Solve the differential equation
dR/dx = a(R^2+16)
Assume a is a non-zero constant, and use C for any constant of integration that you may have in your answer.
R=________

Answer:ts line is pulled taut and casts a 15 ft - shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.

Step-by-step explanation:

$75668.4 is the interest earned in 6 months.

percentage, a relative value indicating hundredth parts of any quantity.

Tom has $84,076 in a savings account that earns 15% annually.

The interest is not compounded.

We have to find the interest he earned in 6 months.

Use the formula i = prt,

where i is the interest earned,

p is the principal (starting amount),

r is the interest rate expressed as a decimal,

and t is the time in years.

i=84076×15/100×6

=84076×0.15×6

=$75668

Hence, $75668.4 is the interest earned in 6 months.

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The required time it will take to fill the tank with gallons of water is 18 minutes.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

Here,
From the figure, the equation of the trend line is given as,
y = 20.83x

Where y =  gallons of water and x is time in minutes

Now, put y = 375
375 = 20.83x
x = 18 min

Thus, the required time it will take to fill the tank with gallons of water is 18 minutes.

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Complete question,

Make Sense and Persevere The graph shows the number of gallons of water in a large tank as it is being filled. Based on the trend line, predict how long it will take to fill the tank with 375 gallons of water.

This sequence converges to e. The sequence (1 + 2/n)^n is a geometric sequence in which each successive term is found by multiplying the previous term by a constant.

This sequence is an example of a geometric sequence where each successive term is found by multiplying the previous term by a constant. In this case, the constant is equal to (1 + 2/n).

By using the limit definition of a geometric sequence, we can see that the limit of this sequence is given by lim n→∞ (1 + 2/n)^n = e. Therefore, the sequence converges to e.

The sequence (1 + 2/n)^n converges to e.

The sequence (1 + 2/n)^n is a geometric sequence in which each successive term is found by multiplying the previous term by a constant. By using the limit definition of a geometric sequence, it can be determined that the limit of this sequence is given by lim n→∞ (1 + 2/n)^n = e. As a result, the sequence converges to e.

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Answer:

answer is d

Step-by-step explanation:

The probability that a randomly chosen appointment is with a patient under 18 years old or is for regular cleaning is 0.95.

The probability of a random appointment being with a patient under 18 or for regular cleaning is calculated as P(Under 18 or Regular Cleaning) = P(Under 18) + P(Regular Cleaning) - P(Under 18 and Regular Cleaning).

P(Under 18) = 0.9

P(Regular Cleaning) = 0.15

P(Under 18 and Regular Cleaning) = 0.14

So, P(Under 18 or Regular Cleaning):

= 0.9 + 0.15 - 0.14

Apply the arithmetic operation, and we get

= 0.91.

Thus, the required probability is 0.91.

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Answer:

is $27.50 per each teacket

The area of a trapezoid is given by the formula A = 1/2(b1 + b2)h. In this case, b1 = 4, b2 = 3, and h = 8.

The area of a trapezoid can be determined using the formula A = 1/2h(b1 + b2), where A is the area, h is the height, and b1 and b2 are the lengths of the top and bottom bases of the trapezoid, respectively. To determine the area of a child's toy harp in square inches, we need to know the length of the top and bottom bases and the height of the trapezoid.

Therefore, the area of the harp is 1/2(4 + 3)8 = 20 square inches. To find the area of the harp, we first need to know the measurements of the base lengths, b1 and b2, as well as the height, h. Once we have these measurements, we can plug them into the formula for the area of a trapezoid and solve for A. In this case, the area of the harp is 20 square inches.

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Answer:

20 square inches

Correct Answer 100%. Pls, give me brainliest. Thank You.

The number that goes in the box is 4, since 4 + (-2) = 2, which is the coefficient of x^2 in the equation. The third step is to add the same number to both sides of the equation, so the box needs to contain 4.

To complete the third step in solving a quadratic equation using the completing the square method, the number that goes in the box is 4. This is because the goal is to make the coefficient of x^2 on the left side of the equation equal to the coefficient of x^2 on the right side. The equation is x^2 - 8x + 2 = 0, so the coefficient of x^2 on the left side is 1, and the coefficient of x^2 on the right side is 2. Therefore, the number that needs to be added to the left side is 1, and the number that needs to be added to the right side is also 1. This means that 4 needs to be added to both sides of the equation, so 4 is the number that goes in the box.

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The Riemann sum formula is ∫(1,5) 2x = 24

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x over the interval [1, 5]

The Riemann sum for f(x) = 2x over the interval [1,5] using the right-hand endpoint for each subinterval is given by the formula:

(Δx/2) * (2c1 + 2c2 + ... + 2cn) where c1, c2, ..., cn are the right-hand endpoints of the subintervals and Δx = (b - a)/n.

