Giai PT: xy'=y+xe^{\frac{y}{x}}

Answer:

Step-by-step explanation:

The balance after 3 years can be calculated as follows:

I = P * r * t

Where:

I = interest

P = principal amount (2200)

r = interest rate (0.0295)

t = time in years (3)

So,

I = 2200 * 0.0295 * 3

I = 153.1

The final balance would be:

P + I = 2200 + 153.1

P + I = 2353.1

The final balance after 3 years is $2353.1, which is closest to option B ($2,329.80).

Answer:

x * 2.54 = centimeters

Step-by-step explanation:

The equation to convert inches to centimeters is as follows:

x inches * 2.54 cm/inch = y centimeters

Where x is the number of inches and y is the equivalent length in centimeters.

To elaborate, the conversion factor between inches and centimeters is 2.54 cm/inch, meaning that for every inch there are 2.54 centimeters. To convert from inches to centimeters, we simply multiply the number of inches by the conversion factor. This gives us the equivalent length in centimeters.

Answer:

Cosine (cos)

Step-by-step explanation:

Sine, Cosine, and Tangent have their own properties.

Cosine is adjacent over hypotenuse. We have the angle of 59, the line adjacent is 17 and the hypotenuse is x. You could also do it for the right angle.

The Proof of ( x + h)² +( y + h)²  =  (a + b)² is shown below.

In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.

Given:

BHC and BCA are similar

HC / BC = CA / BA    

so, h / a  =  b / ( x + y) ........... (1)

Working with your expansion

x² + h²  = a²  and

y² + h²  = b²

So, subtracting out the equal parts we are left with

2xh  + 2yh   =  2ab ..........(3)    divide through by 2

xh + yh  = ab    

h( x + y) = ab  which we can rearrange as

h / a   =  b / ( x+ y)..............(2)

Since this is equal to (1) and it's just a rearrangement of (3) adding all the other equal parts of the expansion shows that

(x² + h²) + (y² + h²) + ( 2xh + 2yh) =  a²+ b²+ 2ab

( x² + 2xh + h²) + ( y² + 2yh + h²)  =  ( a + b)²

( x + h)²   +  ( y + h)²  =  (a + b)²      

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As a result, the original discounted price is $1 while the weekly normal price is $9.

The fundamental formula for calculating a reduction is to increase the initial price by the provided percentage rate in decimal form. We must deduct the reduction from the initial price to determine the item's sale price.

From the given information, we have:

d + 6x = 55 (discounted price for 7 weeks)

d + 11x = 100 (discounted price for 12 weeks)

We can solve this system of equations by eliminating d. Subtracting the first equation from the second, we get:

5x = 45

Dividing both sides by 5, we get:

x = 9

Substituting x = 9 into one of the equations, we can solve for d. Using the first equation, we get:

d + 6(9) = 55

d + 54 = 55

d = 1

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Answer: 3y + 2

Step-by-step explanation: First, you can organize the equation into -3y + 6y + 4 - 2. Then, you get 3y + 2. :)))))

The equation expressing the statement is A = k/r, where k is the constant of proportionality. Given that r = 3 and A = 7, the constant of proportionality can be found by rearranging the equation to k = A × r and substituting the given values to calculate: k = 7 × 3 = 21.

The statement "A varies inversely as r" can be expressed mathematically as an equation: A = k/r, where k is the constant of proportionality. This equation states that A is proportional to 1/r, meaning that as r increases, A decreases, and as r decreases, A increases. To find k, we can rearrange the equation to k = A × r and substitute the given values. In this case, if r = 3 and A = 7, then k = 7 × 3 = 21. Therefore, the constant of proportionality is 21. This equation can be used to determine the values of A, given a value of r, or the values of r, given a value of A. For example, if r = 4, then A = k/4 = 21/4 = 5.25. Conversely, if A = 10, then r = k/A = 21/10 = 2.1. This equation can be used to determine the values of A and r for any given situation.

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Based on the information in the table, a graph can be created to relate the number of Supply Dolls and Demand Dolls with respect to the sale value.

To create a graph with the information in the table, we must identify what information should go on the x-axis and the y-axis. In this case, we are being asked to locate the sale value on the x axis and on the y axis we must locate the number of units supplied and demanded.

