Which quadratic function is represented by the graph?

Step-by-step explanation: First, you have to multiply the numerators, for example, 1/2 x 1/4. 1x1=1. Then the denominator. 2x4=8. So, 1/2x1/4=1/8

Answer:

160

Step-by-step explanation:

68 + 50 + 42 = 160

add the numbers that the bar graphs stop at

HOPE THIS HELPS!!!

Step-by-step explanation:

let x be the distance between B and P

tan(67)=x/5000

x=2.3558 . 5000

x=11779feet

Answer:

11,779 feet

Step-by-step explanation:

Is the answer

The Area of the composite figure = area of the rectangle + area of the triangle = 148.5 cm².

The figure formed by the arrow can be decomposed into a rectangle and a triangle.

The area of the composite figure = area of the rectangle + area of the triangle.

Find the area of the rectangle:

Length = 12 cm

Width = 11 cm

Area of the rectangle = (length)(width) = (12)(11)

Area of the rectangle = 132 cm²

Find the area of the triangle

Base = 11 cm

Height = 15 - 12 = 3 cm

Area of the triangle = 1/2(b)(h) = 1/2(11)(3)

Area of the triangle = 16.5 cm²

Area of the composite figure = area of the rectangle + area of the triangle = 132 + 16.5 = 148.5 cm².

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The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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Answer:

there are 40% black ball a

white ball we don't know

so, we let = x

40\100 × x

now we cutting

ans is 10x

Given the triangles S T U and X Y Z shown in the diagram and △STU ~ △XYZ. We need to select all the true statements. By the definition of similar triangles, the corresponding sides are proportional.

So, Start Fraction ST Over XY End Fraction = Start Fraction TU Over YZ End Fraction.

This statement should be accurate.

Let's check this for the given triangles;

Start Fraction 10 Over 20 End Fraction = Start Fraction 8 Over 16 End Fraction 0.5 = 0.5.

So, the statement is true, actually.

Let's check this for the given triangles;

Start Fraction XY Over ST End Fraction = Start Fraction YZ Over TU End Fraction.

So, the statement should be accurate, actually.

Let's check this for the given triangles;

Start Fraction 20 Over 10 End Fraction = Start Fraction 16 Over 8 End Fraction 2 = 2

So, the statement is true, actually.

Using the angles in the triangles, we can say that the statement ∠S ≅ ∠X and ∠T ≅ ∠Y should be true. Let's check this for the given triangles;

∠S = 100° and ∠X = 100°; ∠T = 40° and ∠Y = 40°.Thus, the statement is true.

Using the ratio of sides in similar triangles, we have

Start Fraction SU Over XZ End Fraction = Start Fraction ST Over XY End Fraction

Multiplying both sides by XY, we get

SU = XZ × Start Fraction ST Over XY End Fraction

We know that ST = 10 and XY = 20

Substituting these values, we have

SU = {XZ × Start Fraction 10}{20 End Fraction SU} = XZ × 0.5

Thus, the statement SU = XZ should be false.

From the given triangles, we have △STU ~ △XYZ. By the definition of similar triangles, the corresponding sides are proportional. Next, using the angles in the triangles, we can say that ∠S ≅ ∠X and ∠T ≅ ∠Y are congruent as the corresponding angles of similar triangles.

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Answer:

No, is not a right triangle

Step-by-step explanation:

If it is a right triangle Pythagoras theorem do apply.

Since the hypotenuse is the side with 16in, sides are 7 and 14 inches

notice

\(\sqrt{7^{2} +16^{2} } = \sqrt{245} \neq 16\)

Answer:

Step-by-step explanation:

that is b

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:

Step-by-step explanation:

x=2  and  g(x) = -2x-3  ⇒ g(2) = -2(2)-3 = -4 - 3 = -7

f(g(x)) and g(x) = -7  ⇒   f(g(x)) = f(-7)

f(x)= -x+4  ⇒  f(-7) = -(-7) + 4 = 7 + 4 = 11

The solution of the given integral \(\int \left(x^2+4\right)^3\cdot \:2xdx\) = \(\frac{1}{4}\left(x^2+4\right)^4\)

Given;

To evaluate the value of a given integral;

