A student has a savings account with $475 in it. She deposits $125 of her paycheck into the account every week. Her goal is to save $7,000 for college.

a.How much will be in the account after 3 weeks?
b.How long will it take before she has $1,350?
c.Write an equation that represents the relationship between the dollar amount in her account and the number of weeks since she started depositing $125 each week.
d.Graph your equation using graphing technology. Mark the points on the graph that represent the amount after 3 weeks, and also the week she has $1,350. Write down the coordinates.
e. How long will it take her to reach her goal?

Answer:

x=9*

Step-by-step explanation:

48*+(5x-3)*+90*=180*    (its is 180* because it is a line)

5x+135*=180*        (combine like terms)

-135*       -135*    (subtract 135*)

5x=45*       (divide by 5)

x=9*

dont mind the asterisks they are my degree signs

hope this helps

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The WACC for Company A is approximately 0.564 or 56.4%.

To calculate the weighted average cost of capital (WACC) for Company A, we need to consider the cost of debt and the cost of equity, weighted by their respective proportions in the company's capital structure.

Given information:

Debt proportion (D/V) = 26%

Equity proportion (E/V) = 100% - 26% = 74%

Before-tax cost of debt (r_d) = 3.2%

Risk-free rate (r_f) = 1.1%

Market risk premium (RPM) = 6%

Beta (β) = 0.9

Marginal tax rate (T) = 30%

The formula to calculate WACC is as follows:

WACC = (D/V) * r_d * (1 - T) + (E/V) * r_e

To calculate the cost of equity (r_e), we can use the Capital Asset Pricing Model (CAPM):

r_e = r_f + β * RPM

Plugging in the given values:

r_e = 1.1% + 0.9 * 6% = 1.1% + 5.4% = 6.5%

Now, let's calculate WACC:

WACC = (0.26) * 3.2% * (1 - 0.30) + (0.74) * 6.5%

WACC = 0.0832 + 0.481

WACC ≈ 0.5642

Rounding to three decimal places, the WACC for Company A is approximately 0.564 or 56.4%.

Please note that the WACC represents the average rate of return required by both debt and equity investors to finance the company.

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The equation min(a; min(b; c)) = min(min(a; b); c) holds true for any real numbers a, b, and c.

To prove the equation min(a; min(b; c)) = min(min(a; b); c), we need to consider the two cases separately.
Case 1: min(a; b) = a
If a is the smaller value between a and b, then min(a; min(b; c)) becomes min(a; c). Since c is either smaller than or equal to b, min(a; c) will be the smaller value between a and c.
On the other hand, min(min(a; b); c) becomes min(a; c) because min(a; b) is a, and a is compared with c. Again, the smaller value between a and c will be selected.
Therefore, in this case, min(a; min(b; c)) = min(min(a; b); c).
Case 2: min(a; b) = b
If b is the smaller value between a and b, then min(a; min(b; c)) becomes min(b; c). Since c is either smaller than or equal to a, min(b; c) will be the smaller value between b and c.
Similarly, min(min(a; b); c) becomes min(b; c) because min(a; b) is b, and b is compared with c. The smaller value between b and c will be selected.
Therefore, in this case as well, min(a; min(b; c)) = min(min(a; b); c).
Since both cases have been considered, we can conclude that min(a; min(b; c)) = min(min(a; b); c) holds true for any real numbers a, b, and c.

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The given relation is a set of ordered pairs {(1, 1), (2, 2), (3, 5), (4, 10), (5, 15)}. The first element of each pair represents the input or domain value, and the second element represents the output or range value.

The domain of the relation is the set of all first elements of the ordered pairs, which is {1, 2, 3, 4, 5}. The range of the relation is the set of all second elements of the ordered pairs, which is {1, 2, 5, 10, 15}.

To check whether the relation is a function or not, we need to ensure that each input value (i.e., element of the domain) is associated with a unique output value (i.e., element of the range). In other words, there should not be more than one ordered pair with the same first element.

