if the simple interest on $6,000 for a year is 900 then what is the interest rate

The question that can be answered using the expression 3 ÷ 1 is "How many 1-pound pieces of fudge are in a 3-pound fudge?". The correct option is B.

The expression "3 ÷ 1" is a mathematical expression that represents a division operation. In this case, the operation is "3 divided by 1".

To understand what this expression means, we can think of it in terms of a real-world scenario. For example, we can think of it as dividing 3 pounds of fudge into 1-pound pieces.

If we divide 3 pounds of fudge into 1-pound pieces, we can ask the question "How many 1-pound pieces of fudge are in 3 pounds of fudge?" This is the question that can be answered using the expression "3 ÷ 1".

To solve this division problem, we simply divide 3 by 1. The result is 3. This means that there are 3 one-pound pieces of fudge in 3 pounds of fudge.

So, to summarize, the expression "3 ÷ 1" means "3 divided by 1" and can be interpreted as dividing 3 pounds of fudge into 1-pound pieces. The answer to the question "How many 1-pound pieces of fudge are in 3 pounds of fudge?" is 3.

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The distance between these two points (2,0) and (2,−5) is 5 unit.

The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.

d=√((2 – 2)² + (-5 – 0)²)

d = √(0+25)

d = 5 unit

if the coordinates of two points P and Q are such that, (x1, 0) and (x2, 0), the distance between PQ will be given by:

PQ = |x2 – x1|

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The angle of depression from the top of the taller building and the angle of elevation from the top of the shorter building are alternate interior angles.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.

The angles of elevation and depression are formed by the line of sight and the horizontal line. When the line of vision is above the horizontal line, the angle is of elevation, and if the line of sight is below the horizontal, the angle is of depression.

If the angle of depression of the taller building is 15° the angle of elevation of the shorter building is 15° too.

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The vertex of the function g(x) is (1,-5).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=-3(x-1)²+2 and g(x)=-3(x-1)²-5.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:

(1,-5)

Focus:

(1,-61/12)

Axis of Symmetry:

x=1

Directrix:

y= -59/12

Therefore, the vertex of g(x) is (1,-5).

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Answer: look at the image for the answer and solution

Step-by-step explanation:

ABCD is a rectangle, and P, Q, R, and S are mid points of the sides AB, BC, CD, and DA, respectively. show that the quadrilateral PQRS is a rhombus

For this data, the IQR is a superior measure of variability because it is less than the range. The greatest way to quantify variability is the IQR, and that number is 11.

The interquartile range (IQR) in descriptive statistics is a measurement of statistical dispersion, or the spread of the data. The IQR is also known as the middle 50%, the fourth spread, or the H-spread. The difference between the data's 75th and 25th percentiles is how it is defined.

The median (middle value) of the lower half and upper half of the data should be found first in order to determine the interquartile range (IQR). The quartile 1 (Q1) and quartile 3 values are these (Q3). The IQR is the difference between Q3 and Q1.

From the given stem-and-leaf plot, we can see that the lowest score is 5, and the highest score is 23. Therefore, the range of the data is:

Range = highest value - lowest value = 23 - 5 = 18

We also need to find the quartiles to calculate the IQR. The median (Q2) of the data is 18, which is the value that separates the lower 50% of the scores from the upper 50%. To find Q1 and Q3, we can split the lower and upper halves of the data, respectively, and find their medians.

The lower half of the data is: 5, 10, 13, 17, 18. The median of this half is (13 + 17)/2 = 15.

The upper half of the data is: 24, 26, 28. The median of this half is 26.

Therefore, Q1 = 15 and Q3 = 26, and the IQR is:

IQR = Q3 - Q1 = 26 - 15 = 11.

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Answer:

IQR 18.5

Step-by-step explanation:

I took the test

The rate of change of Jakes earning is, 0 or no change.

Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.

So formula for the rate is,

m = change in one quantity/change in another quantity = Δy/Δx

On Monday, Jake earned $90 by washing 18 cars.

Therefore, his earning rate was:

= $90 / 18 cars

= $5 per car

On Tuesday, Jake washed 9 cars and earned $45.

