$1,000 is deposited into a savings account. Interest is compounded annually. After 1 year, the value of the account is $1,020. After 2 years, the value of the account is $1,040. 40. This scenario can be represented by an exponential function of the form fx=1000bx, where fxis the amount in the savings account, and x is time in years. What is the value of b?

The values of a, b, and c in the matrix equation are a = 3, b = 1 and c = 8

To determine the values of a, b, and c in the matrix equation:

4 a  +  3  0    = 7  3

3 4      5  b       c   5

By addition operation, we have

a + 0 = 3

3 + 5 = c

4 + b = 5

When the equations evaluated, we have

a = 3

c = 8

b = 1

The above are the values of a b and c

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Complete question

Determine the values of a, b, and c in the following matrix equation.

4 a  +  3  0    = 7  3

3 4      5  b       c   5

Answer:

310.2 cubic units

Step-by-step explanation:

since we know the diameter of the sphere (8.4), the radius is [tex]8.4/2 = 4.2[/tex]

The volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]

Plugging in 3.14 as [tex]\pi[/tex] and 4.2 as r, we get 310.2

The basic arithmetic operators (+,-,*,/) are commonly used in formulas to perform mathematical calculations. They are collectively known as "operators" and are an essential component of mathematical formulas, allowing us to perform complex calculations quickly and efficiently.

The symbols mentioned in the question, i.e., (+,-,*,/) are the basic arithmetic operators that are used in mathematical formulas to perform different types of calculations. These symbols are collectively referred to as "operators" or "mathematical operators."

Operators are an essential part of mathematical formulas as they allow us to perform complex mathematical calculations in a concise and efficient manner. They act as a shorthand way of representing mathematical operations and make it easier to perform calculations without having to write out the entire equation every time.

In addition to the basic arithmetic operators mentioned above, there are other types of operators that can be used in formulas depending on the specific mathematical operation being performed. For example, there are logical operators like AND, OR, and NOT that are used in Boolean algebra to perform logical calculations.

Other operators that can be used in formulas include exponentiation (^), which is used to raise a number to a certain power, and modulo (%), which is used to find the remainder when one number is divided by another.

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Answer: 1 1/4 yards

Step-by-step explanation: To convert from feet to yards, divide the value in feet by 3. So, 3 3/4 ft = (3 3/4)/3 = 1.25 yd (exactly).

Answer:

5/4 yards

Step-by-step explanation:

Convert feet to fraction.

[tex]3+\frac{3}{4} =\frac{(3)(4)+3}{4} =\frac{15}{4}[/tex] ft.

If we know that each yard equals 3 feet, divide by 3:

[tex]\frac{\frac{15}{4} }{3} =\frac{15}{(4)(3)} =\frac{15}{12}[/tex]

Simplified:

[tex]\frac{5}{4}[/tex]  yards

Hope this helps.

The derivative formula for the function is f'(x) = 4ex(1/x + ln(x)).

To find the derivative of the function f(x) = (4 ln(x))ex, we can use the product rule and the chain rule of differentiation.

Let g(x) = 4 ln(x) and h(x) = ex. Then, we have:

f(x) = g(x)h(x)

Using the product rule, we get:

f'(x) = g'(x)h(x) + g(x)h'(x)

Now, we need to find g'(x) and h'(x):

g'(x) = 4/x (since the derivative of ln(x) with respect to x is 1/x)

h'(x) = ex

Substituting these back into the formula for f'(x), we get:

f'(x) = (4/x)ex + 4 ln(x)ex

Simplifying this expression, we get:

f'(x) = 4ex(1/x + ln(x))

Therefore, the derivative formula for the function f(x) = (4 ln(x))ex is:

f'(x) = 4ex(1/x + ln(x)).

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The area of the larger sheet is 180 times greater than the area of the smaller sheet.