In this case, each input value is associated with a unique output value, so the relation is indeed a function. Specifically, it is a function from the set of integers {1, 2, 3, 4, 5} to the set of integers {1, 2, 5, 10, 15}.

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Answer: 11/24

Convert 3/8 to 9/24

Convert 1/12 to 2/24

Add them together to get 11/24

If I did a poor job explaining I can help more in the comments.

Answer:

Hi, there the answer is 11/24

Step-by-step explanation:

9/24+2/24  

9+2/24

11/24

If you didn't understand here's something you can understand I felt like I didn't understand what I wrote on the top

Find the Least Common Multiple

\(\frac{3}{8} +\frac{1}{12}\)

\(\frac{9}{24} +\frac{2}{24}\)

\(\frac{9+2}{24}\)

\(\frac{11}{24}\)

Answer: (43,5)

Step-by-step explanation: did the assignment myself.

Answer:

43, 5

Step-by-step explanation:

Tok the test

Answer:

(-3.5 8.5)

Step-by-step explanation:

Midpoint Formula: (\(\frac{x2 + x1}{2}\), \(\frac{y2 + y1}{2}\))

What I did: -10 + 3 = 7, 7 / 2 = 3.5 x = 3.5 | 9 + 8 = 17, 17 / 2 = 8.5

Midpoint = (-3.5, 8.5)

The probability that the top face has an odd number of dots is 1/2. A die is a small cube that is used in gambling, games, and fortune-telling. A die is a polyhedral object that has six faces, twelve edges, and eight vertices. On the die, each face is numbered with a certain number of dots or digits.

The problem of the probability of the top face having an odd number of dots is being asked. The problem says that one of the dots is removed from the standard die at random with each dot equally likely to be chosen, then the die is rolled. Therefore, the dots will not be the same as in the standard die. An odd number is a number that, when divided by two, gives a remainder of one. 1, 3, and 5 are examples of odd numbers on a standard die. There are three possibilities: one, three, and five. Each face of the die has an equal chance of being chosen. There are only five possible results because one of the dots is removed from the standard die at random. There is a 1 in 5 chance that the missing dot will be an odd number. Hence, the probability that the top face has an odd number of dots is 1/2.

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The given statement is 1. Always true

2. Always true

3. Always true

4. Sometimes true

5. Never true

Statement 1: A line and a point are always coplanar.

Answer: Always true.

Reason: This statement is always true because a line and a point can always be found on the same plane. In Euclidean geometry, a plane is a flat surface that extends infinitely in all directions, and any two points on the plane can be connected by a straight line. Therefore, a line and a point will always lie on the same plane.

Statement 2: Congruent angles form vertical angles.

Answer: Always true.

Reason: Vertical angles are formed by the intersection of two lines. When two angles are congruent, it means they have the same measure. If two angles have the same measure and are formed by the intersection of two lines, then they are vertical angles. Therefore, congruent angles always form vertical angles.

Statement 3: Linear pairs that are congruent are right angles.

Answer: Always true.

Reason: A linear pair consists of two adjacent angles that share a common side and form a straight line. If the two angles of a linear pair are congruent, it means they have the same measure. In Euclidean geometry, a straight angle measures 180 degrees. If two angles in a linear pair are congruent and their measures add up to 180 degrees, then each angle must measure 90 degrees, which is the measure of a right angle. Therefore, linear pairs that are congruent are always right angles.

Statement 4: The sum of angles that form a linear pair is less than 180 degrees.

Answer: Sometimes true.

Reason: The sum of angles that form a linear pair is always equal to 180 degrees, not less than 180 degrees. This is based on the definition of a linear pair, which states that the two angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. However, if the statement said "less than or equal to 180 degrees," then it would be always true.

Statement 5: Vertical angles are complementary.

Answer: Never true.

Reason: Vertical angles are not complementary. Complementary angles are two angles that add up to 90 degrees. Vertical angles, on the other hand, are a pair of non-adjacent angles formed by the intersection of two lines. They do not necessarily have any specific relationship to each other in terms of their angle measures. Therefore, vertical angles are not complementary by definition.

