Milly bakes cookies to sell for a fundraiser. Her goal is to raise $500. The first day, she reaches 38 of her goal. On the second day, she raises 50% of the remaining money needed to meet her goal. How much money does Milly still need to make to reach her goal?

To find first-order linear differential equations solution, we have to derive the general form or representation of the solution.

With the help of the steps shown below, we can learn how to solve the first-order differential equation.

1. Reorder the terms in the given equation so that they have the form [tex]$\frac{dy}{dx}+Py=Q[/tex] where P and Q are constants or functions of the independent variable x only.

2. Integrate P (obtained in step 1) with respect to x and then put this integral as a power of e to determine the integrating factor.

[tex]$e^{\int P d x}[/tex] = IF

3. The linear first-order differential equation's two sides should be multiplied by the IF.

4. The L.H.S of the equation is always a derivative of [tex]$y \times M(x)$[/tex] i.e. L.H.S [tex]$= \frac{d(y \times I . F)}{dx}[/tex]

[tex]$d(y \times I . F) d x=Q \times I . F$[/tex]

5. In order to arrive at the solution, we simply integrate both sides with respect to x in the last step.

Therefore [tex]y \times I . F=\int Q \times I . F d x+C$,[/tex]

where C is some arbitrary constant

Similarly, we can also solve the other form of linear first-order differential equation [tex]$\frac{dy}{dx}+Py=Q[/tex] using the same steps.

P and Q are y's functions in this manner. We determine the solution, which will be, by using the integrating factor (I.F), which is

[tex]$(x) \times(I . F)=\int Q \times I . F d y+c$[/tex]

Now, to get a better insight into the linear differential equation, let us try solving some questions. where C is some arbitrary constant.

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Answer:

  A - scatter plot; it would show the relationship

Step-by-step explanation:

You want to determine if a scatter plot or line graph is a more appropriate way to represent the relationship between a manatee's weight and height.

The variables of concern in the data are weight and height. Time is not involved. (Eliminates choices B and D.)

It seems likely there may not be a functional relationship between weight and height. That is, manatees of the same weight may have different height, and vice versa. This suggests a line graph would not be a useful way to represent the relationship

A scatter plot in this case would be used to relate weight on one axis to height on the other axis. Any relationship between them would show up as grouped data points, or data points that generally fall on a line or curve.

Since the "marine biologist [is] interested in seeing the relationship between a manatee's weight and height", ...

  A scatter plot [is more appropriate] because it would show the association or relationship between the two variables.

__

Additional comment

As is often the case, the wording of the answer that matches the wording of the problem statement tells you which answer is appropriate.

Answer:A scatter plot, because it would show the association or relationship between two variables

Step-by-step explanation:

Answer:

the answer is 38.5 feet

Step-by-step explanation:

divide 7 by two the multiply by 11

Answer: Let's use x to represent the cost of each topping. Then, the cost of a pizza with t toppings can be expressed as:

C = x * t + 15

We know that Kevin's pizza with 3 toppings cost $15.74, so we can write an equation using this information:

15.74 = 3x + 15

Solving for x, we get:

x = (15.74 - 15) / 3 = 0.74

So, each topping costs $0.74. Now we can use the information about Brian's pizza to check our answer:

14.49 = 2x + 15

Substituting x = 0.74, we get:

14.49 = 2 * 0.74 + 15

Which simplifies to:

14.49 = 1.48 + 15

This confirms that x = 0.74 is the correct cost for each topping. Therefore, the equation for the cost of a pizza as a function of the toppings ordered is:

C = 0.74t + 15

Step-by-step explanation:

Answer:

21.15  550 divided by 26 = 21.15.

Step-by-step explanation:

I did the work on my paper. =)

The quadrilateral is a trapezoid. The value of x is 5 by applying midsegment theorem for trapezoids.

The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

The side with length 21 units and 27 units are parallel to each other.

From the given diagram, the expression below is true:

5x-1 = (21 + 27)/2

2(5x - 1) = 21 + 27

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

x = 50/10

x = 5

Hence the value of x is 5

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The image of this question is probably this.

The standard form of the equation of the parabola with focus (0, 7) and the vertex at the origin is y = 1/28 x² + 7

A parabola is a symmetrical U-shaped curve that is defined by the set of all points that are equidistant to a fixed point, called the focus, and a straight line called the directrix. In a parabolic equation, the focus and the vertex are important points that determine the shape and position of the parabola.

