-3p>-6 or 4p + 1 > 13

The amount of light that passes through a camera lens is determined by the aperture, which is the size of the opening in the lens that lets light in. changing from f/1.4 to f/8 reduces the amount of light that can pass through the lens by a factor of 32.49,

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The solution for the given expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex] will be [tex]\frac{xy}{x^{3} + y^{3} }[/tex].

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]

We will solve this equation using the simplification methods,

Since,

a³ + b³ = (a +b)(a² +b² - ab)

From this formula;

=> [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]

=> [tex]\frac{x^{2} + y^{2} }{(x + y)(x^{2} + y^{2} - xy) } - \frac{1}{x + y}[/tex]

taking 1/(x +y) common,

=> 1/(x +y) { (x² + y²)/(x² +y² - xy) - 1}

=>  1/(x +y) { xy/(x² +y² - xy)}

=> xy/(x³ +y³)

Therefore, [tex]\frac{xy}{x^{3} + y^{3} }[/tex] will be the simplified form of the given Equation.

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The two points that would line of fit go through to best fit the data is (1, 9) and (10, 1).

Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.

Given a scatterplot.

There are 10 points which are marked in the scatterplot.

We have to identify the points which are closely related to the general trend of the line.

Those points will be best passing through the line of best fit.

Here the graph will be negative, since the values on the vertical line are decreasing with the increase in the values on horizontal.

Hence the two points are (1, 9) and (10, 1).

Hence the two points are (1, 9) and (10, 1).

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The required straight-line distance between the school and the movie theater is 10 miles, as of the given condition.

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

The straight-line distance between the school and the movie theater can be found using the Pythagorean theorem. If the skate park is 8 miles south of the school and the movie theater is 6 miles east of the skate park, then the distance between the school and the movie theater is given as,
= √8² + 6² =
= √64 + 36
= √100.
= 10 miles

Thus, the straight-line distance between the school and the movie theater is 10 miles.

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Answer: this is the basic d

Step-by-step explanation idf k man comletely honest, i just searched that shi up and i saw that so yeah...

There must be at least one x-value that makes the function undefined if r(x) is a rational function.

If r(x) is a rational function in simplest form where the degree of the numerator is 2 and the degree of the denominator is 2, then it is possible for the function to be undefined for some values of x.

A rational function is defined as the quotient of two polynomials, and when the degree of the numerator is equal to the degree of the denominator, it is possible for the denominator to equal zero for some values of x, which would make the function undefined for those values.

This means that there must be at least one x-value that makes the function undefined. To determine these x-values, we need to find the zeros of the denominator and set the denominator equal to zero, then solve for x.

The x-values that make the denominator equal to zero are known as the vertical asymptotes of the function, and they are the x-values for which the function is undefined.

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1. B has the greater rate of change.

2. A has the greater rate of change.

3. B has the greater rate of change.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the rate of change, we must look at the slope of each function.

From the graph or from a table, the slope is given dividing the change in y by the change in x.

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The required function is continuous at x = -5 when c = 4.

If it is possible to draw the curve without encountering any breaks, the function is considered to be continuous in the interval. If every point in the interval satisfies the function, the function is said to be continuous.

For the function to be continuous at x = -5, the value of the function f(-5) must be equal to the value of c. That is,

f(-5) = c

Since f(x) = 4 when x = 1, we have

f(-5) = 4

Therefore,

c = 4

So the function is continuous at x = -5 when c = 4.

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The area of the triangle with the given vertices is 6.6.

The formula for finding the area of a triangle given its vertices is A = 1/2 abs(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3). To calculate the area of the given triangle, we substitute the coordinates of each vertex into the formula. First we find the three cross-products: x1y2 = 0 * 6 = 0, x2y3 = 2.8 * 6 = 16.8, and x3y1 = 5 * 0 = 0. Then, we find the two products of the y-coordinates: x2y1 = 2.8 * 0 = 0, and x3y2 = 5 * 6 = 30. Lastly, we find the product of the x-coordinates: x1y3 = 0 * 6 = 0. Adding all these up, we get 0 + 16.8 + 0 - 0 - 30 - 0 = -13.2. We then take the absolute value of the result, abs(-13.2) = 13.2. Finally, we multiply the result by 1/2 to get the area of the triangle, A = 1/2 abs(-13.2) = 1/2 * 13.2 = 6.6. Therefore, the area of the triangle with the given vertices is 6.6.

