If you borrow $900 for 6 years at an annual interest rate of 7%, how much will you pay altogether?

Answer:

1) c

2) b

3) d

4) b

5) c

6) b

7) b

8) d

9) c

5 / ( 2 / 3 ) = 7.5

7 full jars

By hypothesis , μ ≤ $200 is the mean cost of science textbooks are no more than $200.

What does "mathematical hypothesis" mean?

A proposition is considered to be a hypothesis if it is plausible given the available information but has not been proven true or wrong. An assertion that will serve as the foundation for hypothesis testing is referred to as a hypothesis in statistics (also known as a statistical hypothesis).

                          The statement "all fours sides of a quadrilateral measure the same, then the quadrilateral is a square" states that if true, the quadrilateral is a square.

Here  n = 143

    the claim that the mean cost of science textbooks are no more than $200.

    H₀  : μ = $200

    H₁  :  μ ≤ $200

Therefore, this problem based on one sample t test for mean .

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To solve the equation 4x+8 = 32, we subtracted 8 from both sides of the equation to isolate the variable x. Then, we divided both sides by 4 to solve for x. The answer is x = 6.

To solve 4x+8 = 32, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 8 from both sides of the equation:

4x+8-8 = 32-8

This simplifies to:

4x = 24

To solve for x, we can divide both sides by 4:

4x/4 = 24/4

Which gives us:

x = 6

Therefore, the answer is A) x = 6.

In summary, to solve the equation 4x+8 = 32, we subtracted 8 from both sides of the equation to isolate the variable x. Then, we divided both sides by 4 to solve for x. The answer is x = 6.

To solve the equation 4x + 8 = 32, follow these steps:

Step 1: Subtract 8 from both sides of the equation to isolate the term with the variable x.
4x + 8 - 8 = 32 - 8

Step 2: Simplify both sides of the equation.
4x = 24

Step 3: Divide both sides of the equation by 4 to solve for x.
4x / 4 = 24 / 4

Step 4: Simplify both sides of the equation.
x = 6

So, the correct answer is x = 6 (Option A).

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There are 109,761 more writers with a bachelor's degree or higher than those with only some college experience and no degree.

From the given data, Percent of writers with some college experience but no degree = 12.4%

Percent of writers with a bachelor's degree or higher = 84.1%The percentage of writers without any college experience can be found by:

Percent of writers without any college experience = 100% - (12.4% + 84.1%)

Percent of writers without any college experience = 3.5%T

Total number of writers with some college experience but no degree = 12.4% of 153,000= 18,972

Total number of writers with a bachelor's degree or higher = 84.1% of 153,000= 128,733

Total number of writers without any college experience = 3.5% of 153,000= 5,355

Therefore, the number of writers with a bachelor's degree or higher than those with only some college experience and no degree is:

128,733 - 18,972 = 109,761

Hence, there are 109,761 more writers with a bachelor's degree or higher than those with only some college experience and no degree.

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Using the CVP Formulas to solve the following. JBL Speakers has annual fixed costs of $2,450,000, and variable costs of $25 per unit. The selling price per unit is $90.

A) 37,692 units

B) 53,077 units

A) To calculate the annual revenue required to break even, we need to find the point where total revenue equals total costs.

Total cost (TC) = Fixed costs (FC) + Variable costs per unit (VC) * Quantity (Q)

Total revenue (TR) = Selling price per unit (SP) * Quantity (Q)

At the break-even point, total revenue equals total cost:

TR = TC

SP * Q = FC + VC * Q

Substituting the given values:

$90 * Q = $2,450,000 + $25 * Q

$90Q - $25Q = $2,450,000

$65Q = $2,450,000

Q = $2,450,000 / $65

Q ≈ 37,692.31

Therefore, approximately 37,692 units need to be sold to break even.

B) To calculate the annual unit sales required to make a $1,000,000 profit, we can use the following formula:

Profit (P) = (SP * Q) - (FC + VC * Q)

Substituting the given values and the desired profit:

$1,000,000 = ($90 * Q) - ($2,450,000 + $25 * Q)

$90Q - $25Q = $1,000,000 + $2,450,000

$65Q = $3,450,000

Q = $3,450,000 / $65

Q ≈ 53,076.92

Therefore, approximately 53,077 units need to be sold to make a $1,000,000 profit.

In conclusion, to break even, JBL Speakers needs to generate an annual revenue of approximately $2,450,000, and to make a $1,000,000 profit, they need to sell approximately 53,077 units annually.

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Answer:

x = 8

The measure of angle A = 30°

Step-by-step explanation:

angle A and B are supplementary and their sum is 180°

6x - 18 + 14x + 38 = 180° add like terms

20x + 20 = 180

20x = 180 - 20

20x = 160 divide both sides by 20

x = 8 and the measure of angle A

6x - 18 ➡ 6 × 8 - 18 = 30°

Answer:

102,300.

