Find the average rate of change of f(x)=x^2+3x+1 from x=−5 to x=−3. Simplify your answer as much as possible.

Answer:

Option 4 [tex]tan[/tex]θ is undefined.

Step-by-step explanation:

Given : θ  [tex]\\=\frac{\pi }{2}[/tex] radians

To find : Which function is undefined

Solution : Put θ  [tex]\\=\frac{\pi }{2}[/tex] in all the given options to check which are undefined

[tex]Cos[/tex]θ  [tex]=cos\frac{\pi }{2} =0[/tex]

[tex]Cot[/tex]θ  [tex]=cot\frac{\pi }{2}=\frac{cos\frac{\pi }{2} }{sin\frac{\pi }{2} } =\frac{0}{1} =0[/tex]

[tex]Csc[/tex]θ  [tex]=cosec\frac{\pi }{2} =\frac{1}{sin\frac{\pi }{2} } =\frac{1}{1}=1[/tex]

[tex]tan[/tex]θ  [tex]=tan\frac{\pi }{2} =\frac{sin\frac{\pi }{2} }{cos\frac{\pi }{2} } =\frac{1}{0} =infinity[/tex]

Therefore, we get that [tex]tan[/tex]θ is not defined or undefined.

The Aerobics instructor teaches 7 classes each Saturday.

what is Algebraic expression?

An Algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.

To find the number of classes the Aerobics instructor teaches on Saturdays, we need to divide the total hours she teaches by the length of each class:

Total hours taught = 5 1/4 hours

Length of each class = 3/4 hour

Number of classes = (Total hours taught) / (Length of each class)

Number of classes = (5 1/4) / (3/4)

We need to convert the mixed number to an improper fraction first:

5 1/4 = (4 x 5 + 1) / 4 = 21/4

Now we can substitute the values:

Number of classes = (21/4) / (3/4)

fractions mean multiplying the first fraction by the reciprocal of the second fraction:

Number of classes = (21/4) * (4/3)

The 4 in the numerator and denominator cancel out, leaving us with:

Number of classes = 21/3

Dividing 21 by 3, we get:

Number of classes = 7

Therefore, To find the number of classes the Aerobics instructor teaches on Saturdays, we need to divide the total hours she teaches by the length of each class:

Total hours taught = 5 1/4 hours

Length of each class = 3/4 hour

Number of classes = (Total hours taught) / (Length of each class)

Number of classes = (5 1/4) / (3/4)

We need to convert the mixed number to an improper fraction first:

5 1/4 = (4 x 5 + 1) / 4 = 21/4

Now we can substitute the values:

Number of classes = (21/4) / (3/4)

Dividing fractions means multiplying the first fraction by the reciprocal of the second fraction:

Number of classes = (21/4) * (4/3)

The 4 in the numerator and denominator cancel out, leaving us with:

Number of classes = 21/3

Dividing 21 by 3, we get:

Number of classes = 7

Therefore, the Aerobics instructor teaches 7 classes each Saturday.

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The required mean of the given frequency table is 6.

There are various mean types in mathematics, particularly in statistics.

Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

For instance, the mean for the collection of values 8, 9, 5, 6, and 7 is 7, since 8 + 9 + 5 + 6 + 7 = 35, and 35/5 = 7.

So, to find the mean:

First, arrange the terms in ascending order as follows:

1, 4, 8, 13

Now, add the middle two numbers and divide by 2 to get the mean:

= 4 + 8/2

= 12/2

= 6

Therefore, the required mean of the given frequency table is 6.

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The total amount for an  of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $5386.42.

Interest is the amount a lender or financial institution receives for lending money. Interest can also refer to a shareholder's ownership interest in a company and is usually expressed as a percentage.

Interest rate indicates the cost of borrowing or the reward for saving. Therefore, if you are a borrower, interest rate is the amount charged to borrow money, expressed as a percentage of the total loan amount.  

Solution according to the information given in the question :

Given, Principal(P) = $5,000

           Compounding per year(n) = 4

          Time(in years)(T) = 5

          Interest rate = 6%

Amount = P× (1 + r/n)^t

             = 5000 × (1 + 6/4×100)⁵

            = 5000 × (1.015)⁵

            = 5000 ×1.07

            = $5286.42

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The population of the culture at the end of 24 hours will be 1600.