To determine which sheet has a larger area, Let's assume that the length of the smaller sheet of paper is l and the width of the smaller sheet is w. Then, we can express the dimensions of the larger sheet in terms of l and w as follows:

Length of larger sheet = 12l

Width of larger sheet = 15w

The area of the smaller sheet can be calculated as:

Area of smaller sheet = length × width = lw

Similarly, the area of the larger sheet can be calculated as:

Area of larger sheet = length × width = (12l) × (15w) = 180lw

To find the factor by which the area of the larger sheet is greater than the area of the smaller sheet, we can divide the area of the larger sheet by the area of the smaller sheet:

Factor = Area of larger sheet / Area of smaller sheet

Factor = (180lw) / (lw)

Simplifying the expression, we get:

Factor = 180

Therefore, the area of the larger sheet is 180 times greater than the area of the smaller sheet.

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The expression (x + 1)(x - 3) represents the Area of base of the prism.

a crystal is a polyhedron containing a n-sided polygon base, a respectable halfway point which is a deciphered duplicate of the first, and n different countenances, fundamentally all parallelograms, joining relating sides of the two bases. Translations of the bases exist in every cross-section that runs parallel to the bases.

The volume of a rectangular prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a square with edge length (x + 1), so its area is (x + 1)^2. The volume of the prism is given as (x + 1)^2(x - 3).

We can find the height of the prism by dividing the volume by the area of the base:

B = V/h = (x + 1)^2(x - 3)/(x + 1) = (x + 1)(x - 3)

Therefore, the expression (x + 1)(x - 3) represents the Area of base of the prism.

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After 666 days, the video will receive approximately 33,621,452 views.

We are given the function V(d) = 4^(1.25d), where d represents the number of days since the video was uploaded and V(d) represents the number of views the video has received at that time. To find the number of views the video will receive after 666 days, we need to evaluate V(666).

Plugging in d = 666 into the function, we get V(666) = 4^(1.25*666). Using a calculator, we can simplify this to V(666) ≈ 33,621,452. Therefore, after 666 days, the video will receive approximately 33,621,452 views.

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The function y = 12x – x^3 is increasing for x < -2, -2 < x < 2, and x > 2, and is decreasing for -2 < x < 2.

The given function is y = 12x – x^3. To determine when the function is increasing or decreasing, we need to take the derivative of the function with respect to x:

y' = 12 - 3x^2

To find where the function is increasing, we need to look for values of x where y' is positive. To find where the function is decreasing, we need to look for values of x where y' is negative.

So, y' > 0 when:

12 - 3x^2 > 0
3x^2 < 12
x^2 < 4
-2 < x < 2

Therefore, the function is increasing for x values less than -2, between -2 and 2, and greater than 2. Specifically:

• Increasing for x < -2
• Increasing for -2 < x < 2
• Increasing for x > 2

On the other hand, y' < 0 when:

12 - 3x^2 < 0
3x^2 > 12
x^2 > 4
x < -2 or x > 2

Therefore, the function is decreasing for x values between -2 and 2. Specifically:

• Decreasing for -2 < x < 2

Overall, we can summarize that the function y = 12x – x^3 is increasing for x < -2, -2 < x < 2, and x > 2, and is decreasing for -2 < x < 2.

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This value will represent the range within which the middle 50% of Emilia's daily miles are distributed

Hi! The box plot represents the miles Emilia ran after school for 21 days. To find the IQR (Interquartile Range), you can use the box plot by identifying the values of the first quartile (Q1) and the third quartile (Q3).

The IQR is calculated by subtracting Q1 from Q3 (IQR = Q3 - Q1). By examining the box plot, locate Q1 and Q3 on the plot, and perform the subtraction to find the IQR.

This value will represent the range within which the middle 50% of Emilia's daily miles are distributed.

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The expected cost of Bob's lunch is $9.69, rounded to the nearest cent.

To figure out the probability of Bob and Anna successfully meeting up, we need to use a unitary method. The probability of Bob choosing a specific time is 1/4, and the probability of Anna choosing the same time is also 1/4. Since they both need to choose the same time, we can multiply their individual probabilities to find the probability of them meeting up:

1/4 x 1/4 = 1/16

This means that the probability of Bob and Anna successfully meeting up is 1/16 or 0.0625.

