Please, someone help me with this answer, I really would appreciate it so much. Show all work. Recall the formula: A = P(1 + 2)² nt Mark invests $7,938 in a retirement account with a fixed annual interest rate of 2% compounded semiannually. What will the account balance be after 19 years​

Answer:

Brief description of the functions of brain cells, blood cells, and muscle cells.

Brain cell (Neuron):

Blood cell (Erythrocyte, Leukocyte, and Platelet):

Muscle cell (Myocyte):

The equation of line B passing through (0,1) and (-1,0) is y = x + 1.

To find the equation of a line, we can use the slope-intercept form, which is given by y = mx + c, where m represents the slope of the line and c represents the y-intercept.

First, let's calculate the slope (m) using the given points (0,1) and (-1,0):

m = (y2 - y1) / (x2 - x1)

= (0 - 1) / (-1 - 0)

= -1 / (-1)

= 1

Now that we have the slope (m = 1), we need to find the y-intercept (c). We can substitute the coordinates of one of the given points into the equation y = mx + c and solve for c.

Using the point (0,1):

1 = 1(0) + c

c = 1

Therefore, the equation of line B passing through (0,1) and (-1,0) is:

y = 1x + 1

or

y = x + 1

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Answer:

4(2x - 1) + 3(2x + 5)

Step-by-step explanation:

4(2x - 1) + 3(2x+5)

Multiply 4 with 2x - 1 and multiply 3 with 2x + 5,

8x - 8 + 6x + 15 = 0

Arrange x and constant,

8x + 6x = 8 - 15

14x = - 7

14x = - 7

x = -7/14

x = -1/2

x = -0.5

Hope this helps! Recheck the answers.

The question is referring to two functions: h(x) and g(x).

The specific functions h(x) and g(x) are not given in the information provided, but we are given the equation of g(x) as -x^2 - 2x + 6. Without knowing the equation of h(x) or having a visual comparison of the functions, we cannot directly compare them.

The question is asking for the correct statement regarding the comparison between h(x) and g(x).

The answer choices are discussing the maximum value and the value at x=3 for both h(x) and g(x).

To identify the maximum of h(x) and g(x), we need either the equations of the functions or a visual representation of their graphs. Without this information, we cannot determine the maximum values.

Similarly, without knowing the equations of the functions or having a graph, we cannot identify the values of h(x) and g(x) at x=3.

Based on the lack of information provided to make direct comparisons between h(x) and g(x), it is not possible to determine the correct answer choice.

Answer: mi = 52 x h or y = 52 times x

distance (mi) = y

time (h) = x

It goes 52 miles per hour!  Hope this helps.

Hey there!

5!

= 5(4)(3)(2)(1)

= 20(3)(2)(1)

= 60(2)(1)

= 120(1)

= 120

Therefore, your answer should be: 120

7!

= 7(6)(5)(4)(3)(2)(1)

= 42(5)(4)(3)(2)(1)

= 210(4)(3)(2)(1)

= 840(3)(2)(1)

= 2,520(2)(1)

= 5,040(1)

= 5,040
Therefore, your answer should be: 5,040

9!
= 9(8)(7)(6)(5)(4)(3)(2)(1)

= 72(7)(6)(5)(4)(3)(2)(1)

= 504(6)(5)(4)(3)(2)(1)

= 3,024(5)(4)(3)(2)(1)

= 15,120(4)(3)(2)(1)

= 60,480(3)(2)(1)

= 181,440(2)(1)

= 362,880(1)

= 362,880

Therefore, your answer should be: 362,880

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The side length of the leg of the special right triangle is equal to 7√2 / 2 units.

In this problem we find the case of special right triangle known as 45° - 90° - 45° triangle, where internal angles are 45°, 90° and 45° and whose side relationship is shown below:

r = √2 · x = √2 · y

Where:

If we know that r = 7, then the side length of the leg is:

x = y = √2 · r / 2

x = y = √2 · 7 / 2

x = y = 7√2 / 2

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Based on the given information, the fair conclusion would be:

C. The current stock price is up for the day by 0.38%.

The statement mentions that the stock price is up for the day, which is indicated by the positive change of 0.27 (+0.38%).