Step-by-step explanation:

102,00 + 300

= 102,300.

the critical points of f(x,y) are: (0,0)

a) To find the critical points of the function f(x,y), we need to find where the partial derivatives of f with respect to x and y are zero:

\(∂f/∂x = 12x^2 - 240x + 12y^2 = 0∂f/∂y = 24xy - 48y = 0\)

The second equation gives us two possibilities: either y = 0 or x = 2. Substituting y = 0 into the first equation, we get:

\(12x^2 - 240x = 0\)

This gives us x(x - 20) = 0, so either x = 0 or x = 20. Therefore, we have three critical points:

(0,0), (2,0), and (20,0).

b) To classify the critical points, we need to use the second partial derivative test. The Hessian matrix of f is:

\(H = [ ∂^2f/∂x^2   ∂^2f/∂x∂y ]    [ ∂^2f/∂y∂x   ∂^2f/∂y^2 ]\)
Taking the partial derivatives of f again, we get:

∂^2f/∂x^2 = 24x - 240
∂^2f/∂y^2 = 24x - 48
∂^2f/∂x∂y = 24y

Substituting the critical points, we get:
H(0,0) = [ -240  0 ]
        [ 0    -48 ]

H(2,0) = [ -336  0 ]
        [ 0    -48 ]

H(20,0) = [ 240  0 ]
         [ 0    -48 ].


For the critical point (0,0), the Hessian matrix is negative definite, so it is a local maximum.

For the critical point (2,0), the Hessian matrix has a negative determinant and a negative eigenvalue, so it is a local maximum.

For the critical point (20,0), the Hessian matrix has a positive determinant and negative eigenvalues, so it is a local maximum along the x-axis and a local minimum along the y-axis.

Therefore, the critical points of f(x,y) are: (0,0)

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Answer:

True :)

Please mark me brainliest!

Answer:

20

Step-by-step explanation:

2 get well cards

4 anniversary cards

6 greeting cards

8 birthday cards

The probability that a piece selected at random and is defective given that it is known to be a plate is 0.0588 or 5.88%.

To calculate the probability, we need to use Bayes' theorem: P(defective|plate) = P(plate|defective) * P(defective) / P(plate).

Therefore, P(defective|plate) = 0.2 * 0.0227 / 0.0818 = 0.0588 or 5.88%.

The probability that a cup will be chosen given that it is defective is 0.4 or 40%.

To calculate the probability, we need to use the information given in the table:

Divide the number of defective cups by the total number of defective products: 10/25 = 0.4 or 40%.

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Complete Question:

The following table shows the relationship of 1100 pieces between good and defective made in a ceramic workshop

cup plate vase total

Good 830 85 1415

Defective 10 5

Overall 510 90

What is the probability that a piece is selected at random and is defective given that it is known to be a plate?

What is the probability that a cup will be chosen given that it is defective?

​

Answer:

d)142º

Step-by-step explanation:

\(\widehat{AB}=2\times71\º=142\º\)

Answer:

c>1

Step-by-step explanation:

9c>10-1

9c>9

9c/9>9/9

c>9/9

so,

c>1

Hope that helps!

Plz mark brainliest

The integrating factor μ(x, y) is \(e^(x^2y + x).\)

The general solution of the given differential equation is given by:

\(\int\(x^2ye^(x^2y + x)) dx = C\)

To make the given differential equation exact,

we need to find an integrating factor.

An integrating factor for a first-order linear differential equation of the form M(x, y)dx + N(x, y)dy = 0 can be found by multiplying an integrating factor function μ(x, y) to both sides of the equation.

In this case, the given differential equation is:

\((2 - x)y' + (x^2y - 1) = 0\)

We can rewrite the equation in the standard form as:

\((2 - x)y' + x^2y = 1\)

Comparing this with the standard form M(x, y)dx + N(x, y)dy = 0, we have:

M(x, y) = (2 - x)

N(x, y) =\(x^2y - 1\)

To find the integrating factor μ(x, y), we use the equation:

\(μ(x, y) = e^\int\(∂N/∂x - ∂M/∂y) dx\)

Let's calculate ∂N/∂x and ∂M/∂y:

∂N/∂x = 2xy

∂M/∂y = -1

Substituting these values into the integrating factor equation, we get:

μ(x, y) = \(e^\int\ (2xy - (-1)) dx\)

        =\(e^(x^2y + x)\)

The integrating factor μ(x, y) is \(e^(x^2y + x).\)

To find the general solution, we multiply both sides of the given differential equation by the integrating factor:

