Nico is saving money for his college education. He invests some money at 8​%, and ​$800 less than that amount at 7%. The investments produced a total of ​$214 interest in 1 yr. How much did he invest at each​ rate?

Both of the solutions differ in their constant integration.

A. ∫6x³(x⁴+1)dx

if we apply the distributive property:

∫6x³(x⁴+1)dx = ∫(6x⁷+ 6x³)dx = (6/8)x⁸ + (6/4)x⁴ + C = (3/4)x⁸ + (3/2)x⁴ + C

A. ∫6x³(x⁴+1)dx

If we use the substitution

w = x⁴+1

⇒ dw = 4x³dx  ⇒  x³dx = (1/4)dw

we have

∫6x³(x⁴+1)dx = 6∫w*(1/4)dw = (6/4)∫w dw = (3/2) (w²/2) + C = (3/4)w² + C

returning the change we get

∫6x³(x⁴+1)dx = (3/4)(x⁴+1)² + C

For these answers, we can apply Notable Identities as follows

(x⁴+1)² = (x⁴)² + 2*x⁴*(1) + (1)² = x⁸ + 2x⁴ + 1

then

(3/4)(x⁴+1)² + C₂ = (3/4)(x⁸ + 2x⁴ + 1) + C = (3/4)*x⁸ + (3/2)*x⁴ + (3/4) + C

We can assume (3/4) + C as a constant, then

∫6x³(x⁴+1)dx = (3/4)*x⁸ + (3/2)*x⁴ + C

Both of the solutions differ in their constant integration.

Both solutions are primitive of the same function, which must only fulfill a condition that is to differentiate into a constant, and in this case, they fulfill it.

It is not usual that using different methods of integration obtain different primitives, but it is not uncommon, there are quite a few known cases in which this happens and absolutely nothing happens.

It is normal. Two functions that differ in a constant have the same derivative and therefore, both functions are primitive of that same derivative.

C is often forgotten as a result.

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the branch of statistics for the scenario given regarding 10,000 Students is Descriptive Statistics.

In a study, descriptive statistics are used to describe the fundamental characteristics of the data. They provide brief summaries regarding the measures and samples. They serve as the foundation for virtually every quantitative data analysis, along with straightforward graphics analysis.

In most cases, descriptive statistics are different from inferential statistics. When you use descriptive statistics, you simply describe what the data show or are. With inferential statistics, you are attempting to draw inferences from data that go beyond the immediate facts. For instance, we attempt to infer what the general population might think from the sample data using inferential statistics.

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The correct statement is: She should calculate the ratio between the number of calories she burned versus the number of miles she ran.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here: The table containing data calories vs miles run.

You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are all the same, the table shows a proportional relationship.

Thus calculating the ratio for each pair of entries we get

1) ratio=118/1.2

      =295:3a  or unit rate 98.33 calories per mile

2) 190/2= 95:1 or unit rate 95 calories per mile

3) 226/2.4=565:6 or unit rate94.1

clea,rly the ratios are different.

Hence, The table containing the data doesn't form a proportional relationship.

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The value of H is 20 in the proportion 4 over H equals 5 over 25.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other

4 over H equals 5 over 25

4/H=5/25

Apply cross multiplication

4×25=5H

100=5H

Divide both sides by 5

20=H

Hence, the value of H is 20 in the proportion 4 over H equals 5 over 25.

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The solution is, 0.75 can be written as fraction = 3/4.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

here, we have,

A terminating decimal, such as 0.75, has an exact number of nonzero digits.

so, it can be written as fraction

0.75

=75/100

=3/4

Hence, The solution is, 0.75 can be written as fraction = 3/4.

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The area of the composite figure is equal to 71.07 in² square yards.

The composite figure is made up of a trapezium and a quarter of a circle, so we shall calculate for the areas of the two figures and then add the result to get the total area of the composite figure as follows:

area of the trapezium = [(6 + 10)/2] yd × 8 yd

area of the trapezium = (16/2) yd × 8 yd

area of the trapezium = 8 yd × 8 yd

area of the trapezium = 64 yd²

area of circle = πr²

area of circle = 22/7 × 3 × 3

area of circle = 198/7

a quarter area of the circle = 198/7 ÷ 4

a quarter area of the circle = 7.07 square yard

total area of the composite figure = 64 yd² + 7.07 yd²

total area of the composite figure = 71.07 yd²

Therefore, the area of the composite figure is equal to 71.07 yd² square yard.