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The truth of each statement depends on the properties of angles and theorems that support them. A line and a point are always coplanar, congruent angles can sometimes form vertical angles, congruent linear pairs are not always right angles, the sum of angles that form a linear pair is always 180 degrees, and vertical angles are never complementary.

To determine the truth of each statement, we need to consider the properties of angles and theorems that support them.

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To find the terms of the multiplication problem (4+6i) * (4-5i) using the FOIL method, we will multiply each term of the first expression by each term of the second expression.

Using the FOIL method, we multiply the terms as follows:

First: (4 * 4) = 16

Outer: (4 * -5i) = -20i

Inner: (6i * 4) = 24i

Last: (6i * -5i) = -30i^2

Simplifying the last term, we know that i^2 = -1, so -30i^2 becomes -30 * (-1) = 30.

Combining all the terms, we get:

(4+6i) * (4-5i) = 16 - 20i + 24i + 30

Simplifying further, we have:

16 + 4i + 30

The final result is:

(4+6i) * (4-5i) = 46 + 4i

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The derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

a) To find f'(x) for f(x) = x*sin(x), we can use the product rule and the derivative of the sine function.

Using the product rule, we have:

f'(x) = (xsin(x))' = xsin'(x) + sin(x)*x'

The derivative of sin(x) is cos(x), and the derivative of x with respect to x is 1. Therefore:

f'(x) = x*cos(x) + sin(x)

So, the derivative of f(x) = xsin(x) is f'(x) = xcos(x) + sin(x).

(b) To find f'(x) for f(x) = sech^(-1)(x^2), we can use the chain rule and the derivative of the inverse hyperbolic secant function.

Let u = x^2. Then, f(x) can be rewritten as f(u) = sech^(-1)(u).

Using the chain rule, we have:

f'(x) = f'(u) * u'

The derivative of sech^(-1)(u) can be found using the derivative of the inverse hyperbolic secant function:

(sech^(-1)(u))' = 1/sqrt(1 - u^2)

Since u = x^2, we have:

f'(x) = 1/sqrt(1 - (x^2)^2) * (x^2)'

Simplifying:

f'(x) = 1/sqrt(1 - x^4) * 2x

So, the derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

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Answer:

John is 18, Frank is 12.

Step-by-step explanation:

This is th eanswer because if John is older that Frank by 6 years, and ^ years ago, double his age, you have to find a number that is twice the number 6.

12 fits that description:

John      Frank

12               6   Let's say these were the ages, twice as old as Frank, but the difference is still 6.

Now, John is 18 (six years later..) and Frank is 12.

I hope you understand the answer and it helps you. :)

Answer:

Answer 4

width = 4

Length = 13

Step-by-step explanation:

Givens

Length = x + 9

width = x

Area = 52

Equation

Area = L * W

Area = x (x + 9 )  = 52

Solution

x (x + 9) = 52            remove the brackets

x^2 + 9x = 52           Subtract 52 from both sides

x^2 + 9x - 52 = 0     Factor

(x + 13)(x - 4) = 0

x + 13 is an extraneous solution. You cannot have a length or width of - 13 or minus anything for that matter.

x - 4 = 0                    Add 4 to both sides

x = 4                         This is the only possible solution.

a) The polynomial written in standard form is -4x^3 + x + 7.

b) It is a cubic polynomial because it has three terms and a degree of 3.

A polynomial is an expression consisting of variables and coefficients, where the variables are raised to non-negative integer powers and the coefficients are constants. The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial -4x^3 + x + 7, the degree is 3 because the highest power of x is 3.

The standard form of a polynomial is when the terms are arranged in descending order of their degrees. This means that the term with the highest power of the variable is written first, followed by the next highest power, and so on, until the constant term is written last. In the case of -4x^3 + x + 7, we rearranged the terms so that the -4x^3 term is first, followed by the x term, and then the constant term of 7.