\(e^(x^2y + x) * (2 - x)y' + e^(x^2y + x) * (x^2y - 1) = 0\)

Simplifying the equation, we have:

\((2 - x)e^(x^2y + x)y' + (x^2y - 1)e^(x^2y + x) = 0\)

This equation is exact. We can now find the solution by integrating with respect to x. After integrating, we equate the result to a constant of integration:

∫(2 - x)e^(x^2y + x) dx + ∫(x^2y - 1)e^(x^2y + x) dx = C

Integrating each term separately, we get:

\(e^(x^2y + x) + ∫(-e^(x^2y + x)) dx + ∫(x^2ye^(x^2y + x)) dx - ∫(e^(x^2y + x)) dx = C\)

Simplifying and rearranging the terms, we have:

\(e^(x^2y + x) - e^(x^2y + x) + ∫(x^2ye^(x^2y + x)) dx = C\)

The first two terms cancel out, and we are left with:

∫\((x^2ye^(x^2y + x)) dx = C\)

Now, we can integrate the remaining term to find the general solution. However, without additional boundary conditions, it is not possible to obtain an explicit solution.

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Answer:

Brainliest Please!!

Step-by-step explanation:

The expression 12x + 36y represents a linear combination of the variables x and y with coefficients 12 and 36, respectively. There are several ways to express this expression, depending on the context or specific requirements.

Here are a few examples:

Expanded Form: 12x + 36y

This is the standard form of the expression and represents the sum of 12 times x and 36 times y.

Factored Form: 12(x + 3y)

By factoring out the common factor of 12, the expression can be rewritten as the product of 12 and the sum of x and 3y.

Distributive Form: 12x + 36y = 12(x + 3y)

The expression can also be expressed using the distributive property, where 12 is distributed to both terms inside the parentheses.

Equivalent Expressions:

The expression 12x + 36y is equivalent to other expressions obtained by combining like terms or applying algebraic manipulations, such as 6(2x + 6y), 4(3x + 9y), or 12(x/2 + 3y/2).

These different forms provide various ways to represent the expression 12x + 36y and allow for flexibility in mathematical calculations or problem-solving situations.

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To sketch the region enclosed by the curves y = x^3 - 4x and y = 12x and determine the appropriate method of integration. By evaluating the definite integral ∫[-4 to 4] (12x - (x^3 - 4x)) dx, we can calculate the area of the region enclosed by the given curves.

The curves intersect when x^3 - 4x = 12x. Simplifying this equation, we get x^3 - 16x = 0. Factoring out x, we have x(x^2 - 16) = 0, which gives us x = 0 and x = ±4 as the intersection points.

To determine whether to integrate with respect to x or y, we can observe that the region is vertically bounded by the curves. Therefore, we'll integrate with respect to x.

To find the area of the region, we'll integrate the difference of the upper and lower curves within the given bounds, from x = -4 to x = 4.

Now, for a more detailed explanation:

First, let's analyze the curves individually. The curve y = x^3 - 4x represents a cubic function, and y = 12x represents a linear function. By plotting these curves on a graph, we can observe that they intersect at three points: (0, 0), (-4, -48), and (4, 48).

To determine the enclosed region, we need to find the x-values at which the curves intersect. Setting the two equations equal to each other, we have x^3 - 4x = 12x. Rearranging this equation, we get x^3 - 16x = 0. Factoring out x, we have x(x^2 - 16) = 0, giving us x = 0 and x = ±4 as the x-values of intersection.

Since the region is vertically bounded by the curves, we'll integrate with respect to x. To find the area, we'll integrate the difference between the upper curve (y = 12x) and the lower curve (y = x^3 - 4x) within the bounds from x = -4 to x = 4.

By evaluating the definite integral ∫[-4 to 4] (12x - (x^3 - 4x)) dx, we can calculate the area of the region enclosed by the given curves.

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Answer:

the father ends up paying 18 dollars after everything

Answer:

Explanation:

If a 4th degree has only the following roots: x=−7,x=3,x=−1/6.

A 4th-degree polynomial must have 4 roots. What this means is that one of the roots is a repeated root.

If -7 is the repeated root, an example of such polynomial is:

The given polynomial is not the only 4th-degree polynomial that has only these roots. Any of the given roots can be the repeated root.

If on the other hand, 3 is the repeated root, then p(x) will be:

Diversity in People can be seen in terms of:

In terms of Ethnicity,  people from various ethnic traditions bring a rich tapestry of sophistications, traditions, and outlooks to society. Access to Healthcare: Ensuring all has access to value healthcare improves the health and comfort of individuals, offspring, and communities.

In terms of Gender, embracing neutral diversity helps promote equal time for all genders in various fields and fights feminine-based bias. : Providing access to instruction for all members of society, although socio-economic rank, etc.