The gravitational force between two planets of equal mass that were abruptly moved from a distance of 1 million miles to a distance of 2 million miles would be only one-fourth as strong as it had been before.

True. The gravitational force between two masses is inversely proportional to the square of their separation, as stated by Newton's law of universal gravitation.

The gravitational attraction between two planets of the same mass would drop by a factor of 1/22 or 1/4 if the distance between them increased from 1 million miles to 2 million miles.

As a result, the gravitational force would be reduced to 1/4 of what it was before.

Therefore, the gravitational attraction between two planets of the same mass would drop by a factor of 1/4 (or 1/22) if their separation doubled (from 1 million miles to 2 million miles).

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The Sample space, a clear set of possible outcomes for choosing one card from the set.

The sample space for choosing one card from a set of 10 labeled cards, where each card is labeled with an expression, would consist of all the possible outcomes of this selection process.

Since there are 10 cards in the set, the sample space would consist of the individual expressions labeled on each card. Let's assume the expressions on the cards are labeled as follows:

Card 1: Expression 1

Card 2: Expression 2

Card 3: Expression 3

...

Card 10: Expression 10

{Expression 1, Expression 2, Expression 3, ..., Expression 10}

This sample space represents all the possible outcomes when selecting one card from the set. Each outcome corresponds to one specific expression labeled on a card.

the sample space only includes the individual expressions and not any particular order or arrangement of the cards. The order of the expressions does not matter in this case, as the focus is solely on the expressions themselves.

the sample space, we establish a clear set of possible outcomes for choosing one card from the set.

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Answer:

9

Step-by-step explanation:

3x^2 + 3x - 9

Substitute x = 2 into the equation.

3(2)^2 + 3(2) - 9

3(4) + 6 - 9

12 + 6 - 9

18 - 9 =

9

Answer: 59/16 or 3 11/16

Step-by-step explanation:

11 4/5 ÷ 3 1/5

= 59/5  ÷ 16/5

= 59/5 x 5/16

= 59 x 5/ 5 x 16

= 295/80

= 295 ÷ 5/ 80 ÷ 5

= 59/16

= 3 11/16

Answer:

(a) - [tex]\sin(y)=-3\cos(x)+4[/tex]

(b) - [tex]y=e^{2x-1}[/tex]

Step-by-step explanation:

Given the two part question...

(a) - Solve the following first-order differential equation with the given initial condition.

[tex]y'=\frac{3\sin(x)}{\cos(y)}; \ y(0)=\frac{\pi}{2}[/tex]

(b) - Given that y=f(x) passes through the point (1,e) and has the property that the slope of the tangent line to the graph at any point "P" is equal to twice the y-coordinate of "P." Find f(x).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Part (a) -

The given DE is a separable differential equation and can be solved in the following manner.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Seperable Differential Equation}}\\\frac{dy}{dx}=f(x)g(y) \\ \rightarrow \int\frac{dy}{g(y)}=\int f(x)dx \end{array}\right}[/tex]

[tex]y'=\frac{3\sin(x)}{\cos(y)} \rightarrow \frac{dy}{dx} =\frac{3\sin(x)}{\cos(y)}\\\\\Longrightarrow \cos(y)dy=3\sin(x)dx\\\\\Longrightarrow \int\cos(y)dy=3\int\sin(x)dx\\\\\Longrightarrow \boxed{\sin(y)=-3\cos(x)+C}\\\\\text{Now for the given initial condition to find the arbitrary constant, "C."}\\\text{Initial condition} \longrightarrow y(0)=\frac{\pi}{2} \\\\\Longrightarrow \sin(\frac{\pi}{2})=-3\cos(0)+C\\\\\Longrightarrow 1=-3(1)+C\\\\\Longrightarrow \boxed{C=4}\\\\[/tex]

[tex]\therefore \boxed{\boxed{\sin(y)=-3\cos(x)+4}}[/tex]

Thus, the DE is solved.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Part (b) -