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The function notation for A would be A(x) = y

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

This means that

The function can be expressed as

y = A(x)

This implies that:

The function A relates x and y

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Complete question

A is a relationship between two variables x and y such that every input x produce exact one output y​. What is the function notation of A

19. We can see here the wrong statement is:

B. The market demand (supply) curve is flatter than the individual demand (supply) monopoly market.

20. D. All of the above reveals basic economic question that every economy should try to resolve.

21. The statement that commits a post-hoc fallacy is: B. It is because of president bush's visit to Germany that the Ethiopian agriculture is backward.

22.  From the PPF the law of increasing opportunity cost is implied by

A. The negative slope of the curve

A logical fallacy known as post hoc occurs when one occurrence is assumed to be the reason for a subsequent event just because it happened earlier (also known as post hoc, ergo propter hoc).

We see here that the given answers above are actually correct.

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To calculate the number of gallons of gasoline required, you need to know the energy consumption of the car in MJ and the distance of the trip.

The first step is to determine the energy consumption of the car in MJ per unit distance (e.g. per mile or per kilometer). This information can be obtained from the car's fuel consumption specifications or from real-world tests.

Once the energy consumption is known, the number of gallons of gasoline required for a given trip can be calculated by dividing the total energy consumption of the trip by the energy content of a gallon of gasoline (120 MJ). This will give you the number of gallons of gasoline required to make the trip.

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Calculating parking ratios involves dividing a building's entire rentable square footage by its overall parking spaces. This offers the square footage available for rent per parking space, which is commonly stated as 1 parking space. 200 SF

The dimensions of a typical perpendicular parking place are nine feet (9') wide by eighteen feet (18') long.

To start, multiply 8 by 24 to determine how far apart each parking space is from the others (in other words the width of the parking lot).

8×24= 192 feet

Given that the question asks for an answer in yards, you know that 1 foot equals 1/3 of a yard and that 192 feet equals 64 yards.

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Answer:

-3/5

Step-by-step explanation:

I attached a photo so you can see my work

First, we can simplify the left side of the equation:

-3(x + 2) = -3x - 6

Now, we can substitute this expression into the equation:

-3x - 6 = 5y

Next, we can isolate the y variable on one side of the equation by dividing both sides by 5:

-3x/5 - 6/5 = y

Finally, to find the value of y when x = -1, we substitute -1 for x in the expression:

-3(-1)/5 - 6/5 = y

-3/5 - 6/5 = y

-9/5 = y

So, when x = -1, y = -9/5.

a) The general solution is: I(t) = (E0/R) * (1 - exp(-Rt/L)) * u(t)

b) The general solution is: I(t) = (E0/R) * (1 - exp(-Rt/L)) * 8(t)

c) The general solution is: I(t) = (E0/sqrt(R^2 + (Lw)^2)) * (sin wt + (R/Lw) * cos wt) * exp(-Rt/L)

a) When E(t) = E0u(t) (where u(t) is the unit step function), the solution to the differential equation L *(dI/dt) +RI = E0u(t) can be found using the method of partial fraction expansion.

The general solution is:

I(t) = (E0/R) * (1 - exp(-Rt/L)) * u(t)

b) When E(t) = E0 8(t) (where 8(t) is the impulse function), the solution to the differential equation L *(dI/dt) +RI = E0 8(t) can be found using Laplace transforms.

The general solution is:

I(t) = (E0/R) * (1 - exp(-Rt/L)) * 8(t)

c) When E(t) = E0 sin wt, the solution to the differential equation L *(dI/dt) +RI = E0 sin wt can be found using Laplace transforms or by solving the characteristic equation.

The general solution is:

I(t) = (E0/sqrt(R^2 + (Lw)^2)) * (sin wt + (R/Lw) * cos wt) * exp(-Rt/L

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Answer:

1a) 75

1b) 135

2a) 60

Step-by-step explanation:

Let's do the first 3 so you can see the pattern I use.