To find this answer, we can use the formula for exponential growth:

P = P₀ * 2^(t/h)

Where P is the final population, P₀ is the initial population, t is the total time in hours, and h is the time it takes for the population to double.

Plugging in the given values, we get:

P = 25 * 2^(24/4)

Simplifying the exponent:

P = 25 * 2^6

Solving for P:

P = 25 * 64

P = 1600

So the population of the culture at the end of 24 hours will be 1600.

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Jack is 13 years old now.

To solve this problem, we can use algebra to set up an equation and solve for Jack's age. Let's let J represent Jack's age now, and A represent Anna's age now.

According to the problem, Jack is ten years older than Anna, so we can write:
J = A + 10

Seven years from now, Jack will be twice as old as Anna, so we can write:
J + 7 = 2(A + 7)

Now we can substitute the first equation into the second equation to solve for A:
A + 10 + 7 = 2(A + 7)
A + 17 = 2A + 14
A = 3

Now that we know Anna's age, we can plug it back into the first equation to find Jack's age:
J = 3 + 10
J = 13

So Jack is 13 years old now.

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Answer:

The probability that Leslie randomly selects a salamander is

1

4

4

1

Step-by-step explanation:

In general, when we are interested in finding the probability of a event, we just need to divide the number of possibilities the event we are interested in can happens by the number of all possible results.

In this case, we have

20

20 differents animals to be chosen and we are interested in when one of the five salamanders is chosen. That is, P(salamander) =

5

20

=

1

4

20

5

=

4

1

Answer:

30 Stamps

Step-by-step explanation:

Since 40% of Jon's collection has boat stamps, that means that 20% of his total collection would be 6 stamps (40%/2  and  12/2).

All that's left to do now is get that % to 100, and we can do this by multiplying that and the number of stamps by 5.  (20%*5=100,  6*5=30)

This means that Jon has a total of 30 stamps in his collection.

Another way you could do this is simply to multiply 12 by 40%, or 0.4.
This will also give you an answer of 30 stamps.

Answer: 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

9

Answer: 1lb 7oz

Step-by-step explanation:

All you have to do is subtract 9lbs and 2oz by 7lbs and 11oz, which is 1lb and 7oz

(16 oz in a pound)

So, with one acute angle measuring 23.58 degrees and another acute Pythagorean theorem angle measuring 66.42 degrees, we may define this triangle as a right triangle.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.  

A triangle with the vertices A, B, and C with sides measuring 5, 12, and 13 units is seen in the illustration.

Let's use our triangle to illustrate this theorem:

[tex]a = 5, b = 12, c = 13\\a^2 + b^2 = 25 + 144 = 169\sc \\a^2 = 13^2 = 169\\[/tex]

Our triangle complies with the Pythagorean theorem because a2 + b2 = c2. Triangle ABC is a right triangle as a result, and the side with the length 13 is opposite the right angle.

[tex]A = arcsin(5/13)[/tex] = 23.58 degrees when sin(A)

= opposite/hypotenuse

= 5/13 A.

[tex]arccos(12/13) = 66.42 degrees B = cos(A) = adjacent/hypotenuse = 12/13[/tex]

A, B, and C are all at 90 degrees.

So, with one acute angle measuring 23.58 degrees and another acute angle measuring 66.42 degrees, we may define this triangle as a right triangle.

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Answer:

2. f(t) = 25^(t+1)

Step-by-step explanation:

25 = 25^1

=> 25^(0+1)

15,625 = 25^3

=> 25^(2+1)

9,765,625 = 25^5

=> 25^(4+1)

So f(t) = 25^(t+1)

A graph that can be used to find the real solution(s) to 3 - 4x = -3 - x² - 4x is shown in the image attached below.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.

Next, we would use an online graphing calculator to plot the given quadratic function 3 - 4x = -3 - x² - 4x as shown in the graph attached below.

By splitting the quadratic function, we have:

y = -3 - x² - 4x

y = 3 - 4x

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Answer:

The graph is a parabola that opens downward. Generally, a parabola has the following equation: y=ax2+bx+c If a is positive it opens upward

Answer:

Scarlett paid $48.51

Step-by-step explanation:

The initial price of the shoes was $49. After using a 10% discount coupon, the price is reduced by $4.90 ($49 x 0.1). Therefore, the price after the discount is $44.10 ($49 - $4.90).