[tex]\text{The slope of the tangent line =} \ \frac{dy}{dx} \\\\\text{According to the question, the slope of the tangent line =} \ 2y\\\\\text{So we can say,}\\\\\longrightarrow \boxed{\frac{dy}{dx}=2y} \ \text{Solve the DE}[/tex]

[tex]\frac{dy}{dx}=2y\\\\\Longrightarrow \frac{dy}{2y}=dx \\\\\Longrightarrow \frac{1}{2} \int\frac{dy}{y}=\int dx\\\\\Longrightarrow \frac{1}{2} \ln(y)=x+C\\\\\Longrightarrow \boxed{\ln(y)=2x+ \bar C}[/tex]

Use the given initial condition to find "C." y(e)=1

[tex]\Longrightarrow \ln(e)=2(1)+ \bar C\\\\\Longrightarrow 1=2+ \bar C\\\\\Longrightarrow \boxed{C=-1}[/tex]

[tex]\Longrightarrow \ln(y)=2x+ \bar C\\\\\Longrightarrow \ln(y)=2x-1\\\\ \therefore \boxed{\boxed{ y=e^{2x-1}}}[/tex]

Thus, f(x) is found.

The missing coordinate to complete the ordered pair is (9). The ordered pair is (1, 9).

An ordered pair is a mathematical concept that consists of two elements, typically represented as (x, y), where x is the first element, also known as the x-coordinate, and y is the second element, also known as the y-coordinate.

It is also known as coordinates, the point (x, y) on a graph where x and y are real numbers.

If x + y = 10, then we can find the missing coordinate by substituting the given x-coordinate (1) into the equation, x + y = 10:

[tex]\sf x + y = 10[/tex]

[tex]\sf y = 10 - 1[/tex]

[tex]\sf y = 9[/tex]

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The solution is; 10 days for Soccer and, 14 days for Baseball camp, are needed to run each of the camps sessions .

Here, we have,

given that,

The Parks and Recreation Department is planning to host sports camps for students during the summer.

Option 1 is to have 8 Soccer and 1 Baseball camp sessions that would last 94 days altogether.

Option 2 has 3 Soccer and 5 Baseball camp sessions that would last 100 days.

now, let,

x days for Soccer and, y days for Baseball camp, are needed to run each of the camps sessions .

then, we have,

8x + y = 94 .....1

3x+ 5y = 100 .....2

solving we get,

equation 1 => 40x + 5y = 470

now, subtracting, we get,

37x = 370

so, x = 10

now, solving we get,

y = 14

Hence, The solution is; 10 days for Soccer and, 14 days for Baseball camp, are needed to run each of the camps sessions .

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The correct statement regarding the transformations is given as follows:

C) Reflection, then dilation results in an image that is not congruent to the original.

Examples of transformations are given as follows:

For the first transformation in this problem, the orientation of the figure is changed, hence it underwent a reflection.

For the second transformation, the figure was reduced, hence it underwent a dilation, meaning that the congruence was lost, as the side lengths are different.

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Arithmetic sequence and Geometric sequence a₁ is an integer, the numerator must be divisible by -21.

Let's denote the common difference of the arithmetic sequence as 'd' and the common ratio of the geometric sequence as 'r'.

Since a4, a7, and a12 form a geometric sequence, we can express the terms as follows:

a4 = a₁ + 3d

a7 = a₁ + 6d

a12 = a₁ + 11d

We know that a7 = 30, so we can substitute it into the equation:

a₁ + 6d = 30

Now, let's examine the ratio between consecutive terms in the geometric sequence:

(a7 / a4) = (a12 / a7)

Substituting the expressions for the terms, we get:

[(a₁ + 6d) / (a₁ + 3d)] = [(a₁ + 11d) / (a₁ + 6d)]

Cross-multiplying, we have:

(a₁ + 6d)(a₁ + 6d) = (a₁ + 3d)(a₁ + 11d)

Expanding the equation, we get:

a₁² + 12ad + 36d² = a₁² + 14ad + 33d²

Simplifying and rearranging terms, we obtain:

2ad = -3d²

Since the sequence is non-constant, the common difference 'd' cannot be zero. Therefore, we can divide both sides of the equation by 'd':