As a general rule:

As n approaches infinity, the width of the subintervals approaches zero,

Also, we have the Riemann sum approaches the definite integral of f(x) = 2x over the interval [1,5], which is x² evaluated at the interval's endpoints.

So, the formula becomes

∫(1,5) 2x = x²

Substitute the intervals

∫(1,5) 2x = 5² - 1²

Evaluate

∫(1,5) 2x = 24

Hence, the formula is ∫(1,5) 2x = 24

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Step-by-step explanation:

                            The equation of the ellipse  

                                       [tex]\displaystyle\\\boxed {\frac{x^2}{a^2} +\frac{y^2}{b^2} =1}[/tex]

                                         [tex]F^2=a^2-b^2[/tex]

Given: F₁(-4,0)    F₂(4,0)    b₁(0,-3)     b₂=(0,3)

[tex]\displaystyle\\a^2=F^2+b^2\\\\a^2=4^2+3^2\\\\a^2=16+9\\\\a^2=25\\\\a_{1,2}=б5\\\\So,\ a_1(-5,0)\ \ \ \ a_2(5,0)\\\\Thus,\ \frac{x^}{(б5)^2} +\frac{y^2}{(б3)^2} =1\\\\\frac{x^2}{25}+\frac{y^2}{9} =1\ \ \ \ -\ the\ equation \ of\ the\ ellipse[/tex]

Answer:

  g(x) = e^(x+2) -3

Step-by-step explanation:

You want the transformed function g(x) of the parent function f(x) = e^x given that g(x) has a horizontal asymptote of -3 and goes through the point (-2, -2).

The parent function goes through the point (0, 1), which has apparently been translated to (-2, -2) by the transformation. That translation looks like ...

  g(x) = f(x -h) +k . . . . . . . . f(x) translated h units right and k units up

Our function has been translated from 0 to -2 in the horizontal direction, or left 2 units: h = -2.

It has been translated from 1 to -2 in the vertical direction, or down 3 units: k = -3.

Then the translated function is ...

  g(x) = f(x +2) -3

  g(x) = e^(x+2) -3

can you include the full picture?

The value of c according to the given equation as described is; -14.

The other root of the equation in discuss is; 7.

As evident in the task content; if -2 is the root of a quadratic equation x²-5x+c=0, then x = -2 holds true for the equation; therefore, we have;

a). (-2)² - 5 (-2) + c = 0

4 + 10 + c = 0

c = -14

Hence, the value of c is; -14.

b). By substituting into the equation; we have;

x² - 5x - 14 = 0

(x - 7) (x + 2) = 0

x = 7 OR x = -2.

Therefore, the other root of the equation is; 7.

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The sample variance of the given data 13,11,15,2,9,14 is 356.6.

Sample variance can be defined as the expectation of the squared difference of data points from the mean of the data set. It is an absolute measure of dispersion and is used to check the deviation of data points with respect to the data's average.

we have data 13, 11, 5, 2, 9, 14, and we have to determine the sample variance of given data.

Sample variance is given by,

[tex]S^2=\frac{\sum^n_1(X_i-X')^2}{(n-1)}[/tex]

where X' is the sample mean,

the mean of given data is,

[tex]X'=\frac{(13+11+5+2+9+14)}{6} \\\\X'=\frac{54}{6} \\\\X'=9[/tex]

now the sample variance is given by,

[tex]S^2=\frac{(13+9)^2+(11+9)^2+(5+9)^2+(9+9)^2+(14+9)^2}{6-1} \\\\S^2=\frac{(484+400+289+81+529)}{5} \\\\S^2=356.6[/tex]

Hence the sample variance is 356.6.

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After examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.

What is Number line ?

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

What is Symbol?

A mark, sign, or term that denotes, denotes, or is taken to denote an idea, an item, or a relationship is known as a symbol. By connecting seemingly unrelated ideas and events, symbols help people look beyond the known and the visible.

In the question given some relation between the real number which are

a) -2/4 < -1/4 because negative number has the property that the those numbers which is smaller is always greater.

b) 3/4 > 2/4 both numbers are positive so clearly it 3/4 comes after 2/4 so it is greater.

c)  -1/4 < 0 zero is always greater than the negative numbers

So, after examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.