Finally, we can name the polynomial based on its degree and number of terms. In this case, we have a polynomial with three terms and a degree of 3, so it is called a cubic polynomial.

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The given question is incomplete, the complete question is:

Write the polynomial in standard form then name the polynomial based on its degree and number of terms. x+ 7 - 4x^3

There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

Answer:

x=35

Step-by-step explanation:

Answer:

45cm

Step-by-step explanation:

(2/5)d -2=16

(2/5)d =16+2

d=18 ×(5/2)=45cm

Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.

1. -x² + x - x² + 1

Combine like terms: -x² + x - x² + 1 = -2x² + x + 1

This polynomial has degree 2 because the highest power of the variable is 2.

2. x² + x + 2x³ - x

Rearrange terms: 2x³ + x² + x - x = 2x³ + x²

This polynomial has degree 3 because the highest power of the variable is 3.

3. 4x + x + x - 2

Combine like terms: 4x + x + x - 2 = 6x - 2

This polynomial has degree 1 because the highest power of the variable is 1.

4. 3x² + 4 - 3x² - 1

Combine like terms: 3x² - 3x² + 4 - 1 = 3

This polynomial has degree 0 because there is no variable term.

Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.

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The 5 most common Pythagorean triples are ( 3 , 4 , 5 ) , ( 5 , 12 , 13 ) ,

( 6 , 8 , 10 ) , ( 9 , 12 , 15 ) , and ( 15 , 20 , 25 ) .

Pythagorean triples:

Any three positive integers that completely satisfy the Pythagorean theorem is considered a Pythagorean triple number. According to the theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle. A Pythagorean triple consists of the three sides of a right triangle. In this article, you will learn how to create multiple Pythagorean triples.

A Pythagorean triple consists of the three natural numbers a, b, c such that a² + b² = c². These triples are usually written as (a, b, c), examples

(3, 4, 5) are well known. If (a, b, c) is a Pythagorean triple, then (ka, kb, kc) is also a Pythagorean triple for all natural k. A primitive Pythagorean triplet is a triplet in which a, b, and c are coprime (i.e., have no common divisor greater than 1). For example, (3, 4, 5) is a basic Pythagorean triple, but (6, 8, 10) is not.

A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle and is necessarily a right triangle.

This name comes from the Pythagorean theorem, which states that the side lengths of each right triangle satisfy the formula a² + b² =c². A Pythagorean triple gives the length of three integers of the sides of a right triangle. However, right triangles whose sides are not integers do not form a Pythagorean triple. For example, a triangle with sides a = b = 1 and c = √2 but, (1,1,2) is not a Pythagorean triple because √2 is not an integer. Also, the numbers 1 and √2 do not have a common multiple because √2 is irrational.

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The inequality of the graph from the boundary line is y ≤ x - 3

From the question, we have the following parameters that can be used in our computation:

Boundary line: y = x  - 3

This means that

The inequality can be any of the following

y > x - 3

y < x - 3

y ≥ x - 3

y ≤ x - 3

In this case, we make use of y ≤ x - 3

So, we plot the graph

See attachment for the graph of the inequality expression y ≤ x - 3

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The equation of the altitude from vertex A of the triangle is y = (3/2)x + 3/2.

To write an equation for the altitude from vertex A of the triangle where point A is (-1,0), point B is (8,-5), and point C is (2,-3), we need to use the slope-intercept form of an equation for the line that contains the side opposite vertex A. Here are the steps:

1. Find the slope of the line containing side BC using the slope formula: m = (yb - yc)/(xb - xc) = (-5 - (-3))/(8 - 2) = -2/3.

2. Find the equation of the line containing side BC using point-slope form: y - yb = m(x - xb). Using point B, we get: y + 5 = (-2/3)(x - 8). Simplifying, we get y = (-2/3)x + 19/3.

3. The altitude from vertex A of the triangle is perpendicular to side BC. Therefore, its slope is the negative reciprocal of the slope of side BC, which is 3/2.