\(\int \left(x^2+4\right)^3\cdot \:2xdx\)

Let;

\(\int \left(x^2+4\right)^3\cdot \:2xdx\) = \(2\cdot \int \left(x^2+4\right)^3xdx\)

Now, assume u = x² + 4

→ \(2\cdot \int \left(x^2+4\right)^3xdx\) = \(2\cdot \int \frac{u^3}{2}du\)

→ \(2\cdot \frac{1}{2}\cdot \frac{u^4}{4}\)

→ \(2\cdot \frac{1}{2}\cdot \frac{u^4}{4}\)

→  \(\frac{1}{4}\left(x^2+4\right)^4\)

By adding constant C;

\(\frac{1}{4}\left(x^2+4\right)^4\)+ C

Hence, the solution of the given integral \(\int \left(x^2+4\right)^3\cdot \:2xdx\) = \(\frac{1}{4}\left(x^2+4\right)^4\)

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Answer:

There are 43 students on each bus.

Step-by-step explanation:

To find out this answer, simply subtract the 4 students that are riding in cars from the total of 391 students:

391 - 4 = 387

Now, we take the 387 students and divide it by how many buses there are which are 9 buses, and we will have our answer:

387 divided by 9 = 43 students per bus.

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Answer:

There are 43 students on each bus

Step-by-step explanation:

Take the total number of students and subtract the number that went in cars

391-4 = 387

This is the number that went on the buses

Take this number and divide by the 9 buses

387 / 9

43

This is the number on each bus

There are 43 students on each bus

It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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1. True. The PESTLE framework categorizes environmental influences into six main types: Political, Economic, Sociocultural, Technological, Legal, and Environmental factors.

These factors help analyze the external macro-environmental forces that can impact an organization's strategies and operations. 2. False. The PESTLE framework analyzes the macro-environmental factors and not the micro-environment of organizations. The micro-environment is examined through other frameworks like Porter's Five Forces, which focus on specific industry dynamics and competitive factors.

3. True. Economic forces, such as inflation, interest rates, exchange rates, and economic growth, are one of the types included in the PESTLE framework. Economic factors play a significant role in shaping business decisions and strategies.

4. False. An organization's strengths are not part of the types studied in the PESTLE framework. Strengths, weaknesses, opportunities, and threats (SWOT) analysis is a separate framework used to assess internal strengths and weaknesses of an organization.

5. True. The PESTLE framework provides a comprehensive list of influences on the possible success or failure of strategies. By considering the political, economic, sociocultural, technological, legal, and environmental factors, organizations can gain insights into the external forces that may impact their strategies and make informed decisions.

The PESTLE framework categorizes environmental influences into six main types, including political, economic, sociocultural, technological, legal, and environmental factors. It analyzes the macro-environmental forces, not the micro-environment of organizations. Economic forces are one of the types studied in the framework, while an organization's strengths are not included. The framework provides a comprehensive list of influences on the success or failure of strategies, allowing organizations to consider various external factors in their decision-making process.

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Answer:

C: 0

Step-by-step explanation:

Let's use 1 for an example first. The opposite of 1 is -1. 2 = -2, 3 = -3, and so on. Since there is no such thing as -0, our answer would be C, 0. It is not -5, -2, 2, or 7 because those are not the negatives of 0.

The doubling time for the bacteria population is 3 hours, as it takes 3 hours for the population to triple.

In the bacteria growing experiment, the biologist observed that the number of bacteria in the culture was tripling every 3 hours. This means that the bacteria population was increasing at a rate of 200% every 3 hours. After 15 hours, it was estimated that there were 2 million bacteria in the culture. This means that the bacteria population had doubled approximately 5 times in the 15 hour period. Therefore, the doubling time for the bacteria population is 3 hours, as it takes 3 hours for the population to double. For example, if the initial population size is 100, then the population size after 3 hours would be 200. This means that the bacteria population was doubling approximately every 3 hours. Doubling time is an important factor to consider when studying population growth, as it can help to predict the size of a population at a certain point in time. Additionally, understanding the doubling time of a population can help to understand the rate of growth and how quickly it may reach a certain size.