Based on this information, we can infer that at a lower sale price, more dolls are demanded, but not as many are supplied. On the contrary, when the price is higher ($4.00) more dolls are supplied but not as many are demanded. This means that the relationship is inversely proportional.

Note: This question is incomplete because there is some misinformation. Here is the complete information:

Task.

Joan King is marketing director for the BurgeRama restaurant chain. BurgerRama has decided to have a cartoon-character doll made to sell at a premium price at participating BurgerRama locations. The company can choose from several different versions of the doll that sell different prices. King's problem is to decide which selling price will best suit the needs of BurgerRama's customers and store managers. King has data from previous similar promotions to help her make a decision.

1. Use the data from the table above to plot points representing selling price and supply price on a graph. (Selling Price of Each Doll should appear on the x-axis, and Number of Dolls Per Week per Store should appear on the y-axis). Draw the line through the data points and write the word "Supply on this line.

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95% CI for the true posttreatment self-esteem score is:

(24.47, 28.73)

The formula for calculating a 95% confidence interval for the mean self-esteem score is as follows:

(standard deviation/square root of sample size) * (mean (critical value)

The standard deviation of a set of data is a measure of its spread or dispersion. It denotes the average deviation of individual values in a data set from the data set's mean.

A low standard deviation indicates that the data points are close to the mean, whereas a high standard deviation indicates that the data points are scattered across a wide range.

For a normal distribution and a 95% confidence level, the critical value is 1.96.

As a result, the 95% confidence interval for the mean posttreatment self-esteem score is as follows:

26.6 ± 1.96 * (7.4/sqrt(21)) = 26.6 ± 2.13

As a result, the 95% CI for the true posttreatment self-esteem score is:

(24.47, 28.73)

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Answer:

Step-by-step explanation:

A function is the inverse of another function if it "undoes" the original function. In other words, if you apply the original function to an input and then apply the inverse function to the result, you get the original input.

To find the inverse of a function, you can swap the input and output values of the original function, and then solve for the new input variable. For example, if the original function is f(x) = y, the inverse function would be f^-1(y) = x.

Given the function f(x) = -2, 3, 8, 13, it is not possible to find a simple algebraic inverse function for the given values of x = -1, 0, 1, 2. The inverse of a function is only well-defined if the function is one-to-one, meaning that for every output value, there is only one input value that maps to it. In this case, the function does not appear to be one-to-one, so it does not have an inverse function.

Answer:

3a^2

Step-by-step explanation:

one way of answering this question is by finding the area of the whole shape, including the non-shaded shape, then taking away the area of the non-shaded shape from the whole thing, leaving you the area of the shaded shape

Step-by-step

find the area of the whole shape

2a x 2a

= 4a^2 (or 4a to the power of 2)

Now that we have the area of the whole shape, we must find the area of the non-shaded shape and take it away from 4a^2, we do this by

a x a

= a^2 (or a to the power of 2)

now we minus the non-shaded shape away from the total area

4a^2 - a^2

= 3a^2 (or 3a to the power of 2)

The size of angle BAC in the given circle is 50°

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Since, no figure is given, we will draw a circle according the given information, [attached in the solution]

So, we get a circle with center O, having chords, BC, which is extended to F, DC and AB,

We have, Angle CBD = 28° and angle FCD = 78°

Therefore,

∠ DCB = 180° - ∠ DCF [Linear pair]

∠ DCB = 180° - 78°

∠ DCB = 102°

In Δ DCB,

∠ DCB + ∠ BCD + ∠ BDC = 180°

∠ BDC = 180° - (102°+28°)

∠ BDC = 50°

Since, the angles made by the same chord are equal in measure,

Therefore,

∠ BDC = ∠ BAC

Therefore,

∠ BAC = 50°

Hence, the size of angle BAC in the given circle is 50°

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Answer:

the number is 78

Step-by-step explanation:

call x is the tens digit (0<x<9)

y is the unit digit (0[tex]\leq[/tex]y[tex]\leq[/tex]9)

we have:

10y+x=[tex]\oveline{yx}[/tex] (1)

10x+y= [tex]\overline{xy}[/tex] (2)

acording (1),(2) and the topic we have: (10y+x)-(10x+y)=9 ⇔9y-9x=9

⇔y-x=1 (3)

and x+y=15 (4)

from (3), (4) we have a system of equation

[tex]\left \{ {{y-x=1} \atop {x+y=15}} \right.[/tex]