2a = -3d

Substituting the value of 'd' from the equation a₁ + 6d = 30, we have:

2a = -3(a₁ + 6d)

Expanding and simplifying:

2a = -3a₁ - 18d

Now, we can substitute the value of 'd' from the equation a₁ + 6d = 30:

2a = -3a₁ - 18(a₁ + 6d)

Expanding and simplifying further:

2a = -3a₁ - 18a₁ - 108d

Since a₁ + 6d = 30, we can substitute it again:

2a = -3a₁ - 18a₁ - 108(a₁ + 6d)

Expanding and simplifying:

2a = -3a₁ - 18a₁ - 108a₁ - 648d

Combining like terms:

2a = -129a₁ - 648d

Now, we can substitute the known value of a₇ = 30 into the equation a₁ + 6d = 30:

a₁ + 6d = 30

Rearranging the equation:

a₁ = 30 - 6d

Substituting this into the previous equation:

2a = -129(30 - 6d) - 648d

Expanding and simplifying:

2a = -3870 + 774d - 648d

Combining like terms:

2a = -3870 + 126d

Now, we can substitute the value of 2a = -3a₁ - 18a₁ - 108d into the equation:

-3a₁ - 18a₁ - 108d = -3870 + 126d

Expanding and simplifying:

-21a₁ - 108d = -3870 + 126d

Rearranging the equation:

-21a₁ = 234d - 3870

Dividing both sides by -21:

a₁ = (234d - 3870) / -21

Since arithmetic sequence and geometric sequence a₁ is an integer, the numerator must be divisible by -21

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To calculate the amount of money in the account after 1 year, we can use the following formula:

A = P(1 + r/n)^nt

Where:

Plugging in the given values, we get:

A = 500(1 + 0.05/4)^4*1

A = 500(1.0125)^4

A = $515.63

Therefore, after 1 year, the account will have $515.63.

The reasoning for the third step of the proof would be "Corresponding parts of congruent triangles are congruent." Let's go through the explanation:

1. Given: Quadrilateral ABCD is a rectangle.

2. Given: AB & CD (Opposite sides of a rectangle are equal).

3. To prove: AC & BD.

To prove that AC is equal to BD, we can utilize the property that opposite sides of a rectangle are equal (step 2). In a rectangle, opposite sides are parallel and congruent. Therefore, we have AB || CD and AB = CD.

Now, we need to show that the triangles ABAD and ACDA are congruent, specifically using the SAS (Side-Angle-Side) congruence theorem. The congruence of these triangles will allow us to establish the equality of their corresponding parts, including AC and BD.

4. Given: AD = AD (Reflexive Property of Equality).

5. By step 2, we know AB = CD. Additionally, AD = AD is given (Reflexive Property of Equality).

6. By step 3, ZBAD = ZCDA.

7. Using SAS triangle congruence theorem, we can conclude that triangles ABAD and ACDA are congruent.

Finally, according to the "Corresponding parts of congruent triangles are congruent" property, we can state that AC = BD. This establishes the equality of the diagonals of the rectangle.

Therefore, the correct reasoning for step 3 is "Corresponding parts of congruent triangles are congruent."

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The Shares for the other teams are indeed 12, 9, and 6, respectively,  confirms that the solution is correct,there were 8 red balls.

The problem step by step. We are given the following information:

1. The total number of balls is 35.

2. One team takes all the red balls.

3. The remainder (non-red balls) is shared among the other teams in the ratio 4:3:2.

4. The smallest share is 6 balls.

Let's assume the number of red balls is "r". Therefore, the number of non-red balls is 35 - r.

According to the ratio, the shares for the other teams are:

Team 1: (4/9) * (35 - r)

Team 2: (3/9) * (35 - r)

Team 3: (2/9) * (35 - r)

Given that the smallest share is 6 balls, we can set up the equation:

(2/9) * (35 - r) = 6

To solve this equation, we can simplify and solve for "r":

(35 - r) = (9/2) * 6

35 - r = 27

r = 35 - 27

r = 8

Therefore, there were 8 red balls.