1a.) 150% of 50

First step I do is take the 150 and put a dot at the end.

150.

Next, I move that dot to the left two times, making it...

1.50

Now I take that and multiply by the number it's asking, which is 50

[tex]1.50 \times 50 = 75[/tex]

1b.) 150% of 90

150.

1.50

[tex]1.50 \times 90 = 135[/tex]

2a.) 100% of 60

100.

1.00

[tex]1.00 \times 60 = 60[/tex]

There are 1365 different ways to pick a president, treasurer, and secretary from a club of fifteen people.

The number of ways to pick a president, treasurer, and secretary from a club of fifteen people can be calculated using the formula for combinations:

[tex]C(n,r) = n! / (r! (n-r)!)[/tex]

Where n is the number of people in the club and r is the number of positions to be filled.

In this case, we want to calculate the number of ways to choose 3 people from a group of 15, so n = 15 and r = 3.

Plugging these numbers into the formula, we get:

[tex]C(15,3) = 15! / (3! (15-3)!) = 15! / (3! 12!) = 15*14*13 / (3*2*1) = 1365[/tex]

Therefore, there are 1365 different ways to pick a president, treasurer, and secretary from a club of fifteen people.

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Answer:

The value 0.031 represents the interest rat, which means the annual compounded interest rate is 3.1%

First option

Step-by-step explanation:

The general equation for amount accrued A with a principal P at an annual compound interest rate of i%(r/100 in decimal) compounded n times a year for t years is given by

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]

Here r = i/100 which is a decimal

Looking at the specific equation
[tex]A = 2400\left(1 + \dfrac{0.031}{4}\right)^{4t}[/tex]

we can see that P = 2440, the initial investment

0.031 is the annual interest rate in decimal

Expressed as percentage that would be 0.031 x 100 = 3.1% per year

So the correct answer is the first option which states
The value 0.031 represents the interest rat, which means the annual compounded interest rate is 3.1%

The total cost of the taxi ride is given by the equation A = $ 19.25

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of taxi ride be represented as A

Now , the equation will be

The initial cost for the pickup = $ 3.50

The cost of the ride per mile = $ 1.75

The cost for riding 9 miles = 9 x cost of the ride per mile

Substituting the values in the equation , we get

The cost for riding 9 miles = 9 x 1.75 = $ 15.75

So , the total cost of taxi ride A = initial cost for the pickup + cost for riding 9 miles

The total cost of taxi ride A = 3.50 + 15.75

The total cost of taxi ride A = $ 19.25

So , if the ride is m miles long , the cost is A = 3.50 + ( 1.75 )m

Hence , the equation is A = $ 19.25

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The rule of functions to solve for C(N(h)) is composition of functions. The cost when h = 8 hours is $3680.

To solve C(N(h)), the rule used is composition of functions, where the output of one function N(h) is used as the input to another function C(x).

First, evaluate C(x) to get its output and then plug that output into N(h) to get the final output.

Given the two functions, the cost in dollars to produce x shovels, C(x) = 12x + 450, and the number of shovels that can be produced in h hours, N(h) = 40h, we can find the cost when h hours of production time is used by finding C(N(h)).

To find C(N(h)), we first find N(h) to get the number of shovels produced in h hours and then plug that into C(x) to find the cost:

C(N(h)) = C(40h) = 12(40h) + 450 = 480h + 450

So, the rule for C(N(h)) is C(N(h)) = 480h + 450.

When h = 8 hours, the cost to produce shovels is given by C(N(8)) = 480(8) + 450 = 3680 dollars.

Therefore, it will cost $3680 to produce shovels in 8 hours.

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Emmet ran 1/8 mile further than he walked.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Emmet ran 3/8 of a mile and walked 1/4 of a mile.

Therefore, The number of more miles he run than he walked can be obtained by subtracting the number of miles he walked from the number of miles he ran which is,

= (3/8 - 1/4) miles.

= (3 - 2)/8.

= 1/8 miles.

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The rule is a linear equation:

y = 2x + 1

We want to write an expression that represents the following rule, it is:

"double the input, then add 1"

The input is represented by the variable x, so if we double it and then we add 1, the rule will be:

y = 2x + 1

So we have a linear equation.