⇔[tex]\left \{ {2y=16} \atop {x+y=15}} \right.[/tex]

⇔[tex]\left \{ {{y=8} \atop {x+8=15}} \right.[/tex]

⇔[tex]\left \{ {{y=8} \atop {x=7}} \right.[/tex] (conditions are satified)

the number is 78

Answer:

4^5 = 1024

Step-by-step explanation:

An equation of the best-fit line of data can be used to estimate untested values. Graphical data can be used to show relationships between variables, but those relationships do not have to be linear and do not always have a positive relationship.

Graphical data is a way of visually representing information in a way that can be easily understood. It is often used to determine relationships between variables, such as the relationship between prices and sales. Graphical data can be used to show correlations, even if the relationship is not linear. An equation of the best-fit line of data can be used to estimate untested values, which can be useful in predicting future values. The x-values and y-values of a graph can both be estimated based on the data presented, and do not necessarily need to start at the origin. Graphical correlations can have both positive and negative relationships, depending on the data presented. Graphical data can be a powerful tool for understanding relationships between data points.

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The unit rate for the games per loss are:

Jules’ Rules unit rate = 3 or 3/1

Pink sox unit rate = 4 or 4/1

Go - Girl unit rate = 4 or 4/1

High- 5s unit rate = 9 or 9/1

Unit rate = Games/Losses

Jules’ Rules unit rate = 36/12

Jules’ Rules unit rate = 3 or 3/1

Pink sox unit rate = 68/17

Pink sox unit rate = 4 or 4/1

Go- Girls unit rate = 52/13

Go - Girl unit rate = 4 or 4/1

High-5s unit rate = 72/8

High- 5s unit rate = 9 or 9/1

Therefore the Jules’ Rules unit rate 3, Pink sox unit rate 4, Go - Girl unit rate 4, High- 5s unit rate 9.

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Answer: 101.6

Since we are trying to find the sides of both the triangles, we will need to use the Sin, Cos, & Tan trigonometry functions. There are 3 equations:

[tex]Sin (Angle) = \frac{Opposite}{Hypotenuse} \\Cos (Angle) = \frac{Adjacent}{Hypotenuse} \\Tan (Angle) = \frac{Opposite}{Adjacent}[/tex]

For this triangle shown in the picture, we can infer that the 88 is OPPOSITE to the 60° and 30° angles. So we already have the opposite, and since we are trying to find the adjacent, we will use the formula that consists both opposite and adjacent, which is the following:

[tex]Tan(Angle) = \frac{Opposite}{Adjacent}[/tex]

Since [tex]x[/tex] is only a part of the long triangle, we will subtract the small triangle's side from the big one, which will give us [tex]x\\[/tex].

We can input our values to solve each triangle's side lengths.

(You have to use the calculator for these)

Small one:

[tex]Tan(60) = \frac{88}{Adjacent}\\Adjacent = \frac{88}{Tan(60)}\\Adjacent = \frac{88\sqrt{3} }{3} = 50.807 (3 d.p)[/tex]

Big one:

[tex]Tan(30) = \frac{88}{Adjacent} \\Adjacent = \frac{88}{Tan(30)} \\Adjacent = 88\sqrt{3} = 152.420 (3d.p)[/tex]

Now, to calculate [tex]x[/tex] , we will subtracat the small one from the big one like this: (it is better to input the values with the surds and not the real numbers for accurate marks and calculations)

[tex]88\sqrt{3} - \frac{88\sqrt{3} }{3} = 101.6 (1 d.p)[/tex]

That is the answer. If you did not understand it completely, please reach me back and I will help you :)

Answer:

$400

Step-by-step explanation:

Here is my crack at it:

To find Heather's weekly salary, we can set up an equation using the information given. Let's call Heather's weekly salary "x".

According to the problem, $20 is 5% of her salary, so we can write this as an equation:

$20 = 0.05x

Now we can solve for x by dividing both sides by 0.05:

x = 400$

So Heather's weekly salary was $400.

Heather’s weekly salary would be 400$.  

If heather saved $20 a week. This was 5% of her salary. Heather’s weekly salary would be

Given, $20 = 5%

As we know, the total salary will be 100 %

If 5% = $20

then, 100% = $400 (multiplying both the sides by 20)

Thus, Heather’s weekly salary was 400$.

