Determine the unique solution, y(x), to the differential equation that satisfies the given initial condition. dy/dx = 8x⁷/y⁴, y(0) = 4
y(x) = ...

Answer:

The answer is 9

Step-by-step explanation:

When x = 2,

f(2) = 3×2^2-3

f(2) = 3×4-3

f(2) = 12-3

f(2)= 9

The probability that the next customer will pay with a credit card is 9/40.

To find the probability that the next customer will pay with a credit card, we need to determine the total number of customers and then calculate the fraction of those who used a credit card.

Step 1: Find the total number of customers.
56 customers paid cash, 6 customers used a debit card, and 18 customers used a credit card.
Total customers = 56 + 6 + 18 = 80 customers

Step 2: Calculate the probability of a customer using a credit card.
Number of customers who used a credit card = 18
Total number of customers = 80

Probability = (Number of customers who used a credit card) / (Total number of customers)
Probability = 18 / 80

Step 3: Simplify the fraction.

Divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 18 and 80 is 2.
18 ÷ 2 = 9
80 ÷ 2 = 40

Simplified fraction: 9/40

So, the probability that the next customer will pay with a credit card is 9/40.

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Answer:

2

Step-by-step explanation:

To solve this problem, we need to first find the current average and median number of AP classes per student, and then use that information to determine the number of AP classes the new student is taking.

To find the current average number of AP classes per student, we can use the information in the table:

(1 AP class) x 6 students = 6 AP classes

(2 AP classes) x 9 students = 18 AP classes

(3 AP classes) x 5 students = 15 AP classes

(4 AP classes) x 4 students = 16 AP classes

Total number of AP classes = 6 + 18 + 15 + 16 = 55

Total number of students = 6 + 9 + 5 + 4 = 24

Average number of AP classes per student = Total number of AP classes / Total number of students

= 55 / 24

= 2.29 (rounded to two decimal places)

To find the current median number of AP classes per student, we need to order the number of AP classes per student from least to greatest:

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4

The median is the middle value when the data is ordered in this way. Since there are 24 students, the median is the average of the 12th and 13th values:

Median = (2 + 2) / 2

= 2

Since we know that the current average and median are not equal, the new student must be taking a number of AP classes that will bring the average up to 2. We can set up an equation to represent this:

(55 + x) / (24 + 1) = 2

where x is the number of AP classes the new student is taking. Solving for x, we get:

55 + x = 50

x = -5

This is a nonsensical answer, as the number of AP classes taken by the new student cannot be negative. Therefore, our assumption that the new student is taking a number of AP classes greater than the current average is incorrect. Instead, the new student must be taking a number of AP classes less than the current average, which will bring the average down to 2.

Let y be the number of AP classes the new student is taking. We can set up a new equation to represent this:

(55 + y) / (24 + 1) = 2 - ((2.29 - 2) / 2)

where the term on the right-hand side represents the amount by which the average needs to decrease in order to reach 2. Solving for y, we get:

55 + y = 46.5

y = 46.5 - 55

y = 8.5

So the new student is taking 8.5 AP classes. However, since the number of AP classes must be a whole number, we need to round this value to the nearest integer. Since 8.5 is closer to 9 than to 8, we round up to 9. Therefore, the answer is:

The new student is taking 9 AP classes. Answer: None of the above (not given as an option).

The amount of accumulated interest the investor can expect in 8 years is $2,880.

To calculate the accumulated interest on the life insurance policy, we can use the simple interest formula:

I = P x r x t

In this case, the principal amount invested is $4,500, the annual interest rate is 8.0% (or 0.08 as a decimal), and the time period is 8 years. Therefore:

I = 4,500 x 0.08 x 8

I = $2,880

Therefore, the investor can expect to earn $2,880 in accumulated interest at the end of 8 years.

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Total string used = Number of bracelets × String used per bracelet

Total string used = 77 × 17.8 = 1370.6 cm

Let's denote the total amount of string used as "T". We know that the girl used xx centimeters of string to make 77 bracelets, and each bracelet required 17.8 centimeters of string.

To find the total string used, we can set up the following equation:

T = 77 * 17.8

Simplifying the equation, we have:

T = 1369.6

Therefore, the girl used a total of 1369.6 centimeters of string to make all the bracelets.

In conclusion, the equation T = 77 * 17.8 can be used to determine the total amount of string used, and the solution to the equation is T = 1369.6 centimeters.