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x>-7/3 is the solution of the inequality −3x+8<15.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is −3x+8<15

Minus three times of x plus eight less than fifteen.

Subtract 8 from both the sides

-3x<7

Divide both sides by 3

-x<7/3

x>-7/3

Hence, x>-7/3 is the solution of the inequality −3x+8<15.

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Colleen had 90 points after ten turns, which was calculated by subtracting 170 from her initial 260 points.

The expression to find how many points Colleen had after her ten turns is 260 - 170 = 90. This expression can be written mathematically as P = 260 - 170, where P is the total points after ten turns. To solve this equation, we first subtract 170 from 260. This yields a total of 90 points, which is the number of points Colleen had after her ten turns. The calculation can be summarized as follows:

P = 260 – 170

P = 90

Therefore, after ten turns,Colleen had 90 points after ten turns, which was calculated by subtracting 170 from her initial 260 points.

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To Calculate the Sum or Difference : x = 12

When two or more numbers or terms are added together, the total is the outcome or answer.

Consequently, the sum is a method of assembling objects.

The process of combining two or more numbers to create a new result or total is known as the sum, to put it another way.

Where Samantha's age at the moment is y and her age in five years is a. In light of the fact that she will turn 17 in 5 years, she is currently 12 years old. Consequently, y in this situation equals 12.

In summary, a = age in 5 years, and y = age right now (12)

Based on the given condition, Write :

x = 17 - 5

Calculate the Sum or Difference : x = 12

x = 12.

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Answer:

When we multiply by a power of 10 (such as 10, 100, 1000, 10000, etc.), the number of digit zeros in the power of 10 is the number of places we move the decimal point to the right.

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Step-by-step explanation:

The correct two expressions have the same solution are,

⇒ 230p - 1010 = 650p - 400 - p

⇒ 23p - 101 = 65p - 40 - 0.1p

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p

Now, We can simplify as;

⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p

Multiply by 10 both side,

⇒ 23p - 101 = 65p - 40 - 0.1p

And, ⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p

Multiply by 100 both side,

⇒ 230p - 1010 = 650p - 400 - p

Thus, The correct two expressions have the same solution are,

⇒ 230p - 1010 = 650p - 400 - p

⇒ 23p - 101 = 65p - 40 - 0.1p

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The complete question is this;

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

The height of the water tank of the air cooler brought by Anu is 40 cm.

Height is the vertical measurement of an object. If the measurement is not made vertically, the measurement is termed the length or width. Volume is a measure of how much space an object can occupy. Volume is used to determine the density of an object.

given,

Length = 50 cm

Width = 20 cm

Maximum tank volume = 40 liters = 40,000 cm3

Tank height?

Steps,

Tank volume = length x width x height

40,000 = 50 x 20 x height

40,000 = 1000 x height

Tank height = 40,000 : 1000

Tank height = 40 cm

So, the height of the air conditioning tank that can hold 40 liters of water is 40 cm.

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The correct statement regarding the transformation and the difference of functions f(x) and g(x) is given as follows:

A.

The graph of g(x) is the graph of f(x) vertically compressed by a factor of three.

The parent function for this problem is given as follows:

f(x) = 7^x.

The transformed function for this problem is given as follows:

g(x) = f(x)/3 = (1/3) x 7^x.

The only transformation is a multiplication by the constant 1/3. As the constant has an absolute value less than 1, the graph of g(x) is a vertical compression of the graph of f(x) by a factor of 3.

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The solution of inequality would be, C = -4, C = 2

What is solution to the inequality?

An inequality is a relationship characterized by a non-equal comparison of two numbers or mathematical expressions.

A number is a solution to an inequality in x if it can be used to replace x with a true statement. Thus, while 8 is not a solution for example 1, 4, it is. The collection of all solutions makes up the inequality solution set.

The solution to the inequality -C + 2 > 1 is C < 1.

So, the answer is:

C = -4

C = 2

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Paying only the minimum balance each month will take the longest period of time to pay off the credit card debt.

Simple interest is defined as the percentage of earnings on the lending for a period of time.

