 = 0[/tex]

This problem can be solved by adding 36 to both sides to obtain:

x^2 = 36

The square root of both sides can then be calculated as follows:

x = ±6

As a result, the answers are x = 6 and x = -6.

The following are the answers, separated by commas:

6, -6

[tex]41. x^2 + 12x + 36 = 0[/tex]

We can factor this equation into: to find its solution.

(x + 6)(x + 6) = 0

The zero product attribute can then be used to identify the answers:

x + 6 = 0

x = -6

Hence, the answer is x = -6. There is just one solution because both components in the factored form are identical.

The answer is: -6.

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As n increases, the area of the regular polygon approaches the area of the circle.

The correct option is (b)

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle.

The polygon area can be expressed in terms of the area of a triangle.

Let s denote the side length of triangle.

r hypotenuse of right triangle.

h height of the triangle.

let n be the number of sides of the regular polygon.

The area of polygon is given by:

polygon area = n(12sh)

The correct statement is:

As n increases, the area of the regular polygon approaches the area of the circle.

As n increases , the triangle will be smaller and smaller. h approaches r so that rh approaches [tex]r^2[/tex]

" Since, as the number of sides of the polygon increases the polygon start approaching to the circumference of circle and as n tends to infinity the polygon will tend to take the shape of the circle "

Therefore, The correct option is (b)

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The given question is incomplete, complete question is:

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle.

Let s be the side length of the polygon,

let r be the hypotenuse of the right triangle,

let h be the height of the triangle, and

let n be the number of sides of the regular polygon.

polygon area = n(12sh)

Which statement is true?

a. As r increases, the area of the regular polygon approaches the area of the circle.

b. As n increases, the area of the regular polygon approaches the area of the circle.

c. As s increases, the area of the regular polygon approaches the area of the circle.

d. As h increases, the area of the regular polygon approaches the area of the circle.

The correct statement is:

E) There is exactly one solution at (1, -2).

What is equation ?

An equation is a mathematical statement that indicates that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation typically consists of two sides separated by an equal sign (=). The values of the variables that make the equation true are called solutions or roots of the equation. Equations are used to model a wide range of phenomena in mathematics, science, engineering, and other fields, and they play a central role in problem-solving and mathematical analysis.

According to given conditions:

To solve the system of equations:

y = 4x - 6 ...(1)

x + 3y = -5 ...(2)

We can use substitution or elimination method. Here, we will use the substitution method:

From equation (1), we have y = 4x - 6.

Substitute y = 4x - 6 in equation (2):

x + 3(4x - 6) = -5

Simplifying the above equation, we get:

13x - 18 = -5

Adding 18 on both sides, we get:

13x = 13

Dividing both sides by 13, we get:

x = 1

Substitute x = 1 in equation (1):

y = 4(1) - 6 = -2

Therefore, the solution to the system of equations is (1, -2).

So, the correct statement is:

A) There is exactly one solution at (0, -6). (Incorrect)

B) There is exactly one solution at (12). (Incorrect)

C) There is no solution. (Incorrect)

D) There are infinitely many solutions. (Incorrect)

The correct statement is:

E) There is exactly one solution at (1, -2).

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The requried, Daniel could expect to find 18 red skittles in the big bag.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Assuming that the ratio of red skittles to the total number of skittles in the bag is the same for both the small bag and the big bag, we can use proportions to solve the problem.

The proportion of red skittles to the total number of skittles in the small bag is,

= 9/45

Simplifying this fraction by dividing both the numerator and denominator by 9, we get 1/5. This means that one-fifth of the skittles in the small bag is red.

To find out how many red skittles Daniel could expect in the big bag, we need to multiply the total number of skittles in the big bag by one-fifth,

= 90 * 1/5 = 18

Therefore, Daniel could expect to find 18 red skittles in the big bag.

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Answer:

-$32

Step-by-step explanation:

Credited = Positive Change

Debited = Negative Change

48-80 = -32

-$32

2) The equation of tangent line is,

⇒ y = 324x log 3  + 84 - 648 log 3

3) And, The value of x is,

⇒ x = nπ ± π/6

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

2) The equation of curve is,

y = 3ˣ² + 3

At x = 2

y = 3⁴ + 3

y = 84

Hence, The value of point = (3, 84)

Now, Find dy/dx as;

y = 3ˣ² + 3

dy/dx = 3ˣ² log 3 × 2x

dy/dx = 2x × 3ˣ² log 3

At x = 2

dy/dx = 2 × 2 × 81 × log 3

m = dy/dx = 324 log 3

We know that;

The slope intercept form of equation of line is,

y = mx + c

y = 324x log 3  + c

At point (x, y) = (2, 84)

84 = 324 × 2 log 3 + c

⇒ c = 84 - 648 log 3

Hence, The equation of tangent line is,

⇒ y = 324x log 3  + 84 - 648 log 3

3) We know that;

Horizontal tangent will have a slope of 0.

Hence, The derivative represent the rate of change of a function.

The equation of graph is,

y = 4x - 3 tan x

y' = 4 - 3 sec²x = 0

sec²x = 4/3

sec²x = (2/√3)²

x = nπ ± π/6

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Answer:

x = 4

Step-by-step explanation:

(4 + 10)
14 x 5 = 70





~ LadyBrainiac

we need to mix milk and water in the ratio of 1:5 to gain a profit of 25% when selling the mixture at cost price.

What is ratio ?

Ratio can be defined as given value divided by total value.

Let's assume that we have x liters of milk and y liters of water. We want to find the ratio in which water must be mixed with milk to gain 25% on selling the mixture at cost price.

If we sell the mixture at cost price, we will not make any profit or loss. So, let's first calculate the cost price of the mixture.

Assuming that the cost price of milk is the same as the cost price of water, the cost price of x liters of milk and y liters of water is:

Cost price = Cost price of milk + Cost price of water

= x * cost price of milk + y * cost price of water

Since we are not making any profit or loss, the selling price of the mixture will be the same as the cost price.

Now, to gain a profit of 25%, the selling price must be 125% of the cost price. So, we have:

Selling price = 125% of cost price

= 1.25 * (x * cost price of milk + y * cost price of water)

We know that the mixture contains only milk and water, so the total volume of the mixture is x + y liters.

Now, we can set up an equation to find the ratio of water to milk:

y/x = (1 - 1.25) / (1.25 - 0)

y/x = -0.2

Simplifying this equation, we get:

y = -0.2x

This means that for every 1 liter of milk, we need to mix it with 0.2 liters of water in order to gain a 25% profit when selling the mixture at cost price.

In terms of ratio, the ratio of water to milk is:

0.2 : 1

or

1 : 5 (by simplifying the ratio by multiplying both sides by 5)

Hence, we need to mix milk and water in the ratio of 1:5 to gain a profit of 25% when selling the mixture at cost price.

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