Therefore, his earning rate was:

= $45 / 9 cars

= $5 per car

On Wednesday, Jake washed 12 cars and earned $60.

Therefore, his earning rate was:

= $60 / 12 cars

= $5 per car

We can see that Jake's earning rate remained constant over the three days at $5 per car.

Therefore, the rate of change of Jake's earnings is 0, or no change.

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The answer would be D. 35x² + 29x +6.

What is the Solution of an Equation?

The value of a variable in an equation is the answer that, when inserted into the equation, makes the equation true. It is discovered by relegating the variable to one side of the equation, with the value on the other side being the solution.

To multiply two polynomials, we use the distributive property.

Starting with the first term, we multiply 5x and 7x, then add 2 and 7x, and then add 2 and 3. The result is:

= (5x + 2)(7x + 3)

= 35x² + 33x + 14x + 6

= 35x² + 29x + 6

Therefore, The answer would be D. 35x² + 29x +6.

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Answer:

-5.5

Step-by-step explanation:

[12*(3/(2^2))]/2-10   [Rewritten to add brackets.

Use PEDMAS to determine order of operation.

P =- parentheses first:

[12*(3/(2^2))]/2-10

[12*(3/(4))]/2-10        [squared the 2]

[12*(3/4)]/2-10          [Removed excess parentheses]

[12*(3/4)]/2-10         [Next parenthses:  12*(3/4)  Divide and Multioply]

[9]/2 - 10                   [Divide and Multiply]

4.5 - 10                     [Add/Subtract]

-5.5                          Result

The actual amount of sale for each bake is $214. As Miguel said it is $215 which is very close to the actual amount, it is reasonable.

To determine if Miguel's estimate of $215 per bake sale is reasonable, we can start by calculating the average amount of money the scout troop made per bake sale. We do this by dividing the total amount they earned by the number of sales they had, as follows:

Total amount earned = $1,498

Number of bake sales = 7

Average amount earned per bake sale = Total amount earned ÷ Number of bake sales

= $1,498 ÷ 7

= $214

This calculation shows that the average amount the scout troop made per bake sale was $214. This means that if they had charged a consistent price for all of their baked goods at each sale, they would have made an average of $214 per sale.

Now, we can compare this average to Miguel's estimate of $215 per bake sale. Since his estimate is very close to the actual average, we can conclude that it is reasonable.

It is possible that the scout troop charged slightly different prices for their baked goods at each sale, which could explain the small discrepancy between the actual average and Miguel's estimate. However, given that the difference between the two values is only $1, it is likely that Miguel's estimate is a good approximation of the actual amount.

Moreover, it is reasonable to assume that the scout troop earned the same amount at each bake sale, especially if they had a set price for their baked goods.

If they had charged different prices at each sale, it would have been more difficult to estimate the average amount they earned per sale, and it would have been less likely that Miguel's estimate of $215 per bake sale would have been close to the actual average.

Therefore, based on the calculation and the context of the problem, we can conclude that Miguel's estimate of $215 per bake sale is reasonable.

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Answer:

Hello if you are solving for x the for the equation -4x+4y=-4

your answer is x=y+1

Step-by-step explanation:

4y -4x= -4

subtract 4y from both sides

-4x = -4y- 4

divide both sides by -4

x= y+1

I HOPE THIS HELPS!

Answer:

Step-by-step explanation:

Since the side lengths are proportional, the ratio of the width to length in the old phone will be equal to the ratio of the width to length in the new phone. That is:

(width of old phone) / (length of old phone) = (width of new phone) / (length of new phone)

We know the length of the old phone is 1.41.4 inches, and the width is 2.82.8 inches, so we can use that information to solve for the width of the new phone:

(2.82.8 inches) / (1.41.4 inches) = (width of new phone) / (1.611.61 inches)

Cross multiplying, we get:

(width of new phone) = (2.82.8 inches) * (1.611.61 inches) / (1.41.4 inches)

Using a calculator, we can find that the width of the new phone is approximately 3.23.2 inches.