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Looking at the spread of your data is part of the data analysis step in the statistical process.

In this step, the data is examined to identify patterns, relationships, and trends in the data.

One aspect of data analysis is understanding the distribution and spread of the data, which can be done through measures of central tendency and measures of variability.

Understanding the spread of the data can help in making decisions about what statistical analyses are appropriate and how to interpret the results.

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(a) First, we need to find the derivative of the cost function, C'(x), with respect to x.

The given function is: C(x) = -10x^2 + 500x + 110

To find the derivative, we will apply the power rule:

C'(x) = d/dx (-10x^2) + d/dx (500x) + d/dx (110)

For each term: d/dx (-10x^2) = -20x d/dx (500x) = 500 d/dx (110) = 0 So, C'(x) = -20x + 500

(b) Now, we need to find the rate of change of the total cost when the level of production is 7 surfboards a day.

To do this, we will substitute x=7 into the derivative function C'(x): C'(7) = -20(7) + 500 C'(7) = -140 + 500 C'(7) = 360

The rate of change of the total cost when the level of production is 7 surfboards a day is $360 per surfboard.

Your answer: a) C'(x) = -20x + 500 b) $360 per surfboard

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The value of the fraction is 3/-2

A fraction can simply be described as the part of a whole variable, a whole number or a whole element.

The different types of fractions in mathematics are;

From the information given, we have that;

4/-2 - 3/-6

find the lowest common factor

12 - 3/-6

subtract the value, we get;

9/-6

Divide the values into simpler forms

3/-2

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The length of time, in seconds, that it will take for the scientist to travel back to sea level at 3.5 feet per second will be 5.0 seconds.

To calculate the amount of time, we will begin by calculating the distance traveled from sea level in all of the instances.

1. 112 seconds × 0.8 feet per second = 89.6 feet

2. 120 seconds × 0.6 feet per second = 72 feet

The distance from sea level is now: 89.6 feet - 72 feet

= 17.6 feet

The time, in seconds, that it will  take for the scientist to travel back to sea level at 3.5 feet per second will be:

17.6 feet ÷  3.5 feet per second

5.0 seconds to the nearest tenth.

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The term which is important in terms of making meaning of those scores is measures of central tendency (mean, median, mode), option A.

A single number that seeks to characterise a set of data by pinpointing the centre location within that set of data is referred to as a measure of central tendency. As a result, measurements of central location are occasionally used to refer to measures of central tendency.

These also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.

The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, certain indicators are more useful than others.

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Answer: 55%

Step-by-step explanation:

To find the percentage of 11/20, we can use the following formula:

Percentage = (Numerator ÷ Denominator) × 100

Substituting the values from 11/20 into the formula, we get:

Percentage = (11 ÷ 20) × 100

Percentage = 0.55 × 100

Percentage = 55%

Therefore, the percentage of 11/20 is 55%.

Answer:

Solution: 11/20 as a percent is 55%

Step-by-step explanation:

First, convert the fraction into a decimal by dividing the numerator by the denominator:

11/20 = 0.55

If we multiply the decimal by 100, we will get the percentage:

00.5 * 100 = 55

We can see that 11/20 is percentage is 55.

The solution of the system of equations is given by the ordered pair (-2, 2).

Based on the table, a x-value that is a solution to the equation is -2.

The solution to the equations are (-6, 3) and (-4, -5).

An ordered pair which is the best estimate for the solution of the system is: A. (-0.5, -1.75).

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

8x - 4y = -24    ......equation 1.

4x - 12y = -32  ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-2, 2).

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Answer: 4.7KL

Step-by-step explanation:

KL=DAL/100

KL=470/100

KL=4.7

The ratios are: surface area 9:121, volume 27:1331, width 3:11.

(a) The ratio of the surface area of the model to the surface area of the original can be found by using the scale factor to find the ratio of the corresponding side lengths. Since surface area is proportional to the square of the side length, we can use this ratio squared to find the ratio of the surface areas.
The ratio of the corresponding side lengths is 3:11, so the ratio of the surface areas is (3/11)^2, which simplifies to 9/121.
Therefore, the ratio of the surface area of the model to the surface area of the original is 9:121.
(b) The ratio of the volume of the model to the volume of the original can be found using the same method as above, but with volume instead of surface area. Since volume is proportional to the cube of the side length, we can use this ratio cubed to find the ratio of the volumes.
The ratio of the corresponding side lengths is 3:11, so the ratio of the volumes is (3/11)^3, which simplifies to 27/1331.
Therefore, the ratio of the volume of the model to the volume of the original is 27:1331.
(c) The ratio of the width of the model to the width of the original can be found directly from the scale factor, since width is one of the corresponding side lengths.
The ratio of the corresponding side lengths is 3:11, so the ratio of the widths is 3:11.
Therefore, the ratio of the width of the model to the width of the original is 3:11.
Overall, the ratios are: surface area  9:121, volume  27:1331, width 3:11.