Now we can use this probability to find the expected cost of Bob's lunch. If Bob and Anna meet up, Bob will get a discount on his lunch and pay $5. If they don't meet up, he'll have to pay the full price of $10. So the expected cost of Bob's lunch is:

(Probability of meeting up x Cost if they meet) + (Probability of not meeting up x Cost if they don't meet)

(1/16 x $5) + (15/16 x $10) = $0.3125 + $9.375 = $9.69

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Lo siento, pero los problemas que ha proporcionado no están relacionados con el cálculo. El problema a) es simplemente una operación de multiplicación y suma, y el problema b) es una operación de multiplicación y suma agrupada. Para crear un problema que pueda resolverse con cálculo, podría plantear algo como:

a) ¿Cuál es la tasa de cambio de la función f(x) = x^2 en el punto x = 3?

b) ¿Cuál es el valor máximo de la función g(x) = 3x^2 - 12x + 5 en el intervalo [0, 4]?

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Answer:

x=10 and y=20, 2x=20=y

Step-by-step explanation:

2x=20 | Divide by 2 on both sides

x=10

4y=80 | Divide by 4 on both sides

y=20

Answer: 40

80 ÷ 2 = 20, so x = 40.

To check your answer;

40 x 2 = 80

We know that the skier would have to go skiing for 5 days in order for both options to cost the same.

To find out how many days a skier would have to go skiing for both options to cost the same, we need to set up an equation. Let's use "d" to represent the number of days the skier goes skiing.

For the daily pass option:
Total cost = $48 x d

For the season pass option:
Total cost = $190 + ($10 x d)

Now we can set up the equation:

$48 x d = $190 + ($10 x d)

Simplifying this equation, we get:

$38 x d = $190

Solving for "d", we get:

d = 5

Therefore, the skier would have to go skiing for 5 days in order for both options to cost the same.

So the answer is A. 5 days.

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The probability of getting a prime number on the spinner is 2/4 or 1/2.

There are four possible outcomes on the spinner: 6, 7, 8, and 9. To determine the probability of getting a prime number, we need to first identify which of these numbers are prime. Prime numbers are numbers greater than 1 that can only be divided by 1 and themselves without leaving a remainder.

Out of the four possible outcomes, only two of them are prime: 7 and 9. Therefore, the probability of getting a prime number is the number of favorable outcomes (2) divided by the total number of possible outcomes (4), which simplifies to 1/2.

To see why this is true, we can think of the probability as a fraction where the numerator is the number of ways to get a prime number and the denominator is the total number of possible outcomes. In this case, there are two ways to get a prime number (7 and 9), and four possible outcomes (6, 7, 8, and 9). Therefore, the probability r is 2/4 or 1/2.

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When a train takes 17 seconds to pass a 206-meter long bridge at normal speed. The length of train is equals to the 227.86 metres.

We have a train with a normal speed. With a normal speed, the length of long bridge covered by train in 17 seconds

= 206 meter

Let the length of train and normal speed of train be 'x meter' and 's m/sec ' respectively. As we know speed of an object ratio of covered distance to the time taken by object to covered the distance

=> s = (206 + x)/ 17 m/sec --(1)

In case second, the speed of same train which covered a length 170 m of bridge in 45 seconds = one-third of the normal speed

=> s/3 = (170 + x) /45 m/sec --(2)

We have to determine the length of train.

Using substitution, substitute value of s in equation(2) from equation (1) ,

=> (206+ x)/17 = (170 + x)/45

Cross multiplication

=> 45( 206 + x) = ( 170 + x) 17

=> 45 x - 17x = 45× 206 - 170 × 17

=> x = 227.86 m

Hence, required value is 227.86 m.

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The equation that represents the statement is

50 = x/3 and x is 150

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

Word problem are brain teaser that allows people to think properly. The first step is to represent the unknown by a letter.

Representing the number by x

therefore:

The product of 5 and 10 is 5 × 10

5 × 10 = 1/3 × x

50 = x/3

therefore the equation is 50 = x/3 and the value of x is 150.

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Answer:

26r^2 + 36r.

Step-by-step explanation:

The slope of the curve y = x^3 at point P(2, 8) is 12.

To find the slope of the curve y = x^3 at point P with coordinates (2, 8), we need to determine the derivative of the function and then evaluate it at x = 2.

Step 1: Find the derivative of the function y = x^3.
The derivative, dy/dx, represents the slope of the curve. To find the derivative of y = x^3, apply the power rule: d(x^n)/dx = n * x^(n-1).
So, dy/dx = 3 * x^(3-1) = 3x^2.