The total number of strings that satisfy the given conditions is 24.

Let us count the number of strings where the two ones that are next to each other are in the first two positions, and the third one is in the fifth position. There are two choices for the value of the fourth digit (0 or 1), and two choices for the value of the last digit (0 or 1). Therefore, there are 2 \cdot 2 = 4 strings with this property: 110010, 110100, 111010, and 111100.

We can obtain the same number of strings by considering the case where the two ones that are next to each other are in the last two positions, and the third one is in the fifth position.

Now, let us count the number of strings where the two ones that are next to each other are in the first two positions, and the third one is in the sixth position. There are two choices for the value of the third digit (0 or 1), and two choices for the value of each of the other digits (digits 4 and 5 must be different from each other and from digit 3). Therefore, there are 2 \cdot 2 \cdot 2 = 8 strings with this property: 1100010, 1101010, 1110010, 1111010, 1000110, 1001110, 1010110, and 1011110.

Again, we can obtain the same number of strings by considering the case where the two ones that are next to each other are in the last two positions, and the third one is in the sixth position.

Thus, the total number of strings that satisfy the given conditions is 4+4+8+8=24.

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By completing the square, the equation. x2 + 20x + 82 = 7. The solutions are x = -15 and x = -5, going from least to largest.

The square of half the x-coefficient must equal the constant on the left:

 (20/2)^2 = 100

To get it to that value, we can add 18 to both sides of the equation:

 x^2 + 20x + 100 = 25 . . . add 18 to both sides of the equation

 (x + 10)^2 = 25 . . . . . . .  . write the left side as a square

 x + 10 = ±√25 = ±5 . . . . . take the square root

 x = - 10 ± 5 = {-15, -5}

The solutions are x = -15 and x = -5.

The attached graph shows the solutions to ...

 x^2 + 20x + 82 -7 = 0 . . . . . the result of subtracting 7 from both sides

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The differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.

1. y' = x: This differential equation corresponds to a phase line with a slope of 1, since the y' term is equal to the x term.

2. y' = -x: This differential equation corresponds to a phase line with a slope of -1, since the y' term is equal to the negative of the x term.

3. y' = [tex]x^2[/tex]: This differential equation corresponds to a phase line with a slope of 2x, since the y' term is equal to the x squared term.

4. y' = [tex]-x^2[/tex]: This differential equation corresponds to a phase line with a slope of -2x, since the y' term is equal to the negative of the x squared term.

5. y' =[tex]x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]3x^2[/tex], since the y' term is equal to the x cubed term.

6. y' = [tex]-x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-3x^2[/tex], since the y' term is equal to the negative of the x cubed term.

7. y' = [tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]nx^(n-1)[/tex], since the y' term is equal to the x to the power of n term.

8. y' = -[tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-nx^(n-1),[/tex] since the y' term is equal to the negative of the x to the power of n term.

In summary, the differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.

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Complete question:

Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct. ?

1.  y' = x

2. y' = -x

3.  y' = [tex]x^2[/tex]

4. y' = [tex]-x^2[/tex]

5.y' =[tex]x^3[/tex]

6.y' = [tex]-x^3[/tex]

7. y' = [tex]x^n[/tex]

8. y' = -[tex]x^n[/tex]

If one her 4 numbers come up, she wins $40 (and gets to keep her bet!). Alyssa can expect to lose 47 cents per bet over the long run.

The expected value of a game is the average amount that a player can expect to win or lose per bet, taking into account both the probabilities and the payouts of each possible outcome. To find the expected value, we multiply the probability of each outcome by the amount won or lost for that outcome, and then sum up these products.

In this case, Alyssa bets $5 on a block of 4 numbers, which gives her a probability of winning of 4/38, or approximately 0.1053. If one of her 4 numbers comes up, she wins $40, for a net gain of $35 (since she gets to keep her $5 bet as well). If none of her 4 numbers comes up, she loses her $5 bet.