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a) To verify that the points A(14, 9) and B(7, 16) are on the circle with center C(2, 4) and radius 13, we can use the distance formula:

Distance between point A and C:

d_AC = sqrt[(x_A - x_C)^2 + (y_A - y_C)^2]

    = sqrt[(14 - 2)^2 + (9 - 4)^2]

    = sqrt[144 + 25]

    = sqrt(169)

    = 13

Since the distance between point A and C is equal to the radius of the circle, point A is on the circle.

Distance between point B and C:

d_BC = sqrt[(x_B - x_C)^2 + (y_B - y_C)^2]

    = sqrt[(7 - 2)^2 + (16 - 4)^2]

    = sqrt[25 + 144]

    = sqrt(169)

    = 13

Since the distance between point B and C is equal to the radius of the circle, point B is also on the circle.

Therefore, points A and B are on the circle with center C(2, 4) and radius 13.

b) The midpoint of line segment AB can be found using the midpoint formula:

M = [(x_A + x_B)/2, (y_A + y_B)/2]

 = [(14 + 7)/2, (9 + 16)/2]

 = [10.5, 12.5]

The slope of line segment AB can be found using the slope formula:

m_AB = (y_B - y_A)/(x_B - x_A)

    = (16 - 9)/(7 - 14)

    = -7/-7

    = 1

The slope of a line perpendicular to AB will be the negative reciprocal of m_AB:

m_CM = -1/m_AB

    = -1/1

    = -1

The equation of the line passing through points C(2, 4) and M(10.5, 12.5) can be found using the point-slope form:

y - y_C = m_CM(x - x_C)

y - 4 = -1(x - 2)

y = -x + 6

The slope of line CM is -1, which is the negative reciprocal of the slope of line AB. Therefore, line CM is perpendicular to line AB.

Hence, we have shown that line segment CM is perpendicular to line segment AB.

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The value for each conversion is: 12,000 g = 12 kg 120 cm = 1200 mm 2 L = 2000 mL 1,200 cm = 12 m 0.12 m = 120 mm.

Here are the completed conversions using the provided numbers:

1. 12,000 g = 12 kg (To convert grams to kilograms, divide by 1,000)

2. 120 cm = 1,200 mm (To convert centimeters to millimeters, multiply by 10)

3. 1.2 L = 1,200 mL (To convert liters to milliliters, multiply by 1,000)

4. 1,200 cm = 12 m (To convert centimeters to meters, divide by 100)

5. 0.12 m = 120 mm (To convert meters to millimeters, multiply by 1,000)

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The value of f(4) rounded to the nearest tenth is approximately 194.9.

The value of f(4) can be found by substituting x=4 in the given function f(x) = [tex]4e^x[/tex], so we get:

f(4) = [tex]4e^4[/tex]

Using a calculator, we can evaluate this expression as:

f(4) ≈ 194.92

Rounding this to the nearest tenth gives:

f(4) ≈ 194.9

Therefore, the value of f(4) rounded to the nearest tenth is approximately 194.9.

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Answer:

C) 6

Step-by-step explanation:

n=6

6( 6 + 1) + 3 =45

36 + 6 + 3 = 45

36 + 9 = 45

The equation of the line parallel to the graph of y = (-1/2)x - 1 and containing the point (-4, 5) is y = (-1/2)x + 3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of the graph

y = (-1/2)x - 1

The equation of a line parallel to the graph of y = (-1/2)x - 1 will have the same slope as the given line, which is -1/2.

Now. using the point-slope form, we can find the equation of the line that passes through the point (-4, 5) with slope -1/2:

y - y1 = m(x - x1)

y - 5 = (-1/2)(x - (-4))

y - 5 = (-1/2)x - 2

y = (-1/2)x + 3

Therefore, the equation of the parallel line is y = (-1/2)x + 3.