Step 2: Evaluate the derivative at the given point P (2, 8).
To find the slope at point P, substitute the x-coordinate (2) into the derivative: 3 * (2)^2 = 3 * 4 = 12.

Thus, the slope of the curve y = x^3 at point P(2, 8) is 12.

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The fourth equation i.e. cos (60°) = [tex]\frac{a}{12}[/tex] can be used to find one of the missing side lengths in the triangle. This has been obtained using trigonometry.

What is trigonometry?

Trigonometry is a branch of mathematics that focuses on right-angled triangles, including their sides, angles, and connections.

We are given a right angled triangle with perpendicular as b, base as a and hypotenuse measuring 12 units.

We know by trigonometry that cos θ is the proportion of the adjacent side to the hypotenuse.

So, only the fourth equation is the one which can be used to find the missing length.

So, the equation is cos(60°) = [tex]\frac{a}{12}[/tex].

Hence, the fourth option is the correct answer.

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Answer:

Not enough info

Step-by-step explanation:

Volume of cone formula is: V = 1/3 π r²h

You did not give the radius so it is not possible to find the solution

If radius is given, isolate h by dividing the V by 1/3 π r²

Then simplify the left side of the equation and that is what h is

Using the Empirical Rule.  The percentage of small business stock prices that are more than $81. 67 is 0.30%

To use the Empirical Rule, we need to assume that the distribution of small business stock prices is approximately normal.

First, we need to find the z-score for $81.67:

z = (81.67 - 54.82) / 8.95 = 2.99

Next, we can use the Empirical Rule to estimate the percentage of small business stock prices that are more than $81.67:

About 99.7% of the data falls within 3 standard deviations of the mean.

Therefore, about 0.3% of the data falls more than 3 standard deviations above the mean.

Since $81.67 is more than 3 standard deviations above the mean, we can estimate that the percentage of small business stock prices that are more than $81.67 is about 0.3%.

Rounded to the nearest hundredth, the estimated percentage is 0.30%.

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None of the given expressions (A, B, C, D, E) are equal to 45 x 67.

To find which expressions are equal to 45 x 67, we simply need to simplify each of the expressions given.

Therefore, none of the expressions are equal to 45 x 67.

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Step-by-step explanation:

number 2

number 3

number 6

number 7

To optimize the given function e - 222 - 4xy - 2y^2 subject to the constraint 0x^2 - 4xy + ly^2 = 10, we'll first set up the Lagrange function L(x, y, λ) as follows:

Langrange- L(x, y, λ) = e - 222 - 4xy - 2y^2 + λ(0x^2 - 4xy + ly^2 - 10)
Now, we'll get the partial derivatives of L with respect to x, y, and λ and set them equal to zero:
Step:1. ∂L/∂x = -4y - λ(-4y) = 0
Step:2. ∂L/∂y = -4x - 4y - 2λy = 0
Step:3. ∂L/∂λ = 0x^2 - 4xy + ly^2 - 10 = 0
These three equations represent the system of equations we need to solve to find the critical points. To reiterate, the equations are:
1. -4y + 4yλ = 0
2. -4x - 4y - 2λy = 0
3. -4xy + ly^2 - 10 = 0

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Answer:

x=7

Step-by-step explanation:

Because all the bases are the same you can ignore the 8's.

Instead solve for 15=x+8

in which you would subtract the 8 to the left side, and 15-8=7

Step-by-step explanation:

See image....check my math !  ( I didn't)

The equation of the line with given coordinates in slope intercept form is given by y = 6x.

Use the slope-intercept form of the equation of a line,

y = mx + b,

where m is the slope of the line

And b is the y-intercept.

The slope of the line is equals to,

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line.

Using the coordinates (-3, -18) and (3, 18), we get,

⇒m = (18 - (-18)) / (3 - (-3))

⇒m = 36 / 6

⇒m = 6

So the slope of the line is 6.

Now we can use the slope-intercept form of the equation of a line .

Substitute in the slope and one of the points, say (-3, -18) to get the y-intercept,

y = mx + b

⇒ -18 = 6(-3) + b

⇒ -18 = -18 + b

⇒ b = 0

So the y-intercept is 0.