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See text below

Now we make a table and mention two examples of diversity in people and two examples of common good in society

After 20 years, the value of the fox population will be 640.

The population of the fox after 20 years is calculated as follows;

The given function is;

y = 40 x 4ˣ

Where;

how many 10 years period make up 20 years?

x = 2

The value of the fox population is calculated as follows

y = 40 x 4²

y = 40 x 16

y = 640

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Diameter = 17 cm

Radius = r = Diameter /2 = 17/2 =8.5 cm

Surface area of a sphere: 4 π r^2

Replacing with the values given:

SA = 4 π (8.5) ^2 = 907.92 cm^2

Answer:

57.55 ounces

Step-by-step explanation:

Given data

Each book weighs 12.235 ounces

Hence the weight of 4 books is

=12.235x4

=49.3 ounces

Each pencil weighs 8.25 ounces

Hence the weight of 4 books is

=8.25x1

=8.25ounces

Total weight is

=49.3+8.25

=57.55 ounces

Answer:

BAC and DAE are two acronyms for BAC and DAE, respectively. Since they are angles at a point, an arc measuring 204 degrees is 360 degrees. BAC is measured at 11 degrees. 5(11)° = 55° is the measure of DAE.

Step-by-step explanation:

(a) T(−15, 30) ≈ 0.62 and fv(−15, 30) ≈ -1.82 found using the given actual temperature is T and the wind speed is v.

The wind-chill index W is the perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v).

a) Estimation of the values of fT(−15, 30) and fv(−15, 30) is as follows:

Let's calculate fT (−15, 30) by using the formula:fT (−15, 30) = limh→0 f(−15+h, 30) - f(−15, 30) / h

Where h is the difference between T and T + h, which is a small number.

Now, we can find f(−15+h, 30) by using the formula W = 13.12 + 0.6215T - 11.37v0.16W(−15+h, 30) = 13.12 + 0.6215(−15+h) - 11.37(30)0.16 = -33.76 + 0.6215h + 72.672 = 38.9 + 0.6215h

Likewise,f(−15, 30) = W(−15, 30) = 13.12 + 0.6215(−15) - 11.37(30)0.16 = -17.73

Therefore,fT (−15, 30) = limh→0 [f(−15+h, 30) - f(−15, 30)] / h = limh→0 [38.9 + 0.6215h + 17.73] / h = limh→0 (56.63 + 0.6215h) / h = 0.6215 = 0.62 (approximately)fT(−15, 30) ≈ 0.62

The above value is rounded off to two decimal places.

Now, let's calculate fv(−15, 30) by using the formula fv (T, v) = limh→0 f(T, v + h) - f(T, v) / h

Where h is the difference between v and v + h, which is a small number.

Now, we can find f(−15, 30 + h) by using the formula W = 13.12 + 0.6215T - 11.37v0.16W(−15, 30 + h) = 13.12 + 0.6215(−15) - 11.37(30 + h)0.16 = -372.55 - 1.819h

Likewise,f(−15, 30) = W(−15, 30) = 13.12 + 0.6215(−15) - 11.37(30)0.16 = -17.73Therefore,fv (−15, 30) = limh→0 [f(−15, 30 + h) - f(−15, 30)] / h = limh→0 [-372.55 - 1.819h + 17.73] / h = limh→0 (-354.82 - 1.819h) / h = -1.819 = -1.82 (approximately)fv(−15, 30) ≈ -1.82

The above value is rounded off to two decimal places. fT(−15, 30) ≈ 0.62 and fv(−15, 30) ≈ -1.82.

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For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

\(C = \frac{5}{9} (F- 32)\)

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

The directional derivative of the function in the direction of the given vector is positive, indicating that the function is increasing in that direction.

The directional derivative is a measure of the rate of change of a function in a particular direction. To calculate the directional derivative, we need to take the dot product of the gradient of the function with the unit vector in the given direction. The sign of the directional derivative tells us whether the function is increasing or decreasing in that direction.
In this case, we are given that the angle between the vector and a unit vector is 99 degrees. Since the dot product of two vectors is equal to the product of their magnitudes times the cosine of the angle between them, we can write:
cos(99) = (u . v) / (|u| |v|)
where u is the given vector and v is the unit vector. We know that the magnitude of the unit vector is 1, so we can

simplify:
cos(99) = u . v / |u|
Multiplying both sides by |u|, we get:
cos(99) |u| = u . v
This tells us the magnitude of the projection of the vector u onto the unit vector v. If u and v point in the same direction, the projection is positive; if they point in opposite directions, the projection is negative.
Since u is nonzero and the angle between u and v is less than 180 degrees (i.e., they point in the same direction), the sign of the projection is positive.

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