In the case of the parabola with focus (0, 7) and the vertex at the origin (0,0), we can use the standard form of the equation of a parabola to write its equation. The standard form of a parabola is given by:

y = a(x - h)² + k

Where (h,k) is the vertex of the parabola and a is the coefficient that determines the direction and width of the parabola. To write the equation of this parabola, we need to find the value of a.

Since the focus is (0, 7) and the vertex is (0,0), we can use the formula:

a = 1/(4f)

Where f is the distance from the vertex to the focus. In this case, f = 7. Therefore, a = 1/(4 * 7) = 1/28.

Finally, we can substitute these values into the standard form to get the equation of the parabola:

y = 1/28 x² + 7

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The correct statement is -

company {R} charges less money for 1 hour of service compared to company {P}.

Given is that Limousine Company {P} charges a rental fee plus an additional charge per hour. The equation {y} = 50 + 30x shows the total cost. The cost to rent a limousine from Company {R} is shown below in the table as -

Time :   1       2        3         4       5

Cost : $100  $125  $150  $175  $200

We can write the unit charge for company {P} as -

{r₁} = $30

We can write the unit charge for company {R} can be calculated as -

{r₂} = (125 - 100)/(2 - 1)

{r₂} = $25

We can conclude -

company {R} charges less money for 1 hour of service compared to company {P}.

Therefore, the correct statement is -

company {R} charges less money for 1 hour of service compared to company {P}.

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Answer: I would say B.

Step-by-step explanation: why not pick B…..

Hope this help^^

The quadratic equation x² - 12x + 6 = 0 is factorized and the solution to the equations are x = 6 ± √30

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² - 12x + 6 = 0   be equation (1)

Now , to calculate the solution of x ,

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = 12 ± √ ( 144 ) - ( 24 ) / 2

x = 12 ± 2√30 / 2

x = 6 ± √30

Hence , the solutions to the equation are x = 6 + √30 or x = 6 - √30

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Spike-and-slab regression is a method used to model the relationship between a response variable and a set of predictor variables, and nonlinear constraints can be applied to the model to specify relationships between the predictor variables, such as monotonicity or convexity.

Spike-and-slab regression is a statistical method used to model the relationship between a response variable and a set of predictor variables, where the predictor variables are partitioned into two groups: a set of important predictors (spikes) and a set of unimportant predictors (slabs). Nonlinear constraints can be applied to the model to specify relationships between the predictor variables, such as monotonicity or convexity. These constraints can be used to enforce prior knowledge or assumptions about the relationships between the predictor variables, and can help to improve the accuracy and interpretability of the model. Examples of nonlinear constraints that can be used in spike-and-slab regression include the convexity constraint and the total variation penalty.

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Answer:

6.57+59=65.57 (I saw that 65.57 is not on there but that is the answer)

Step-by-step explanation:

Given:

[tex]2.19g+59[/tex] when [tex]g=3[/tex].

Substitute 3 into g.

[tex]2.19(3)+59[/tex]

Solve:

[tex]6.57+59=65.57[/tex]

The polynomial 6x³ - 8x⁴ + 5x + 12x² - 9 in standard form is -8x⁴ + 6x³ + 12x² + 5x - 9.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number.

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

Hence, let's write the polynomial in standard form as follows:

6x³ - 8x⁴ + 5x + 12x² - 9

Hence, in standard form,

6x³ - 8x⁴ + 5x + 12x² - 9 = -8x⁴ + 6x³ + 12x² + 5x - 9

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The age of the mammal hide is 3567 years

Radioactivity can be used to determine the age of rocks, minerals, and fossils through a method called radiometric dating. This method is based on the principle that certain isotopes of elements decay at a known rate over time, producing new isotopes. By measuring the relative amounts of the original parent isotope and the newly formed daughter isotope, scientists can determine how much time has passed since the rock, mineral, or fossil was formed.

0.70 = 1 * e^-0.0001t

Take the logarithm of both sides:

log0.70 = loge^-0.0001t

-0.1549 = -0.0001t * 0.43429

t = -0.1549 / (-0.0001 * 0.43429)

t = 3566.74

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6z-2z+4 4+2z-6z

4z+4 4-4z

No

Answer:

i think Pythagorean theorem

Step-by-step explanation:

c^2=a^2+b^2

Answer:

The answer to 19.32-23.5 is -4.18

The constant of variation for this relation is 10.

If y varies directly as x, we can write it as y = kx, where k is the constant of variation. This constant represents the relationship between x and y, and it determines how much y changes for a given change in x.