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Answer:

D. A(n) = (n-1)(p•n)^i, where n is any real number

Step-by-step explanation:

The simple interest formula is P x R x T

------------

100

In this question I'm not completely sure what they mean but I'd go with the closest answer. D

Answer:

630 000

Step-by-step explanation:

We have to find 18% of the number 3 500 000:

\( \frac{3500000 \times 18\%}{100\%} = 630000\)

If 55% of the students are girls, 45% of the students are boys

It means there are 810 boys. From this number, 70% take the bus to school

It means 567 boys take the bus to school.

To find two numbers whose sum is 11 and whose product is maximum, we can use a mathematical approach.

Let's denote the two numbers as x and 11 - x, where x represents the first number. The sum of these numbers is 11, so we can write the equation x + (11 - x) = 11. Simplifying this equation gives us 2x = 11, and solving for x results in x = 11/2 or 5.5. Therefore, the two numbers are 5.5 and 5.5.

To explain this answer, we can consider the properties of quadratic functions. When we multiply two numbers, their product is maximized when the numbers are equal. By representing one number as x and the other as 11 - x, we ensure that their sum is 11. We then set up an equation using the sum constraint and solve for x. In this case, we find that x = 5.5, indicating that both numbers are 5.5. As a result, their product is maximized at 30.25.

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The volume of the solid bounded below by the circular cone z = 2√x² + y² and above by the sphere x² + y²+ z² = 3.5 z  is  

V = ∫[0, 2π] ∫[0, (49/16)^(1/2)] (2r) r dr dθ

To find the volume of the solid bounded below by the circular cone z = 2√(x² + y²) and above by the sphere x² + y² + z² = 3.5z, we can use a double integral in cylindrical coordinates.

First, let's find the intersection points between the cone and the sphere.

For the cone equation, z = 2√(x² + y²), we can rewrite it in terms of cylindrical coordinates as z = 2r.

For the sphere equation, x²+ y² + z² = 3.5z, we substitute z = 2r from the cone equation to get:

x² + y² + (2r)² = 3.5(2r)

x² + y² + 4r²= 7r

x² + y² - 7r + 4r² = 0

Now, we need to find the limits of integration for r and θ.

Since the solid is bounded below by the cone, the lowest value for r is 0.

To find the upper limit for r, we set the equation x² + y² - 7r + 4r² = 0 equal to 0 and solve for r: 4r² - 7r + x² + y² = 0

This is a quadratic equation in r. The discriminant of the equation must be greater than or equal to 0 to have real solutions:

b² - 4ac ≥ 0

(-7)² - 4(4)(x² + y²) ≥ 0

49 - 16(x² + y²) ≥ 0

49 - 16x² - 16y² ≥ 0

Simplifying, we have:

16x² + 16y²≤ 49

Dividing both sides by 16, we get: x²+ y² ≤ 49/16

This represents the region inside a circle of radius (49/16)^(1/2) centered at the origin. So the upper limit for r is (49/16)^(1/2).

For θ, we can choose the full range of 0 to 2π.

Now, we can set up the double integral to find the volume:

V = ∬[R] z dA

where R represents the region in the xy-plane bounded by the circle x^2 + y^2 ≤ (49/16) and dA represents the differential area element in polar coordinates.

The integral becomes:

V = ∫[0, 2π] ∫[0, (49/16)^(1/2)] (2r) r dr dθ

Evaluating this double integral will give us the volume of the solid.

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Answer:

9p⁸ + 12p⁴q⁴ + 4q⁸

Step-by-step explanation:

(3p⁴ + 2q⁴)²​ ⇒ The square of (3p⁴ + 2q⁴)

Squares are such bases that multiply itself two times.