Therefore, the expected value for each bet is:

(0.1053 × $35) + (0.8947 × -$5) = -$0.47

So if she plays many times, she can expect to lose money overall. It's important to keep in mind that expected value is not a guarantee of what will happen on any particular bet, but rather a long-term average based on probabilities.

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The Linear Equation for the line with slope as -1/3 and the point (-9,-1) is y = (-1/3)x - 4   .

We use the point slope form of a linear equation to write the equation of a line with its slope and a point on the line.

The point-slope form is ⇒ y - y₁ = m(x - x₁)  ;

Where m is = slope of line, and (x₁, y₁) is a point on line.

The Slope (m) of line  is  = -1/3 and point on line (x₁, y₁) is = (-9, -1),

Now , we substitute  these values ;

we get ;

⇒ y - (-1) = (-1/3)(x - (-9)) ;

⇒ y + 1 = (-1/3)(x + 9)  ;

Simplifying further ,

we get ;

⇒ y + 1 = (-1/3)x - 9/3  ;

Subtracting 1 from both sides, we get:

⇒ y = (-1/3)x - 4

Therefore, the equation of the line is y = (-1/3)x - 4  .

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Answer:

Step-by-step explanation:

The answer is 4x^2y+8x^3+y^2-2xy

John has average 2 books and Peter has 4 books. Together, they have 6 books.

John has 2 books

Peter has twice books more than John = 2 * 2 = 4 books

Total books they have together = 2 + 4 = 6 books

John has 2 books, so Peter has twice books more than John. This means that Peter has 2 * 2 = 4 books. Together, John and Peter have 2 + 4 = 6 books. John’s books are the starting point of the problem, so it is important to keep track of John’s books. Since Peter has twice books more than John, we can calculate the number of books that Peter has by multiplying the number of books that John has by two. Once we have calculated the number of books that Peter has, we can add the number of books that John has to the number of books that Peter has and get the total number of books that they have together. In this example, the total number of books that John and Peter have together is 6. This can be arrived at by adding the number of books that John has (2) to the number of books that Peter has (4).

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The solution set of the system of equations is {(2,2), (4,-2)}

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

4x+2y =12------>(1)

Take some random values for x. Find the corresponding y  values

Example: when x=0

(1) => 4(0)+2y = 12

  =>  0+2y = 12

  =>      2y =12

 =>     y= 12/2 = 6

The point obtained is (x,y) = (0,6)

This way, we get a line when we graph the equation 4x+2y =12.

Similarly, when we graph the equation  y= -x² + 4x -2 , we get a parabola

Graph is attached:

In the graph, both graphs intersect at the points (2,2) and (4,-2)

Thus, the solution set of the system of equations is {(2,2), (4,-2)}

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Answer: a and b

Step-by-step explanation: lol it obvious

Answer: Quadrilateral, Parallelogram

Step-by-step explanation:

A Quadrilateral is any closed 4 sided figure

A Parallelogram is a quadrilateral with two sets of parallel and opposite sides.

The initial amount A is 1 and the growth factor B is 1.4 in the Exponential function f(t)=14^x.

Given,

f(x) = 1.4^x

It is an exponential function.

y = a.b^x

where a is the initial quantity and b is the growth/ decay component.

Now we are able to examine the given feature with

A = 1

B = 1.4

An exponential function is a mathematical function that has the form f(x) = a^x, where a is a constant greater than zero and not equal to one, and x is a variable. This function is widely used in a variety of fields, such as finance, physics, and biology, due to its ability to model growth, decay, and change over time.

Exponential functions are essential in understanding various natural phenomena, from population growth to radioactive decay, and they play a crucial role in the advancement of scientific research.The exponential function has several unique properties, such as exponential growth, where the function grows at an increasing rate as x increases. Additionally, the function has an asymptotic relationship with the x-axis, meaning it never actually touches the x-axis but gets infinitely close to it.