To find the constant of variation, we need to know the value of y and x. In this case, we are told that y is 12 when x is 1.2. Using this information, we can solve for k by dividing both sides of the equation by x:

y = kx

12 = k * 1.2

12 / 1.2 = k

k = 10

So the constant of variation is 10. This means that for every change of 1 in x, y will change by 10. In other words, if x increases by 1, y will increase by 10, and if x decreases by 1, y will decrease by 10.

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The answer to this is 50/12, which is not a whole number. She would need 5 shelves (you have to round up a number because 4 shelves would only be able to fit 48 books)

Answer: 5 shelves  

Step-by-step explanation: you times 12x4 which gives you 48 but you need all 50 so you add a extra shelve so the total shelves is 5

The correct statement regarding the similarity of the circles is given as follows:

A. Circle 1 is always similar to circle 2.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Two circles are similar when one circle is a dilation of the other circle, and in this problem, we have that:

Hence the two circles are always similar and option a is correct.

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Answer:

first

1/3 ÷ 4

we can use the kfc mode =

k= keep the first fraction the same

f= flip the division to multication

c=change the second fraction to it's inverse

the answer will be

1/3 ÷ 4

=1/3÷4/1

=1/3×4/1

= 4/3

Answer:

Step-by-step explanation:

3/4

Answer:

Hi dear !!

area of semicircle = πr²/2

=> 3.14× 6x6 /2

3.14× 6× 3

=> 56.52 cm².

area of rectangle= l x b = 13 x 12 = 169

total area = 169 +56.52 = 225.5 cm²

Answer:

Step-by-step explanation:

kaboom hope this helps

The volume of concrete is required to make the cylindrical tank is approximately 14 cubic meters.

Given that, external diameter = 10 m and an internal height = 3 m.

We know that, the volume of a cylinder is πr²h.

Volume of a tank with external dimensions = 3.14×5²×3

= 3.14×25×3

= 235.5 cm³

The walls and bottom of the tank are 30 cm thick

So, internal diameter = 1000-30 (10 m =1000 cm)

= 970 cm

= 9.7 m

= 4.85 m

Volume of a tank with internal dimensions = 3.14×4.85²×3

= 3.14×23.5225×3

= 221.58195 cm³

So, volume of concrete = 235.5-221.58195

= 13.91805

≈ 14 cm³

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Marisol keeps the account open for 12 years if Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.

It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.

Given that, Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.

Simple interest: SI = PRT

P = $5000

r = 5.75% = 0.0575

I = $8,450 - $5000 = $3450

3400 = 5000(0.0575[tex])^t[/tex]

t = 12 years

Thus, Marisol keeps the account open for 12 years if Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.

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Answer:

106.

Step-by-step explanation:

7^2 + [ 81 - (4 x 6)]        First work out the exponential:

= 49 + (81 - (4 * 6)]         Work out the expression in the inner parentheses:

= 49 + [81 - 24]              Work out the expression in the parenthes:      

= 49 + 57                       Add:

= 106.

Answer:

x = 4.5

Step-by-step explanation:

Using Pythagoras theorem,

Hyp² = Opp² + Adj²

From the question,

Hyp = 9

Adj = Opp

Since Adj = Opp

Let,

Adj = Opp = a

and,

Hyp = b

Therefore,

b² = a² + a²

9² = 2a²

Cancelling equal exponents,

2a = 9

a= 4.5

Answer:

19 and 12

Step-by-step explanation:

The rule is y = 2x - 1

If x = 10, y = 19 because 20 - 1 = 19

If y = 23, x = 12 because 24 / 2 = 12

Answer:

34

Step-by-step explanation:

Insert 3 in for x in the equation.

9(3) + 7

9*3 = 27

27 + 7 = 34

Answer: 34

Step-by-step explanation:

if x =3 the equation will become 9(3)+7

We multiply to get 27+7

Add to get 34

The radius and center of the translated circle are,

Radius = 7 units

Center = (10, - 2)

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The equation of circle is,

x² + y² - 18x + 8y + 48 = 0

Now, We can simplify the equation as;

x² + y² - 18x + 8y + 48 = 0

x² - 18x + 81 - 81 + y² + 8y + 16 - 16 + 48 = 0

(x - 9)² + (y + 4)² = 49

(x - 9)² + (y + 4)² = 7²

Hence, The radius of circle = 7

And, Center = (9, - 4)

Let the center of circle after translated one unit right and two units down is, (h', k')

Hence, We get;

h' = 9 + 1 = 10

k' = - 4 + 2 = - 2

Thus, The equation of the translated circle is,

(x - 10)² + (y - (- 2))² = 7

Hence, the radius and center of the translated circle are,

Radius = 7 units

Center = (10, - 2)

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