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Answer:

The slope is [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

The slope formula would be: [tex]\frac{y2-y1}{x2-x1}[/tex]

So for (-2,9) and (-4,6), we can plug in the variables: (x1, y1) and (x2, y2)

Let's use the numbers in the equation provided above:

[tex]\frac{6-9}{-4-(-2)}[/tex]

= [tex]\frac{-3}{-2}[/tex]

= [tex]\frac{3}{2}[/tex]

Answer:

3/2

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1} = \frac{6-9}{-4-(-2)} = \frac{-3}{-2} =\frac{3}{2}[/tex]

Answer:

Rs. 94

Step-by-step explanation:

We will denote the almirahs as A1 and A2 for ease of explanation. I am omitting currency until the final answer

For the following computations note that x% = x/100 in decimal so
15% = 15/100 = 0.15
13 1/3% = 13 1/3 ÷ 100 = 40/3 ÷ 100 = 40/300

Cost of A1 = 4800

A1 was sold for a loss of 15%

Loss = 15% of 3640 = 0.15 x 3640  = Rs 546

A2 bought at 4800 was sold at a gain of 13 1/3%

Gain from sale = 13 1/3% of 4800 = 40/300 x 4800 =Rs 640

We have to treat gain as positive and loss as negative to arrive at the answer

Net gain/loss = 640  - 546 = Rs. 94

On solving the provided question, we can say that  x = 6 a solution to the equation x + 13 = 18, no, because 6 + 13 = 18 is not true, as 6 + 13 = 19

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

x = 6 a solution to the equation x + 13 = 18

No, because 6 + 13 = 18 is not true, as 6 + 13 = 19

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The confidence interval from Part (b) is narrower than the confidence interval from Part (a) because the proportion of Americans age 8 to 18 who own an MP3 music player is higher than the proportion of Americans age 8 to 18 who own a cell phone.

a. 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone:

(1321/2002) ± (1.645*sqrt( (1321/2002)*(1-(1321/2002)) / 2002)) = (0.6608 ± 0.0402)

Interpretation: We are 90% confident that the true proportion of all Americans age 8 to 18 who own a cell phone is between 0.6206 and 0.7010.

b. 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own an MP3 music player:

(1522/2002) ± (1.645*sqrt( (1522/2002)*(1-(1522/2002)) / 2002)) = (0.7610 ± 0.0346)

Interpretation: We are 90% confident that the true proportion of all Americans age 8 to 18 who own an MP3 music player is between 0.7264 and 0.7956.

c. The confidence interval from Part (b) is narrower than the confidence interval from Part (a) because the proportion of Americans age 8 to 18 who own an MP3 music player is higher than the proportion of Americans age 8 to 18 who own a cell phone. This means that the sample size is more likely to result in a more accurate estimation of the true population proportion for the MP3 music player than for the cell phone.

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Since the input value of domain -4 has two different output values (7 and 6), the relation is not a function.

By definition, a relation is a function if each input value has only one output value.

Given the relation:

(-4,6)

(-4,7)

(6,5)

(7,9)

The domain is the set of the x-coordinates of each ordered pair (You do not need to write 4 twice):

domain ={-4 ,6,5}

The range is the set of the y-coordinates of each ordered pair :

range=  {6,7,5,9}

Since the input value 4 has two different output values (7 and 6), the relation is not a function.

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A triangle's third side must always be between (but not exactly equal to) the other two sides' total and difference in length. Take the numbers 2, 6, and 7 as an example. In light of this, the third side length must be more than 4 and lower than 8.

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Answer:

The independent variable, x, represents the number of years working at the company. The dependent variable, C(x), represents the salary. The salary depends on the number of years working at the company because the salary increases by $2,000 for each year of work. A function relating these variables is C(x) = 35,000 + 2,000x, where x is the number of years working at the company and C(x) is the salary. So C(4) = 35,000 + 2,000(4) = $43,000 meaning that if Emily works for 4 years, her salary will be $43,000.

4x⁴ +12x³ +15x² +9x −6 is the expression which can represent function f(g(x)). Thus, option D is correct.

A rule that transforms one number into another is called a function. However, not every rule outlines an appropriate function. In addition to introducing some of the mathematical terms related to functions, this unit explains how to determine if a given rule describes a valid function.

Given

f(x) = x² + 3x - 6

g(x) = 2x² +3x

To find expression for f(g(x))

Put the value of g(x) place of x, f(x)

f(x) = x² + 3x - 6

(2x² +3x)² + 3(2x² +3x) - 6

4x⁴ +12x³ +15x² +9x −6

Thus, 4x⁴ +12x³ +15x² +9x −6 is the expression which can represent f(g(x)).

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Option(c) is the correct answer i.e. the scale factor of the given triangle is 4/9.

What is Scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.

Let's take the measurement of one side of the original triangle and dashed triangle.