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Using the gradient of the curve given, the value of a is 6

The stationary point of a curve is a point where the slope of the curve is equal to zero. So, to find the value of a, we need to set the derivative of the curve equal to zero and solve for x.

dy/dx = 2(x + 3)^(1/2) - x

Setting this equal to zero, we have:

2(x + 3)^(1/2) - x = 0

Expanding the square root and rearranging, we get:

x = 2(x + 3)^(1/2)

Squaring both sides of the equation, we have:

x^2 = 4(x + 3)

Expanding the right side and rearranging, we have:

x^2 - 4x - 12 = 0

Using the quadratic formula, we can find the values of x that satisfy this equation:

x = [-(-4) ± √((-4)^2 - 4(1)(-12))] / 2(1)

x = [4 ± √(16 + 48)] / 2

x = [4 ± √64] / 2

x = [4 ± 8] / 2

So, the two possible values of x are:

x = 6, x = -2

Since we are looking for a positive value of x, the only solution that works is x = 6.

Therefore, the value of a is equal to 6.

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The scale of the blueprint is 1 in : 4 ft.

A map scale is the relationship between a distance on a map and the corresponding distance on the earth.

Given that, on a blueprint of a house, the kitchen is 5 inches long, the actual kitchen is 20 feet long, we are asked to find the scale of the blueprint.

Since, the kitchen in the map is 5 in long whereas n earth it is 20 ft long.

Therefore, the ratio =

5 in / 20 ft = 1 in / 4 ft

Hence, the scale of the blueprint is 1 in : 4 ft.

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The solution to the given differential equation is y = e⁽ˣ³⁾⁽²⁸ˣ ⁺ ᶜ⁾, where C is a constant.

To solve the first-order linear differential equation of the form y' + p(x)y = q(x), where p(x) and q(x) are functions of x:

Find the integrating factor (IF) = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾

Multiply both sides of the equation by the IF.

Apply the product rule to the left side and simplify the right side.

Integrate both sides with respect to x.

Solve for y.

Using this method, for the given equation:

y' - 3x²y = 28e⁽ˣ³⁾

Find the integrating factor (IF):

IF = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾ = e⁽⁻³/¹ * ∫ˣ²ᵈˣ⁾ = e⁽⁻ˣ³⁾

Multiply both sides by the IF:

e⁽⁻ˣ³⁾y' - 3x²e⁽⁻ˣ³⁾y = 28

Apply the product rule to the left side and simplify the right side:

d/dx (e⁽⁻ˣ³⁾y) = 28

Integrate both sides with respect to x:

e⁽⁻ˣ³⁾)y = 28x + C, where C is the constant of integration.

Solve for y:

y = e⁽ˣ³⁾(28x + C)

Therefore, the solution to the given differential equation is y = e⁽ˣ³⁾(28x + C), where C is a constant.

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Complete question:

How to solve the first order linear differential equation

Y'- 3x²y=28eˣ³

The answer to the equation (5+12i) + (7-5i) is found to be 12-7i.

The provided equation is a simple algebraic relation between two complex numbers.

The given complex numbers are 5+12i and 7-5i.

We have to add these two complex numbers.

We will add the real part of the complex number to the real part and complex part of one complex number to the complex part of the complex number.

Sum of number = (5+12i) + (7-5i)

Sum of number = 12-7i

The sum of the two complex numbers is also complex number that has a real part has 12 and the imaginary or the complex part as -7.

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Answer:

1. The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle. To find the area of the 12" pizza, we first need to find the radius:

r = 12 / 2 = 6 inches

The area of the pizza is then:

A = πr^2 = π * 6^2 = 36π square inches

2. To find the radius of a pizza that is 25% larger, we can first find the amount by which the radius will increase:

increase = 6 * 0.25 = 1.5 inches

The new radius will then be:

new_r = 6 + 1.5 = 7.5 inches.

Step-by-step explanation:

Answer:

113.1, 8

The equation to find the area of a circle is:

Now we can input 12 into the equation:

To find the radius of a pizza that is %25 larger, we can use this equation:

Well, that's a good question! If we were to multiply by 0.25, the radius would get smaller, instead of bigger. We add the 1.0 because we have to add the original radius, not just the added length.

Fitting the radius into the equation:

Therefore, the area of the pizza is 113.1, and the radius of a pizza that is %25 larger is 8.