To verify the solution, we can calculate the shares for the other teams:

Team 1: (4/9) * (35 - 8) = 4 * 27/9 = 12

Team 2: (3/9) * (35 - 8) = 3 * 27/9 = 9

Team 3: (2/9) * (35 - 8) = 2 * 27/9 = 6

The shares for the other teams are indeed 12, 9, and 6, respectively, which confirms that the solution is correct.

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The equation that satisfies the data in the table is: A. y = 2/15(x) + 2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 - 0)/(0 + 15)

Slope (m) = 2/15

At data point (0, 2) and a slope of 2/15, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 2/15(x - 0)  

y = 2/15(x) + 2.

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Step-by-step explanation:

angle x =   180 - 90 - 60   degrees     ( because the anglse of atriangle add to 180 degrees)

x = 30 degrees

The characteristic of the researcher having direct control over at least one variable to both surveys and Observational .

The option that is not a characteristic of both surveys and observational studies is:

a. The researcher has direct control over at least one variable.

Surveys and observational studies have several characteristics in common, such as collecting data about a population and not proving cause and effect. However, the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies.

In a survey, the researcher collects data by asking questions to individuals or groups. They do not have direct control over the variables being studied but rather collect information based on participants' responses. The researcher's role is primarily in designing the survey, selecting the sample, and analyzing the data.

In an observational study, the researcher observes and records data without intervening or manipulating any variables. The researcher does not have control over the variables being observed; instead, they observe and document the existing conditions or behaviors.

the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies. Both methods involve data collection about a population and do not establish cause and effect relationships, but control over variables is not a shared characteristic.

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The total surface area required to wrap the 15 cubed-shaped gift boxes is 3.6 square meters.

To calculate the total surface area of 15 cubed-shaped gift boxes, we need to find the surface area of one gift box and then multiply it by the total number of boxes.

The surface area of a cube can be calculated using the formula:

Surface Area = 6 * [tex](side length)^2[/tex]

Given that the length of each side of the cube-shaped gift box is 20 cm, we can substitute this value into the formula:

Surface Area of one gift box = 6 * (20 cm)^2

= 6 * [tex](400 cm^2)[/tex]

= 2400 [tex]cm^2[/tex]

Since we have 15 gift boxes, we multiply the surface area of one gift box by 15:

Total Surface Area = Surface Area of one gift box * Number of gift boxes

= 2400 [tex]cm^2 * 15[/tex]

= 36000 [tex]cm^2[/tex]

Now, we need to convert the area from square centimeters [tex](cm^2[/tex]) to square meters [tex](m^2).[/tex] There are 10000 square centimeters in a square meter:

Total Surface Area in square meters = Total Surface Area in square centimeters / 10000

= 36000 [tex]cm^2[/tex] / 10000

= 3.6[tex]m^2[/tex]

Therefore, the total surface area required to wrap the 15 cubed-shaped gift boxes is 3.6 square meters.

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The equation for the instantaneous velocity, v(t), of the bumblebee at any point in time is v(t) = 12 - 18t²

To find the equation for the instantaneous velocity of the bumblebee at any point in time, we need to take the derivative of the distance function, p(t), with respect to time (t).

Given that p(t) = 12t - 6t³ + 1, we can find the derivative using the power rule of differentiation.

Derivative of p(t) with respect to t:

p'(t) = d/dt (12t - 6t³ + 1)

= 12 - 18t²

Therefore, the equation for the instantaneous velocity, v(t), of the bumblebee at any point in time is:

v(t) = 12 - 18t²

That the velocity function v(t) is the derivative of the distance function p(t).

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The value of probability P (A or B) is,

⇒ P (A or B) = 48

We have to given that,

The Venn diagram of the probability is shown in image.

Now, By given diagram,

⇒ P (A) = 24 + 14

⇒ P (A) = 38

⇒ P (B) = 24 + 10

⇒ P (B) = 34

⇒ P (A and B) = 24

We have to given that,

The expression is,

P (A or B) = P (A) + P (B) - P (A and B)

Substitute all the values, we get;

P (A or B) = 38 + 34 - 24

P (A or B) = 48

Thus, The value of probability P (A or B) is,

⇒ P (A or B) = 48

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