5/7 divided by 8/11
A. 56/55
B. 55/56
C. 2/7
D. 11/3

Answer:

p = 6 , q = 43

Step-by-step explanation:

x² + 12x - 7

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

=x² + 2(6)x + 36 - 36 - 7

= (x + 6)² - 43 ← in the form (x + p)² - q

with p = 6 and q = 43

Answer:

41.4

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos x = 9/12

Taking the inverse cos of each side

cos ^-1 ( cos x) = cos ^-1 (9/12)

x = 41.41

To the nearest tenth

x = 41.4

Answer:

Lion area: 60

Lion Perimeter: 34

Tiger Area: 60

Tiger perimeter: 64

Step-by-step explanation:

Answer:

87

Step-by-step explanation:

Hope this helps! Pls give brainliest!

The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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This is not a question!!!!!!!!!

please delete this one

The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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\(\\ \rm\longmapsto Length(Breadth)=Area\)

\(\\ \rm\longmapsto Length(7)=672\)

\(\\ \rm\longmapsto Length=\dfrac{672}{7}\)

\(\\ \rm\longmapsto Length=96m\)

Answer:

volume = 798.58 cm³ (nearest hundredth)

surface area = 678.31 cm³ (nearest hundredth)

Step-by-step explanation:

Volume of a cylinder:   \(V=\pi r^2h\)

Surface area of a cylinder:   \(SA=2\pi r^2+2\pi rh\)

Circumference:  \(C=2\pi r\)

(where r is the radius and h is the height)

Given circumference = 56

⇒ \(56 = 2\pi r\)

⇒ \(r=\dfrac{56}{2\pi }=\dfrac{28}{\pi }\)

\(V=\pi \left(\dfrac{28}{\pi}\right)^2 \times3.2=\dfrac{2508.8}{\pi}=798.58 \textsf{ cm}^3 \textsf{ (nearest hundredth)}\)

\(SA=2\pi \left(\dfrac{28}{\pi}\right)^2+56 \times3.2=\dfrac{1568}{\pi}+179.2=678.31 \textsf{ cm}^3 \textsf{ (nearest hundredth)}\)

Answer:

\(Scale\ Factor = 1.5\)

Step-by-step explanation:

See attachment for proper presentation of question.

From the attachment, we have:

\(A = 7\)

\(A' = 10.5\)

Required

Determine the scale factor

To solve this, simply divide the circumference of A' by that of A.

This gives the scale factor used

i.e.

\(Scale\ Factor = \frac{A'}{A}\)

Substitute values for A and A'

\(Scale\ Factor = \frac{10.5}{7}\)

\(Scale\ Factor = 1.5\)

Hence, the scale factor used is 1.5

Additional Note:

If the given parameters had been the area of A and A', you'll need to first solve for the radius of both circles.

Then determine the scale factor by A'/A

Answer:

7((x-2)(3x+4))

Step-by-step explanation:

Common factor of 7 in this quadratic formula. \(7(3x^2-2x-8)\); -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product.  You get 7((x-2)(3x+4))

The value of the first and second integers are 54 and 55 respectively.

Let

First integer = x

Second integer = x + 1

Sum of the integers = 109

So,

First integer + Second integer = Sum of the integers

x + (x + 1) = 109

x + x + 1 = 109

2x + 1 = 109

Subtract 1 from both sides

2x = 109 - 1

2x = 108

divide both sides by 2

x = 108/2

x = 54

Ultimately,

First integer = x

= 54

Second integer = x + 1

= 54 + 1

= 55

Therefore, the solution in 4 steps are;

Step 1: x + (x + 1) = 109

Step 2: 2x + 1 = 109

Step 3: 2x = 108

Step 4: x = 54

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Answer:

-1.33333 < x

Step-by-step explanation:

subtract 5 from both sides

get -4<3x

divde 3 by both sides

-1.33< x

Hi, there!

 _______

The first step is:

» Subtract both sides by 5

\(\sf{-4 < 3x}\)

Now divide each term by 3:

\(\sf{-\dfrac{4}{3} < x}\)

We can flip it over:

\(\sf{x > -\dfrac{4}{3}}\)

Hope the answer - and explanation - made sense,

happy studying!!

Answer:

The correct answer is 5.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

sin of 52 radians = 0.98662759204

Step-by-step explanation:

Answer: 0.98

Step-by-step explanation:

Approximately 1, you shouldn't have to answer 0.988 etc on the test.

The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.

To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.

Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π

The length of the 45° arc is approximately 3.14 miles.

Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.

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No, the given experiment does not have a sample space with equally likely outcomes.

The term "loaded" means that the die is not fair, and certain numbers are more likely to appear than others. This means that the probabilities of each possible outcome are not equal, and therefore the sample space does not have equally likely outcomes. For example, if a die is loaded to favor rolling a 6, then the probability of rolling a 6 is higher than the probability of rolling any other number. Therefore, the sample space of this experiment is not uniform, and outcomes are not equally likely.

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Answer:

1.

a. 2

b. 0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.

c. 0.1428 = 14.28% probability that delays will occur.

2.

a. 0.4512 = 45.12% probability that the service time is one minute or less.

b. 0.6988 = 69.88% probability that the service time is two minutes or less.

c. 0.3012 = 30.12% probability that the service time is more than two minutes.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

\(f(x) = \mu e^{-\mu x}\)

In which \(\mu = \frac{1}{m}\) is the decay parameter.