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Answer:

Step-by-step explanation:

The cost of 1 pound of peanuts can be found by dividing the total cost of 8 pounds by 8:

Cost of 1 pound of peanuts = $24 / 8 pounds = $3 per pound

The cost of 1 pound of walnuts can be found by dividing the total cost of 6 pounds by 6 and then multiplying by 2 (since the cost of 6 pounds is half that of the peanuts for the same weight):

Cost of 1 pound of walnuts = ($24 / 6 pounds) x 2 = $8 per pound

Therefore, we see that walnuts are more expensive than peanuts by $5 per pound ($8 - $3).

In other words, 1 pound of walnuts costs $5 more than 1 pound of peanuts.

Answer:  B   g(x)=1/4f(x)    odd

Step-by-step explanation:

First Page:

Points from the graph

Points from f(x)                         points from g(x)

(1,2)                                                (1, 1/2)

(4, 16)                                             (4, 4)

f(x) was multiplied by 1/4 to get to g(x)

Second Page:

Even functions are symmetrical about the y-axis: . Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x).

lets test for even:  does f(x)=f(-x)   =>    f(1)=f(-1)  no   -2[tex]\neq[/tex]2

see image for plotted points

lets test for odd:  does f(x)= -f(-x)   =>    f(1) = -f(-1)  yes  -2 = -2

Answer:

[tex]\textsf{B)} \quad g(x)=\dfrac{1}{4}f(x)[/tex]

[tex]\textsf{B)} \quad \textsf{odd}[/tex]

Step-by-step explanation:

Functions f(x) and g(x) are exponential functions.

From inspection of the given points on both graphs:

When x = 4, the y-value of function f(x) is four times the y-value of function g(x). Therefore, function g(x) is ¹/₄ of function f(x):

[tex]g(x)=\dfrac{1}{4}f(x)[/tex]

[tex]\hrulefill[/tex]

And even function is symmetric about the y-axis:

According to the table, f(3) = -4 and f(-3) = 4.

Therefore, as f(x) ≠ f(-x), the function is not even.

An odd function is symmetric about the origin:

According to the table, f(-3) = 4 and f(3) = -4. So -f(3) = -(-4) = 4.

Therefore, as f(-3) = -f(3), the function is odd.

[tex]\hrulefill[/tex]

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The number of cones that can be filled with the ice cream from the container is 10.

Let's start with the container. We are given that it is a right circular cylinder with a diameter of 12 cm and a height of 15 cm. To find the volume of this cylinder, we use the formula:

Volume of cylinder = πr²h

where r is the radius of the cylinder (which is half of the diameter), and h is the height. Substituting the given values, we get:

Volume of cylinder = π(6 cm)²(15 cm) = 540π cubic cm

So the container has a volume of 540π cubic cm.

Now, let's move on to the cones. We are given that the cones have a height of 12 cm and a diameter of 6 cm. The cones have a hemispherical shape on the top, so we can consider them as a combination of a cone and a hemisphere. The formula for the volume of a cone is:

Volume of cone = (1/3)πr²h

where r is the radius of the base of the cone, and h is the height. Substituting the given values, we get:

Volume of cone = (1/3)π(3 cm)²(12 cm) = 36π cubic cm

The formula for the volume of a hemisphere is:

Volume of hemisphere = (2/3)πr³

where r is the radius of the hemisphere. Substituting the given values (the radius is half the diameter of the cone, which is 3 cm), we get:

Volume of hemisphere = (2/3)π(3 cm)³ = 18π cubic cm

So the total volume of each cone is:

Volume of cone + hemisphere = 36π + 18π = 54π cubic cm

To find out how many cones can be filled with the ice cream from the container, we divide the volume of the container by the volume of each cone:

Number of cones = Volume of container / Volume of each cone Number of cones

=> (540π cubic cm) / (54π cubic cm) Number of cones = 10

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Complete Question:

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Step-by-step explanation:

sqrt (5/3)  = sqrt 5 / sqrt 3    

  multiply by ONE in the form   sqrt (3) / sqrt 3

      sqrt 5 / sqrt 3    *    sqrt 3 / sqrt 3

             = sqrt 15 / 3    

Or maybe you meant  

  sqrt (5) / 3  =  .745

To find the absolute value of the difference between theoretical and experimental probabilities, you need to follow these steps:

1. Calculate the theoretical probability: This is the probability of an event occurring based on the total number of possible outcomes. It can be found by dividing the number of successful outcomes by the total number of possible outcomes.