Paying only the minimum balance each month will take the longest period of time to pay off the credit card debt. This method is often referred to as "minimum payment plan." By making only the minimum payment each month, the credit card holder will pay mostly interest, and very little of the principal balance. This will result in a longer period of time to pay off the debt, as the outstanding balance will only decrease slowly each month.

In contrast, making fixed payments each month, regardless of the minimum payment, will result in paying off the debt more quickly. Snowballing payments according to the highest interest rate or the lowest balance will also help pay off the debt more quickly, as these methods prioritize paying off the credit cards with the highest interest rate or the lowest balance first.

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The value of θ for which | r | has maximum value if r = sinθ is θ = π/2.

Given r = sinθ and the range of θ is 0 < θ < π

If 0 < θ < π the range of sinθ is:

                                      0 ≤ sinθ ≤ 1

So, in  0 < θ < π, the maximum value of sinθ is 1 and this value occurs at θ = π/2.

Now, we are asked to determine the value θ for which | r | is maximum and it is also given that r = sinθ and we have already found out that the maximum of sinθ in 0 < θ < π is 1.

Therefore, the maximum value of | r | is 1 and this value occurs at θ = π/2.

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Answer:

Step-by-step explanation:

10π cm * 12 cm = 120π cm² ≈ 377 cm²

Let the vector pace P2 have the inner product the following for p=2x, q=5x2 for ∫4−4p(x)q(x)dx are

1) For ⟨p,q⟩=∫4−4p(x)q(x)dx we can put the value of the  p=2x, q=5x² so  

⟨p, q⟩= ∫4− 4(2x)(5x²) dx

= ∫4−40x³ dx

2) For d(p,q)=  4−40x³dx  ............( after derivating)

= 0 - 120 x²

= -120x²

3) ∥p∥ = ||2x||  = 2||x||   ( ||x|| > 0)

given that p is not any number which will be not affected by any sign of the x and will remain positive.

4) ∥q∥ = ||5x²|| = 5||x²||   (||x² > 0)

given that q is not any number which will be not affected by any sign of the x² and will remain positive.

In mathematics, objects called vectors have both magnitude and direction. The vector's magnitude determines its length. It is shown as a line with an arrow, with the length of the line indicating the vector's magnitude and the direction of the arrow indicating its direction. Other names for it include Euclidean vector, Geometric vector, Spatial vector, and simply "vector."

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A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.

The number of sides (n) of the pentagon is:

n =5

The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).

To draw the pentagon onto itself, the pentagon has to be rotated.

The angle of rotation is:

θ [tex]= \frac{360}{n}[/tex]

θ  [tex]=\frac{360}{5} = 72[/tex]

Other possible angles of rotation must be multiple of 72. i.e.

θ= 72, 144, 216, 288...

Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.

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The complete question is:

A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?

a. A reflection across line m

b. A reflection across the x-axis

c) A clockwise rotation of 144 degrees about the origin

The experimental probability of landing on a number greater than 5 is 2/15.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1.

Given A number cube is tossed 60 times,

Outcome       Frequency

1                         12

2                        13

3                         11

4                         6

5                         10

6                          8

The number of times greater than 5 comes up = 8 (frequency of 6 is 8)

Probability of getting a number greater than 5

=  (frequency of getting6) / (total number of trials)

⇒ probability of getting a number greater than 5  = 8 / 60 = 2/15

Hence probability is 2/15.

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A normal distribution with a mean of 10 and standard deviation of 25, the z score for the value of 35 is 1.

A mean = 10

Standard Deviation = 25

We have to determine the z score for the value of 35. So X = 35.

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of 0 indicates that the data point's value is equal to the mean score.

The formula is:

Z = (X - mean)/Standard Deviation

Now putting the values

Z = (35 - 10)/25

Z = 25/25

Z = 1

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The amount of the old monthly payment = $879

The amount of the new monthly payment = $724.5

Then the small amount of principal that has been paid = -17.57%

Given that,

Natan Nave bought a home with a 13% adjustable rate mortgage for 20 years.

He paid $11. 72 monthly per thousand on his original loan.

At the end of 4 years he owes the bank $75,000.

Now that interest rates have gone down to 10%

The bank will renew the mortgage at this rate or Natan can pay $75,000.

Natan decides to renew and will pay $9. 66 monthly per thousand on this loan.