⇒ (3p⁴ + 2q⁴)(3p⁴ + 2q⁴)

Simplifying the expression using (a + b)(a + b) = (a x a) + (ab) + (ab) + (b²)

⇒ (9p⁸ + 6p⁴q⁴ + 6p⁴q⁴ + 4q⁸)

⇒ (9p⁸ + 12p⁴q⁴ + 4q⁸) = 9p⁸ + 12p⁴q⁴ + 4q⁸

We know the identity

So

\(\\ \rm\Rrightarrow (3p^4+2q^4)^2\)

\(\\ \rm\Rrightarrow (3p^4)^2+(2q^4)^2+2(3p^4)(2q^4)\)

\(\\ \rm\Rrightarrow 9p^8+4q^8+12p^4q^4\)

Done

Answer:

A 5

solution:7x=1

divide both side buy 7

7x/7=1/7

x=0.143

Answer:

\(A. \: 3x + 6 = 4 x \: + \: 7 \: is \: equivalent \: with \: option \: 4. \\ B. \: 3(x + 6) = 4 x+ 7 \: is \: equivalent \: with \: option \: 2.\\ C.\: 4x + 3x = 7 - 6 \: is \: equivalent \: with \: option \: 5.\)

Step-by-step explanation:

\(all \: you \:need \: to \: do \: is \: to \: identify \: the \\ \: equations \: that \: have \: the \: same \: value \: of \: x. \\ A. \\ \: 3x + 6 = 4 x+ 7 \\ x = 6 - 7 \\ x = - 1. \\ \: so \: 3x + 6 = 4 x+ 7 \: is \: equal \: with \: \: option \: 4.\\ B. \\ 3(x + 6) = 4x + 7 \\ 3x + 18 = 4x + 7 \\ x = 18 - 7 \\ x = 11. \\ \: so \: 3(x + 6) = 4 x+ 7 \: is \: equal \: with \: \: option \: 2. \\ C .\\ 4x + 3x = 7 - 6 \\ 7x = 1 \\ x = \frac{1}{7} \\ so \: 4x + 3x = 7 - 6\: is \: equal \: with \: \: option \: 5. \)

Answer:

\(= \frac{2m^2n^8}{3}\)

Step-by-step explanation:

Given expression is

\((\frac{4m^{-2}n^8}{9m^{-6}n^{-8}} )^{\frac{1}{2}\)

The correct simplified form is shown below:-

From the above equation, we will simplify

we will shift \(m^{-6}\) to the numerator and we will use the negative exponent rule, that is

\(= (\frac{4m^{-2}n^8m^6}{9n^{-8}} )^{\frac{1}{2}\)

now we will shift the \(n^{-8}\) to the numerator and we will use the negative exponent rule, that is

\(= (\frac{4m^{-2}n^8m^6n^8}{9} )^{\frac{1}{2}\)

here we will solve the above equation which is shown below

\(= (\frac{4m^4n^{16}}{9}) ^\frac{1}{2}\)

So,

\(= (\frac{(2)^2(m^2)^2(n^8)^2}{(3)^2} ^\frac{1}{2}\)

Which gives result

\(= \frac{2m^2n^8}{3}\)

The set of three numbers that have a range of 7 and mode of 3 are: 3, 3, 7.

The range = largest value - least value.

Mode of a data = data point that appears most.

Since there are three positive numbers and the mode is 3, we can assume two of the numbers are 3's, since the range is 7.

Therefore, it 3 subtracted from a number will give us a range of 7. Thus, that number will be 10.

Therefore, the three numbers are: 3, 3, 10.

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The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data

The answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.

In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.

Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.

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Answer:

The probability is 9/100

Step-by-step explanation:

First, we know that 70% of the students are with brown eyes. Since we have a total of 20 students, this corresponds to 70/100 * 20 = 14 students

The number of students without brown eyes is thus 20 -14 = 6 students

Now, the probability of selecting a student without brown eyes is 14/20 = 7/10 while the probability of selecting a student with brown eyes is 6/20 = 3/10

Now the probability of selecting two students without brown eyes mean, the first selected is without brown eyes and also the second selected is without brown eyes.

In probability, once we have the work and, we multiply.

So our answer here is 3/10 * 3/10 = 9/100

The closest measurement to the volume of the container would be 738 cubic centimeters.

Assuming that the container has a cylindrical shape, the volume can be calculated using the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height of the cylinder.

Since the diameter of the container is given as 8 centimeters, the radius is half of that, which is 4 centimeters.

Therefore, the volume of the container is:

V = π(4 cm)^2(14 cm) = 704π/3 ≈ 738.18 cubic centimeters

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Answer:

x = 6

MP = 30

Step-by-step explanation:

5x = 3x + 12

2x = 12

x = 6

MP = 5x = 5 × 6

MP = 30