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The other endpoint of the line segment is (13.8, 6).

The midpoint of a line segment is the point that lies exactly halfway between the two endpoints.

In this case, we have one endpoint, (6.9), and the midpoint (0,-6). Here is how we find the other endpoint:

To find the other endpoint, we need to subtract the midpoint from the given endpoint and then multiply by 2. The midpoint formula is given by:

M = (x1 + x2) / 2 and (y1 + y2) / 2

Where M is the midpoint, (x1, y1) and (x2, y2) are the coordinates of the two endpoints.

So, in our case, the other endpoint will be given by:

(x2, y2) = 2 * (6.9, 0) - (0, -6)

Expanding the expression, we get:

x2 = 2 * 6.9 - 0 = 13.8

y2 = 2 * 0 - (-6) = 6

Therefore, the other endpoint of the line segment is (13.8, 6).

Complete question:

Find the other end point of the line segment with the given endpoint and midpoint endpoint: (6.9), midpoint (0,-6)

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Answer:

3

28

Step-by-step explanation:

The expression (f/g) (4) is equal to f(4) / g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f/g) (4) = 21 / 7 = 3.

The expression (f + g) (4) is equal to f(4) + g(4).

f(4) = 4^2 + 2*4 - 3 = 16 + 8 - 3 = 21

g(4) = 4^2 - 9 = 16 - 9 = 7

So, (f + g) (4) = 21 + 7 = 28.

===========================================

Work Shown:

[tex](f+g)(\text{x}) = f(\text{x})+g(\text{x})\\\\(f+g)(\text{x}) = (\text{x}+3)+(\text{x}^2-2)\\\\(f+g)(\text{x}) = \text{x}^2+\text{x}+1\\\\(f+g)(2) = 2^2+2+1\\\\(f+g)(2) = 4+2+1\\\\(f+g)(2) = 7\\\\[/tex]

----------------------------

Another approach:

[tex]\begin{array}{lll}f(\text{x}) = \text{x}+3& & g(\text{x}) = \text{x}^2-2\\f(2) = 2+3 & \text{ and } & g(2) = 2^2-2\\f(2) = 5 & & g(2) = 2\\\end{array}\\\\\\\text{Therefore, } (f+g)(2) = f(2)+g(2) = 5+2 = 7[/tex]

The value for x vector is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

Given a vector v ∈ R² let (x, y) be its standard coordinates, i.e., coordinates with respect to the standard basis [tex]e_1=\left[\begin{array}{ccc}5\\-1\end{array}\right][/tex] and [tex]e_1=\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex].

The desired coordinates x, y satisfy -

v = xe1 + ye1

So, the vector v is -

[tex]v=2\left[\begin{array}{ccc}5\\-1\end{array}\right] +5\left[\begin{array}{ccc}-7\\-4\end{array}\right][/tex]

[tex]v=\left[\begin{array}{ccc}10\\-2\end{array}\right] +\left[\begin{array}{ccc}-35\\-20\end{array}\right][/tex]

[tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex]

Therefore, the matrix is [tex]v=\left[\begin{array}{ccc}-25\\-22\end{array}\right][/tex].

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The shaded region in the graph represents the possible solution sets to the inequality.

Given is the inequality -

x² + 15 ≥ 23

The given inequality is -

x² + 15 ≥ 23

Refer to the graph attached.

The shaded region represents the possible solution sets to the inequality above.

Therefore, the shaded region in the graph represents the possible solution sets to the inequality.

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The probability that the two tallest are in the same subgroup is given as follows:

2/n².

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

In this problem, we have that:

For each student, the probability of belonging to a group is given as follows:

1/n.

Hence the probability that the two tallest are in the same subgroup is obtained as follow:

2 x 1/n x 1/n = 2/n².

The multiplication by 2 is because there are two groups.