Putting it all together, the equation of the line in slope-intercept form is,

y = 6x + 0

⇒ y = 6x

Therefore, the slope intercept form of the line is equal to y = 6x.

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The equation of the tangent plane to the surface with equation - in (9) +-3 at the point (2,1,9),  first need to find the partial derivatives of the function with respect to x, y, and z. However, the surface equation provided seems to be incorrect or incomplete. Please provide the correct surface equation in the form f(x, y, z) = constant.

Let's call the function f(x, y, z) = - in (9) +-3.
∂f/∂x = 0  (since there is no x term in the function)
∂f/∂y = 0  (since there is no y term in the function)
∂f/∂z = -3/((z-9)^2)
Now we can use the formula for the equation of the tangent plane at a point (a,b,c) on a surface z=f(x,y):
z - f(a,b) = (∂f/∂x)(a,b)(x-a) + (∂f/∂y)(a,b)(y-b)
+ (∂f/∂z)(a,b)(z-c)
Plugging in the values we have, we get:
z - (- in (9) +-3)|_(2,1) = 0(x-2) + 0(y-1) - (3/((z-9)^2))|_(2,1,9)(z-9)
Simplifying:
z + in (9) - 3 = -3(z-9)
4z = 30
z = 7.5
So the equation of the tangent plane is:
z - (- in (9) +-3)|_(2,1) = (-3/((z-9)^2))|_(2,1,9)(z-9)
z - in (9) - 3 = -3(7.5-9)
z - in (9) - 3 = 4.5
z = 12.5
Therefore, the equation of the tangent plane to the surface with equation - in (9) +-3 at the point (2,1,9) is:

z - in (9) - 3 = -3/((z-9)^2)(z-9)
z - in (9) - 3 = -3(z-9)/(z-9)^2
z - in (9) - 3 = -3/(z-9)
z = 3/(z-9) + in (9) + 3
or
3x + 3y - 4z = -27 + in (9)
To find the equation of the tangent plane to the surface with equation ln(9) +- 3 at the point (x, y, z) = (2, 1, 9), follow these steps:
1. Determine the gradient vector of the given surface at the point (2, 1, 9).
2. Use the gradient vector as the normal vector of the tangent plane.
3. Write the equation of the tangent plane using the normal vector and the given point.
However, the surface equation provided seems to be incorrect or incomplete. Please provide the correct surface equation in the form f(x, y, z) = constant, so that I can help you find the equation of the tangent plane.

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The function giving the distance between the point (0,-6) and the line y = 8x - 5 is: S = 47 / sqrt(65).

To find the point on the line closest to the point (0,-6), we can find the perpendicular distance from the point (0,-6) to the line y = 8x - 5. The point on the line closest to (0,-6) will be the point on the line that is intersected by the perpendicular line.

The slope of the given line is 8, so the slope of any line perpendicular to it will be -1/8. Let (a,b) be the point on the line y = 8x - 5 that is closest to (0,-6). The equation of the line passing through (0,-6) with slope -1/8 is:

y + 6 = (-1/8)x

Simplifying this equation, we get:

y = (-1/8)x - 6

The point (a,b) will lie on both the given line and the perpendicular line. Therefore, we can substitute y = 8x - 5 in the equation y = (-1/8)x - 6 to obtain:

8x - 5 = (-1/8)x - 6

Solving for x, we get:

x = 37/65

Substituting x = 37/65 in y = 8x - 5, we get:

y = 231/65

Therefore, the point on the line y = 8x - 5 closest to the point (0,-6) is (37/65, 231/65).

The distance S between the point (0,-6) and the line y = 8x - 5 can be found by using the formula:

S = |ax + by + c| / sqrt(a^2 + b^2)

where a, b, and c are the coefficients of the general form of the line equation, which is ax + by + c = 0.

In this case, the equation of the line is y - 8x + 5 = 0. Therefore, a = -8, b = 1, and c = 5. Substituting these values in the formula for S, we get:

S = |(-8)(0) + (1)(-6) + 5| / sqrt((-8)^2 + 1^2)

= 47 / sqrt(65)

Therefore, the function giving the distance between the point (0,-6) and the line y = 8x - 5 is:

S = 47 / sqrt(65)

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