Per thousand value = 75000/1000 = 75

What was the old monthly payment,

$[tex]11.72*75[/tex] = $879

What is the new monthly payment,

$[tex]9.66*75[/tex] = $724.5

What is the percent decrease in his monthly payment (to the nearest tenth),

= [tex](\frac{9.66}{11.72} )-1 *100[/tex]

= -17.57%

Therefore,

The amount of the old monthly payment = $879

The amount of the new monthly payment = $724.5

Then the small amount of principal that has been paid = -17.57%

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The polynomial that satisfies the conditions is: p(t) = (1/4)(t - 1)² (t - 2)³

This polynomial has a root of multiplicity 2 at t = 1 and a root of multiplicity 3 at t = 2, and also satisfies p(0) = 2 and p'(0) = 1.

The other root of p(t) can be found by factoring the polynomial further, but since the degree of the polynomial is 6, it will have 3 additional roots, which can be found using various mathematical methods such as the Rational Root Theorem or numerical methods.

Polynomials are mathematical expressions that involve variables raised to a power and are combined using addition and subtraction operations. The degree of a polynomial is the highest power of the variable in the expression.

A zero of a polynomial is a value of the variable for which the polynomial evaluates to zero. The multiplicity of a zero is the number of times the factor (t - zero) appears in the polynomial's factorization.

Given the conditions that the polynomial p(t) has a zero of multiplicity 2 at t = 1 and a zero of multiplicity 3 at t = 2, we can write p(t) as the product of factors (t - 1)² and (t - 2)³:

p(t) = a(t - 1)² (t - 2)³

where a is some constant. To find the value of a, we use the fact that p(0) = 2 and p'(0) = 1. We evaluate p(0) and p'(0) using the polynomial expression above, then solve for a.

First, we find p(0):

p(0) = a(0 - 1)² (0 - 2)³ = a(-1)² (-2)³ = a * 8

Next, we find p'(0):

p'(t) = 2a(t - 1)(t - 2)³ + a(t - 1)² * 3(t - 2)²

p'(0) = 2a(-1)(-2)³ + a(-1)² * 3(-2)² = 16a + 12a = 28a

Now that we have expressions for p(0) and p'(0), we can solve for a:

p(0) = a * 8 = 2 => a = 1/4

p'(0) = 28a = 1 => 28 * 1/4 = 1

So the polynomial that satisfies the conditions is:

p(t) = (1/4)(t - 1)² (t - 2)³

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Answer: $2.15

Step-by-step explanation: Let x represent the price of a pen.

5x + (x - 1.30) = 11.60

6x - 1.30 = 11.60

6x = 12.90

x = 2.15

Answer:  r and b are both positive or both negative

Reason:

The correlation coefficient r is between -1 and 1

[tex]-1 \le r \le 1[/tex]

If r = -1, then we have perfect negative correlation. All points are on the same straight line that goes downhill as you move to the right. This slope is negative. If -1 < r < 0, then we still have negative slope but the points aren't all on the same line.

If r = 1, then the slope is positive. The regression line moves upward as you move to the right. All points are on this line. If 0 < r < 1, then the points aren't on the same line but we have a positive slope.

If r = 0, then we have no linear correlation at all. Either the points are randomly scattered or they fall on a curve (eg: parabola).

In short:

The graph of y = 10 + 20x that represents the situation is shown in the attachment.

A graph of a linear equation is a straight line on a coordinate plane that represents all the solutions to the equation. A linear equation can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope and y-intercept determine the position and direction of the line on the coordinate plane. Points on the line satisfy the equation, and any x and y values that satisfy the equation can be plotted on the graph to form the line. The graph of a linear equation can be used to visualize relationships between variables and to make predictions about the values of the variables based on the line.

Thus, the equation y = 10 + 20x will have a graph that has a y-intercept of 10 and a slope of 20. The graph is shown below.

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Answer:

what the person above said pls give the brainliest

Step-by-step explanation:

Answer:

X = 17

Step-by-step explanation:

Since M = N then,

(3x - 22) = (2x-5)

What we can do next is get the X's on one side and the numbers on the other side of the equal sign

Let's subtract 2x from both sides

3x - 2x is just X, so

X - 22 = -5

Now we can add 22 to both sides. -5+22 = 17

X = 17

Plug in 17 to make sure

(3x - 22) = 3(17)-22 = 51-22 = 29

(2x-5) = 2(17)-5 = 34 - 5 = 29