2. Calculate the experimental probability: This is the probability of an event occurring based on actual experiments or trials. It can be found by dividing the number of successful outcomes by the total number of trials conducted.

3. Find the difference: Subtract the experimental probability from the theoretical probability.

4. Take the absolute value: The absolute value is the non-negative value of a number, disregarding its sign. To find the absolute value of the difference, simply remove the negative sign if the result is negative.

By following these steps, you'll find the absolute value of the difference between theoretical and experimental probabilities, which is an important measure to assess the accuracy of experiments and predictions.

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The value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the tangent TU and the secant through U which intersect the circle at points V and W;

TU² = UV × VW {secant tangent segments}

(5x)² = 9 × 16

(5x)² = 144

5x = √144 {take square root of both sides}

5x = 12

x = 12/5

so;

TU = 5(12/5)

TU = 12

Therefore, the value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12

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Answer:

(-∞, 1) ∪ (1, ∞)

Step-by-step explanation:

1 - x = 0

-x = -1

x = 1

In interval notation, the domain is (-∞, 1) U (1, ∞)

The measure of the quadrilateral are

88 - 4 = 84

2 * 88 - 78 = 98

88 + 8 = 96

A quadrilateral is a polygon with four sides and four vertices (corners). There are many different types of quadrilaterals, including squares, rectangles, parallelograms, trapezoids, and kites. The angles and sides of a quadrilateral can vary depending on its specific type, but the sum of the internal angles of any quadrilateral is always 360 degrees.

x - 4 + x + 8 = 180

we have to find the value of x

x = 88

The angles would be

88 - 4 = 84

2 * 88 - 78 =

88 + 8 = 98

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To calculate the rate of change of the simple index over 1 day, we need to first calculate the index value for Monday and Tuesday.

On Monday, the value of stock A is 10,000 x $5.50 = $55,000, and the value of stock B is 8,000 x $6.25 = $50,000. The total value of the index on Monday is $55,000 + $50,000 = $105,000.

On Tuesday, the value of stock A is 10,000 x $5.80 = $58,000, and the value of stock B is 8,000 x $6.65 = $53,200. The total value of the index on Tuesday is $58,000 + $53,200 = $111,200.

To calculate the rate of change, we can use the formula:

(rate of change) = (new value - old value) / old value x 100%

Using this formula, we get:

(rate of change) = ($111,200 - $105,000) / $105,000 x 100% = 5.90%

Therefore, the rate of change of this simple index over 1 day is 5.90%.

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Answer:

20 tanks

Step-by-step explanation:

if each tank holds 6 fish and there are 115 fish, you need to divide the amount of fish total by amount that go in 1 tank:

115/6 = 19.1666666667

Now we round up bc we cant leave any fish out right?

So your answer is 20 tanks will be needed to hold 115 fish if it’s 6 fish per tank.

Check this by multiplying the tanks and fish in every tank:

20 x 6 = 120

Meaning that 115 fish go into 20 tanks, one of the tanks just having 1 fish :D

Answer: 20 is the correct option.

Step-by-step explanation:Given that a pet store has 115 fish that need to be placed into fish tanks and each tank hold 6 fish.

We are to find the number of tanks that the store need.

We will be using the UNITARY method to solve the given problem.

Number of tanks needed to store 6 fishes = 1.

So, number of tanks needed to store 1 fish will be [tex]\frac{1}{6}[/tex]

Therefore, number of tanks needed to store 115 fishes is given by

[tex]\frac{1}{6}[/tex] × 155 =[tex]\frac{115}{6}[/tex]= 19 [tex]\frac{1}{6}[/tex] = 19.16.

Since we cannot have 0.16 tank, so we need one tank more than 19 to store all fishes.

Thus, the store needs 20 tanks for 115 fishes.

Hope this helps :)

The volume of the cone is (5/3)π(9²) cubic units ≈ 381.7 cubic units.

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the circular base and h is the height of the cone. However, we are given the base area B instead of the radius, so we need to find the radius first.

We know that the area of a circle is A = πr², so if the base area of the cone is B = 5π square units, then πr² = 5π, which means r² = 5. Solving for r, we get r = √5.

Now that we have the height h = 9 units and the radius r = √5 units,

we can use the formula for the volume of a cone:

V = (1/3)πr²h.

Substituting the values, we get

V = (1/3)π(√5)²(9) = (5/3)π(9²) cubic units, which simplifies to ≈ 381.7 cubic units.

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