Then, a 10% processing fee is applied to this discounted price. This fee amounts to $4.41 ($44.10 x 0.1).

So the final amount Scarlett paid is the sum of the discounted price and the processing fee:

$44.10 + $4.41 = $48.51

Therefore, Scarlett paid $48.51 for the shoes in the end.

Answer:1 and 2/3 lb per person

Step-by-step explanation:

5 pund divided by 3 ppl = 5/3

The value of x from the given exponential function is -8.159.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given equation is [tex]9^{3x}=4^{5x+2}[/tex].

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Here, [tex]ln(9^{3x})=ln(4^{5x+2})[/tex]

x=2ln(4)/3ln(9)-5ln(4)

x= -8.159

Therefore, the value of x is -8.159.

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Rounded to the nearest hundredth, the relative frequency of a student being a twelfth grader that gets their news from the internet is 0.25.

The proportion of times a particular value or event occurs within a set of data is termed as Relative frequency.

It is calculated by dividing the frequency of the event by the total number of observations. It is often expressed as a percentage or decimal value between 0 and 1.

The relative frequency of a student being a twelfth grader that gets their news from the internet can be calculated by dividing the number of twelfth graders who get their news from the internet by the total number of students surveyed:

Relative frequency = (number of twelfth graders who get news from the internet) / (total number of students surveyed)

Relative frequency = 43 / 175

Relative frequency = 0.2457 (rounded to four decimal places)

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9 can be expressed as 3² where value larger than the base.

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

Given:

A power with a positive base and a positive integer exponent will always have a value larger than the base.

We can take example as

5³ = 125

Here the base is 5 and value is 125 which is larger than base.

So, to express 9 as such form is

3² = 9

Here Base (3) < Value (9)

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The value of (g times f)(x) is 6x² + x - 2. So correct is C.

The input values of a function are called the domain, and the output values are called the range. The domain can be any set of values, but each input value must have a unique corresponding output value. If there are multiple input values that produce the same output value, the function is not considered to be well-defined. Functions are used to model a wide range of phenomena in many different fields, including science, engineering, and economics. They are also used in calculus to study rates of change and slopes of curves.

Overall, functions are a fundamental concept in mathematics, and have many practical applications in the real world.

To find g(x) times f(x), we need to multiply the two functions together.

(g times f)(x) = g(x) * f(x)

First, we need to find g(f(x)):

g(f(x)) = g(3x+2) = 2(3x+2) - 1 = 6x + 3

Now we can substitute this into the expression for (g times f)(x):

(g times f)(x) = g(x) * f(x) = (2x-1) * (3x+2)

Using the distributive property, we get:

(g times f)(x) = 6x² + 4x - 3x - 2 = 6x² + x - 2

Therefore, (g times f)(x) = 6x² + x - 2.

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The first derivative of a function equals zero on an interval, the function has a relative extremum on that interval.

Answer: The interval on which the function g(x) increases and decreases.The g function's vertex is at (-5, 2), and we need to figure out where the function increases and decreases. When a function has a vertex, it always opens up or down. As a result, the vertex serves as the function's minimum or maximum point.Given the above, we can assume that g(x) decreases to the left of x = -5 and increases to the right of x = -5. If we want to be more precise about the intervals, we can use the first derivative test. The first derivative of g(x) is as follows:g'(x) = 3x + 15The first derivative test states that if the first derivative of a function is greater than zero on an interval, the function is increasing on that interval. If the first derivative of a function is less than zero on an interval, the function is decreasing on that interval. Finally, if the first derivative of a function equals zero on an interval, the function has a relative extremum on that interval. We now need to find where g'(x) > 0 and where g'(x) < 0.3x + 15 > 0 => x > -5g(x) is increasing on the interval (-5, ∞)3x + 15 < 0 => x < -5g(x) is decreasing on the interval (-∞, -5)

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Using the area formula, it is obtained that Tanner has enough spray paint to cover the arrow with one can of spray paint.

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

To determine if Tanner has enough spray paint for his arrow, we need to find the total area of the arrow and compare it to the coverage of one can of spray paint.

The arrow consists of a rectangle and a triangle.