The side of Original triangle is 18 units and,

The side of dashed(new) triangle is 8 units

We know that,

Scale factor = dimension of new figure ÷ dimension of original figure

                    = 8 units / 18 units

                   = 4/9.

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The probability of picking a 2 and then picking a 1 would be = 1/2

Probability is definitely as the expression that to represents the number of outcomes of an event.

The number of cards such as 1,2,3,4 = 4 cards.

The cards picked at random = a 1 and a 2

Therefore, the probability = 2/4 = 1/2

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You need to find the four constants, a, b, c, and d. At x = -1000, you have a value for f(x).

A)Outline it:

f(-1000) = -1000 = a (-1000)^3 b(-1000)^2 + c (-1000) + d

At x = 1000, you have a value for f(x).

B)Outline it:

f(+1000) = a (1000)^3 + b (1000)^2 + c (1000) + d

You know the slope's value, f'(x), and when x = -1000, f'(-1000) equals 3 a (-1000)2 + 2 b (-1000) + c.

At x = + 1000 f'(1000), you have a value for the slope: 3 a (1000)2 + 2 b (1000) + c

C) That is four linear equations with a, b, c, and d as the four unknowns.

When you simultaneously solve all four equations, you will get the function and its derivative, which you may graph.

D) The steepest part is where the derivative's absolute value is at its highest.

You can find that extreme by setting the derivative of the derivative equal to zero.

6 a x + 2 b = 0

solve for x and calculate the slope at that point.

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The mean of their ratings is 7.

Mean (also called the average) is used to describe the central tendency of a set of numerical data. It is calculated by summing up all the values in the data set and dividing by the number of values.

Since We have the ratings:

Destiny 9, Taylor 6, Jeremiah 5

Mean = (9 + 6 + 5)/3 = 20/3 = 7

Note: we divide by 3 because there are 3 people

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The area the polygon in the diagram with, a length from the center to the vertex 6√2 in is 144.0 in².

Any closed curve that consists entirely of connected line segments (sides) without any intersections is known as a polygon in geometry. The three simplest polygons are pentagons, triangles with three sides, and quadrilaterals with four sides (five sides). The two types are concave and convex polygons.

Convex polygons are those without any extended sides crossing over them. Equilateral refers to a polygon with equal sides. Interior angles of equiangular shapes are equal. Every equilateral and equiangular polygon is a regular polygon (e.g., an equilateral triangle or a square).

As all sides are equal, all diagonals are equal too, and the angle of adjacent diagonals are 90° with vertical opposite angle.

Therefore,

Each side = [tex]\sqrt{\text {diagonal}^2+ \text {diagonal}^2}[/tex]

Each side = [tex]\sqrt{(6\sqrt{2} )^2+(6\sqrt{2} )^2}[/tex]

Each side = [tex]\sqrt{(36\times 2+36\times 2}[/tex]

Each side = [tex]\sqrt{144}[/tex]

Each side = 12 inch

Area =  12 × 12

         = 144.0 in²

Thus, the area the polygon in the diagram with, a length from the center to the vertex 6√2 in is 144.0 in².

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Answer:

  $3213

Step-by-step explanation:

You want to know the total spent on rent and food if rent is 7/20 of your budget and food is 1/2 of your budget of $3780 per month.

The amount spent on each item is the product of the fraction of the budget it is and the total amount being budgeted (your income).

  rent = 7/20 × 3780 = 1323

  food = 1/2 × 3780 = 1890

The total spent on these items is the sum of these amounts:

  rent + food = 1323 +1890 = 3213

A total of $3213 is budgeted for rent and food.

__

Additional comment

Your calculator can figure this handily.

You can factor out the income amount and add the fractions first:

  (7/20·3780) +(1/2·3780) = 3780(7/20 +1/2) = 3780(7/20 +10/20)

  = 3780(17/20) = 3213

[tex]Answer:\ \boxed{96\pi }\ cm^2[/tex]

Step-by-step explanation:

[tex]R=6\ cm \ \ \ \ V_c=72\pi \ cm^3\ \ \ \ S_c=?[/tex]

[tex]V_c=\pi R^2H\\[/tex]

[tex]72\pi =\pi 6^2H\\\\72=36H\\[/tex]

Divide both parts of the equation by 36:

[tex]2=H\\\\Thus,\ H=2\ cm[/tex]

[tex]S_c=2(\pi R^2)+2\pi R(H)\\\\S_c=2\pi (6^2)+2\pi 6(2)\\\\S_c=2\pi(36)+12\pi (2) \\\\S_c=72\pi +24\pi \\\\S_c=96\pi\ cm^2[/tex]