And, using the notation on the image, we can write this as:

x → 2x + 1 → y

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You and three friends buy a pizza with 8 slices to share. Each friend gets 2 slices each because 1 divided by 1/4 is 25% and 25% of that pizza is 2 slices

Here's a sample code in Python that uses the scikit-learn library to perform linear regression on the given data:

import numpy as np

from sklearn.linear_model import LinearRegression

# Angle data

angle = np.array([0, 30, 45, 60, 90]).reshape(-1, 1)

# Modeling the relationship using Linear Regression

reg = LinearRegression().fit(angle, angle)

# Predicting the values

angle_pred = reg.predict(angle)

print("Predicted values: ", angle_pred)

The task is to develop a Python program that uses a linear regression model to predict the relationship between a dependent variable (angle) and an independent variable (in this case, the angle itself).

The code above models a trivial relationship between the angle and itself. This is just a simple example to show how linear regression can be performed in Python. Please make sure to use appropriate data and fit the model based on the problem statement.

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Option C is correct, the graph shows a dashed line, which passes through a point negative 2 comma 0 and a point 0 comma negative 2, with shading above the line.

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

The given inequality is −3x − 3y < 6

Minus three times  of x minus three times of y less than six.

Now let us solve for y

-3y<6+3x

Divide both sides by 3

-y<2+x

y>-x-2

The graph of the inequality is given in the attachment.

When we observe the graph the line is dashed line, which passes through a point negative 2 comma 0 and a point 0 comma negative 2, with shading above the line.

Hence, Option C is correct, the graph shows a dashed line, which passes through a point negative 2 comma 0 and a point 0 comma negative 2, with shading above the line.

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Based on the information in the graphs, it can be inferred that the correct conclusion is Fewer shops sell sandwiches for under $10 near City College than near Main Line University.

To identify the correct conclusion we must read each of the options and compare with the graphics to verify the veracity of each of the statements. In accordance with the above, we can discard the first three statements and select the last option as the correct one because it is the one that matches the information in the graph.

In this case the percentage of stores that sell large sandwiches in City College is less than Main Line University.

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Answer:

[tex]3 \frac{3}{4} [/tex]

Answer:

3.75 or 15/4

Step-by-step explanation:

3⋅5 = 15

8 divided by 2 = 4

15/4

El grafico de la ecuación cuadratica se puede ver en la imagen del final.

Digamos por ejemplo que queremos completar la tabla de abajo:

x: -1, 0, 1, 2

y:

Para ello, debemos evaluar la ecuación cuadratica que nos dieron en esos valores de x.

si x= -1

y = 2*(-1)²+3 = 5

si x = 0

y = 2*(0)²+3 = 3

si x = 1

y = 2*(1)²+3 = 5

si x = 2

y = 2*(2)²+3 = 11

Entonces the table is:

x: -1, 0, 1, 2

y:  5, 3, 5, 11

Para graficar esto, simplemente grafica todos los puntos que conocemos y debemos conectarlos con una curva, el grafico está abajo.

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The gross elasticity of demand for car polish with respect to the price of a car wash is 3.

The elasticity of demand refers to the change in demand when there is a change in another economic factor, such as price or income.

Given that, Sparkle clean car decreased the price of a car wash from $12 to $9 and noticed that the weekly quantity demanded for car polish increased from 200 to 350.

We are asked to find elasticity of demand,

First, we will find the increase in the customers:

Customer increasing = 350 - 200 / 200 × 100

= 75

Now, the fluctuation in the price =

Price fluctuation = 12 - 9 / 12 × 100

= 25

Elasticity = increased rate / fluctuated price

= 75 / 25

= 3

The elasticity of demand is 3 which is greater than 1, so, that mean, the demand is elastic.

Hence, the gross elasticity of demand for car polish with respect to the price of a car wash is 3.

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The number of 20-sided die in 80 is 33

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

The table of values

On the table, we have

20-sided = 5

Total = 12

So, we have

P(20-sided) = 5/12

For 80 dice, we have

Expected value = 5/12 * 80

Expected value = 33

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