The rectangle has a length of 2 feet and a width of 5 1/3 feet, so its area is -

Area of rectangle = length × width

= 2 ft × 5 1/3 ft

= 10 2/3 sq. ft.

The triangle has a base of 3 feet and a height of the difference between the width of the rectangle (5 1/3 feet) and the width of the arrow (6 feet):

Height of triangle = 6 ft - 5 1/3 ft = 2/3 ft

Area of triangle = 1/2 x base x height = 1/2 x 3 ft x 2/3 ft = 1 sq. ft.

The total area of the arrow is the sum of the area of the rectangle and the area of the triangle -

Total area of arrow = Area of rectangle + Area of triangle

Total area of arrow = 10 2/3 sq. ft. + 1 sq. ft.

Total area of arrow = 32/3 sq. ft. + 1 sq. ft.

Total area of arrow = 11 2/3 sq. ft.

Therefore, since one can of spray paint covers up to 12 square feet, Tanner has enough spray paint to cover the arrow with one can of spray paint.

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The value of x for the given equation is 16.

To find the value of x in the equation x + 10 = 26, we need to isolate x on one side of the equation by performing the same operation to both sides of the equation.

We can start by subtracting 10 from both sides of the equation:

x + 10 - 10 = 26 - 10

Simplifying the left-hand side gives:

x = 16

Therefore, the value of x is 16, as this is the solution that satisfies the equation x + 10 = 26.

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The complete question is below:

Find the value of x: for x +10 = 26

you assume the opposite of what you want to prove, and then show that this assumption leads to a contradiction or an absurdity. In this case, we want to prove that "if -3x + 4 < 7, then x > -1" indirectly.

Assume the opposite of what we want to prove, which is "if -3x + 4 < 7, then x ≤ -1".

Adding 3x to both sides of the inequality, we get:

4 < 3x + 7

Subtracting 7 from both sides, we get:

-3 < 3x

Dividing both sides by 3, we get:

-1 < x

This contradicts our assumption that x ≤ -1. Therefore, our assumption is false, and the original statement "if -3x + 4 < 7, then x > -1" is true. This completes the indirect proof.

The measure of line KR is 8 inches

It is important that we know the properties of an isosceles trapezoid.

From the information given, we have that;

KR = 1/2x + 5

DH = 2x - 4

Since the non- parallel sides of an isosceles trapezoid are equal, then, we have;

KR = DH

1/2x + 5 = 2x - 4

collect the like terns, we have

1/2x - 2x = -4 - 5

x - 4x  /2 = - 9

cross multiply

-3x = -18

x = 6

KR =  1/2(6) + 5 = 8 inches

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Two possible lengths of the bases of a trapezoid with a height of 1 foot and an area of 9 square feet are 6 feet and 12 feet, or 4 feet and 14 feet.

Let's denote the lengths of the two bases of the trapezoid as b1 and b2 (where b1 is the longer base), and the height as h = 1 foot. The formula for the area of a trapezoid is,

A = (b1 + b2) / 2 × h

Given that the area is 9 square feet, we can plug in the values and solve for one of the bases,

9 = (b1 + b2) / 2 × 1

9 = (b1 + b2) / 2

18 = b1 + b2

b2 = 18 - b1

We can substitute b2 in terms of b1 in the formula for the area to get:

9 = (b1 + (18 - b1)) / 2 × 1

9 = 18 / 2

9 = 9

This equation is true for any value of b1, which means that there are infinitely many possible trapezoids with a height of 1 foot and an area of 9 square feet. However, we can find two specific values of b1 that correspond to different trapezoids:

If we let b1 = 6 feet, then b2 = 18 - b1 = 12 feet. This trapezoid has bases of length 6 feet and 12 feet, and a height of 1 foot.

If we let b1 = 4 feet, then b2 = 18 - b1 = 14 feet. This trapezoid has bases of length 4 feet and 14 feet, and a height of 1 foot.

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Answer:

40%

Step-by-step explanation:

percent = part/total × 100%

percent = 88/220 × 100%

percent = 40%

Answer:

40%

Step-by-step explanation:

Our total amount of shoes to sell is 220, right? So we have to find which percentage 88 is of 220! To do this, we use division!

Instead of how you might think to do it, 220/88, we have to do the opposite!
88/220 = 0.4

0.4 is 40% of 1. Therefore 88 is 40% of 220.