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Answer:

[tex]y=x-2[/tex]

Step-by-step explanation:

The slant, or oblique asymptote, is found by taking the quotient of the two polynomials and disregarding the remainder:

-3 |  1  1  2

____  -3_6

      1 -2 | 8

Hence, our slant asymptote is [tex]y=x-2[/tex]

Answer:For part (a), the overall percentage of American voters who say the government shutdown is a "very serious problem for the country" can be calculated as follows:

P(A) = 54% (probability of being a Democrat)

P(B|A) = 80% (probability of saying the shutdown is a "very serious problem" given that the person is a Democrat)

P(A and B) = P(A) * P(B|A) = 54% * 80% = 43.2%

P(B) = 35% (probability of saying the shutdown is a "very serious problem" for Republicans)

P(A|B) = (P(A and B) / P(B)) = (43.2% / 35%) = 123.14%

P(A or B) = P(A) + P(B) - P(A and B) = 54% + 35% - 43.2% = 45.8%

Therefore, the overall percentage of American voters who say the government shutdown is a "very serious problem for the country" is 45.8%.

For part (b), the 2x2 probability table can be set up as follows:

Serious Not serious Total

Democrat 43.2% 6.8% 50%

Republican 10.5% 35.5% 46%

Total 53.7% 42.3% 100%

Step-by-step explanation:

The length of a pendulum that makes one full swing in 1.9 seconds is 3 feet.

As per the given data, the given formula is:

[tex]$T=2 \pi \sqrt{\left(\frac{L}{32}\right)}[/tex] gives the time it takes in seconds.

Where,

T is the time it takes for a pendulum to make one full swing back and forth (in seconds).

L is the length of the pendulum, in feet.

Here we need to find the length of a pendulum that makes one full swing in 1.9 seconds to the nearest foot.

Substitute the given parameters into the formula will give;

[tex]$1.9=2 \pi \sqrt{\left(\frac{L}{32}\right)}[/tex]

Now divide both sides by 2π.

[tex]$ \frac{1.9}{2 \pi}=\sqrt{\left(\frac{L}{32}\right)} \\[/tex]

[tex]$ 0.3024=\sqrt{\left(\frac{L}{32}\right)}[/tex]

Then taking square on both sides.

[tex]$ (0.3024)^2=\frac{L}{32} \\[/tex]

0.09144576 = [tex]$\frac{L}{32}[/tex]

Later multiply both sides by 32.

2.9262 = L

The approximate value of the length of a pendulum:

L ≈ 3

Therefore, the length of a pendulum is about 3 feet.

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The break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.

In business accounting, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company within a specified time period.

To calculate the break-even point in units use the formula:

Break-Even point (units) = Fixed Costs ÷ (Sales price per unit – Variable costs per unit) or in sales dollars using the formula: Break-Even point (sales dollars) = Fixed Costs ÷ Contribution Margin.

Insurance Requirements the part of a commercial contract in which the types and minimum amounts of insurance the parties agree to provide in connection with their performance of the contract are specified.

A break even point is used in multiple areas of business and finance. In accounting terms, it refers to the production level at which total production revenue equals total production costs. In investing, the break even point is the point at which the original cost equals the market price.

Therefore, the break-even point refers to the amount of revenue necessary to cover the total fixed and variable expenses incurred by a company.

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The variance clearing account is used to accumulate individual variances until they can be allocated to their respective variance accounts, and the formula used to calculate the variance clearing account is the sum of all the individual variances, plus the beginning balance of the account.

A variance clearing account is a temporary ledger account used to accumulate individual variances such as direct labor cost, direct material cost, and overhead cost. The variance clearing account is used to collect all the individual variances in one account until it can be allocated to its respective variance accounts. This account has a debit side and a credit side. The debit side of the variance clearing account is used to accumulate all the unfavorable variances, while the credit side is used to accumulate all the favorable variances.

The formula used to calculate the variance clearing account is the sum of all the individual variances, plus the beginning balance of the account. This can be expressed as follows:

Variance Clearing Account = Beginning Balance + Sum of All Individual Variances

For example, if the beginning balance of the variance clearing account is $500, and the sum of all individual variances is $400, the balance in the variance clearing account would be $900 ($500 + $400). This balance can then be allocated to the respective variance accounts.

The variance clearing account is used to accumulate individual variances until they can be allocated to their respective variance accounts, and the formula used to calculate the variance clearing account is the sum of all the individual variances, plus the beginning balance of the account.

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The area of the topper will be 24 square units.

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The area of the glass topper will be:-

Area = Length x Width

Area = 6 x 4

Area = 24 square units

The image of the glass topper is attached with the answer below.

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