The probability that x is lower or equal to a is given by:

\(P(X \leq x) = \int\limits^a_0 {f(x)} \, dx\)

Which has the following solution:

\(P(X \leq x) = 1 - e^{-\mu x}\)

The probability of finding a value higher than x is:

\(P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}\)

Question 1:

a. What is the mean or expected number of customers that will arrive in a five-minute period?

0.4 customers per minute, so for 5 minutes:

\(\mu = 0.4*5 = 2\)

So 2 is the answer.

Question b:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353\)

\(P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707\)

\(P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707\)

\(P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1805\)

0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.

Question c:

This is:

\(P(X > 3) = 1 - P(X \leq 3)\)

In which:

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)

The values we have in item b, so:

\(P(X \leq 3) = 0.1353 + 0.2707 + 0.2707 + 0.1805 = 0.8572\)

\(P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8572 = 0.1428\)

0.1428 = 14.28% probability that delays will occur.

Question 2:

\(\mu = 0.6\)

a. What is the probability that the service time is one minute or less?

\(P(X \leq 1) = 1 - e^{-0.6} = 0.4512\)

0.4512 = 45.12% probability that the service time is one minute or less.

b. What is the probability that the service time is two minutes or less?

\(P(X \leq 2) = 1 - e^{-0.6(2)} = 1 - e^{-1.2} = 0.6988\)

0.6988 = 69.88% probability that the service time is two minutes or less.

c. What is the probability that the service time is more than two minutes?

\(P(X > 2) = e^{-1.2} = 0.3012\)

0.3012 = 30.12% probability that the service time is more than two minutes.

Answer: Question 1:

4 / 38 = 2/19

Alternative answer = 0.105

Question 2:

4 / 83 = 4/83

Alternative answer = 0.048

Step-by-step explanation:

Answer:

The probability of getting a 2, 4, or 6 when a dice is rolled is 1/2, or 50%. This is because there are six possible outcomes when a dice is rolled, and three of them are favorable outcomes (2, 4, or 6). Therefore, the probability of getting a 2, 4, or 6 is 3/6, which simplifies to 1/2 or 50%.

Answer:

Counting the number of sign changes in the function f(x)

The number of positive roots is equal to the number of sign changes in the function f(x) or less than that by an even integer.

Here, f(x)=3x^4-5x^3-x^2 has two sign changes (from + to -, and from - to +), so the number of positive roots is either 2 or 0.

Counting the number of sign changes in the function f(-x)

The number of negative roots is equal to the number of sign changes in the function f(-x) or less than that by an even integer.

Here, f(-x)=3x^4+5x^3-x^2 has one sign change (from - to +), so the number of negative roots is either 1 or 0.

Counting the number of non-real roots (complex roots)

The number of non-real roots (complex roots) is equal to the difference between the total number of roots (4 in this case) and the number of real roots (which we found above).

Therefore, the possible number of positive roots is 2 or 0, the possible number of negative roots is 1 or 0, and the possible number of complex roots is 2 or 4.

Step-by-step explanation:

Answer:

The answer to this question is due to the algebraic equality of the equation

Step-by-step explanation:

\(2(m - n) = 7 = y\)

\(y = \frac{7}{2} \)

That is, option C

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

Step-by-step explanation:

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y = 1 - Ce^-kt/A is a solution to dydt=k(Ay−1).

Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.

Given, Let A and k be positive constants.

The differential equation dy/dt = k(Ay-1) is a separable first-order differential equation that can be solved using the separation of variables.

First, we can separate the variables by dividing both sides by (Ay-1):

1/(Ay-1) dy/dt = k

Then, we can integrate both sides with respect to t and y, respectively:

∫ 1/(Ay-1) dy = ∫ k dt

To integrate the left-hand side, we can use the substitution u = Ay-1, which gives:

du = A dy

dy = du/A

Substituting back into the integral:

∫ 1/(Ay-1) dy = ∫ 1/u du = ln|u| + C₁

where C₁ is the constant of integration. Substituting back for u and simplifying:

ln|Ay-1| + C₁ = kt + C₂

where C₂ is another constant of integration. Solving for y:

ln|Ay-1| = kt + C₃

where C₃ = C₂ - C₁. Taking the exponential of both sides:

|Ay-1| = e^(kt+C₃) = Ce^kt

where C = ±e^C₃. Taking the absolute value accounts for the possibility of a negative solution.

Solving for y, we have two possible solutions:

Ay-1 = Ce^kt, or y = 1 + Ce^kt/A

or

1-Ay = Ce^-kt, or y = 1 - Ce^-kt/A

where A, k, and C are constants determined by initial conditions or other constraints.

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Answer:

A

Step-by-step explanation:

z = -3 - 5i

z (i) = i (-3 - 5 i)

z (i) = -3i - 5i^2

z (i) = -3i - 5 (-1)

z (i) = -3i + 5

z (i) = 5 - 3i

Therefore, letter A is the correct answer.

The required simplified value of the given numerical expression is 223.39.

Given that,
To evaluate the numerical expression,

= (25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
= (25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]
= 5000÷ 23 + [24 ÷8 ]
= 217.39 + 6
= 223.39

Thus, the required simplified value of the given numerical expression is 223.39.

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