4. We can find the equation of the altitude by using point-slope form again, this time using point A: y - ya = m(x - xa). Using point A and the slope 3/2, we get: y - 0 = (3/2)(x + 1). Simplifying, we get: y = (3/2)x + 3/2.

Summary: To find the equation of the altitude from vertex A of the given triangle, we first found the slope of the line containing the side opposite vertex A, which is BC. Then, we found the equation of this line using point-slope form. Next, we used the fact that the altitude is perpendicular to side BC and found its slope, which is the negative reciprocal of the slope of side BC. Finally, we used the point-slope form again to find the equation of the altitude using point A and its slope. The equation we obtained is y = (3/2)x + 3/2.

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The angle, a, between the Vectors u and W is  2.0 radians (rounded to the nearest tenth).

The angle, a, between the vectors u = <-4, -3> and W = <-1, 5>, we can use the dot product formula:

u · W = |u| |W| cos(a)

Where u · W is the dot product of u and W, |u| is the magnitude of u, |W| is the magnitude of W, and a is the angle between the vectors.

First, let's calculate the dot product:

u · W = (-4)(-1) + (-3)(5)

      = 4 - 15

      = -11

Next, let's calculate the magnitudes of the vectors:

\(|u| = \sqrt{((-4)^2 + (-3)^2)}\\= \sqrt{(16 + 9)}\\= \sqrt{(25)}\\= 5\)

\(|W| = \sqrt{((-1)^2 + 5^2)}\\= \sqrt{(1 + 25)}\\= \sqrt{(26)\)

Now, we can substitute the values into the dot product formula:

\(-11 = (5)(\sqrt{(26)}) cos(a)\)

To find cos(a), we can rearrange the equation:

cos(a) = \(-11 / (5 \times \sqrt{(26))\)

Now, let's calculate the value of cos(a):

cos(a) ≈ -11 / (5 * 5.099)

      ≈ -11 / 25.495

      ≈ -0.431

To find the angle a, we can take the inverse cosine (arccos) of cos(a):

a ≈ arccos(-0.431)

 ≈ 1.994 radians (rounded to the nearest tenth)

Therefore, the angle, a, between the vectors u and W is approximately 2.0 radians (rounded to the nearest tenth).

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Answer:

angle 1 = 45° because vertical angles

angle 2 = 135° because supplementary angles

Step-by-step explanation:

∠1 = ∠a, ∠a = 45°

∠2 + ∠a (45°) = 180°

180° - 45° = 135°

Answer:

Angle 1= 45 degrees, angel 2= 135

Step-by-step explanation:

you know that line b has a 45 degree angle on a 180 total, so to find angle 1 you just move the 45 as they are the same, to find angle b you substract 45 from 180 getting 135

Based on this evaluation, the correct answer is:

d. "false : 14 is 104"

The value of 's' after the given statement can be determined by evaluating each part of the expression step by step:

1. Evaluate (!true): Since 'true' is negated using the '!' operator, this expression becomes 'false'.

2. Concatenate " : " to "false": The resulting string also becomes "false : ".

3. Calculate (10 + 4): This arithmetic expression is equals to  14.

4. Concatenate "14" to "false : ": The resulting string becomes equal to "false : 14".

5. Finally, concatenate " is 104" to "false : 14": The final value of 's' becomes "false : 14 is 104".

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The far left of the chart is the minimum(low) value of the box plot.

Answered by Gauthmath must click thanks and mark brainliest

Step-by-step explanation:

let x be the distance between B and P

tan(67)=x/5000

x=2.3558 . 5000

x=11779feet

Answer:

11,779 feet

Step-by-step explanation:

Is the answer

Answer:

3rd one

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of room = 6×9.5=57m2

Area of room including verandah = 12×8.5=102m2

So area of verandah = 102−57=45m2

So cost of cementing the floor of this verandah = 45×80=3600rupees

The correlation between the number of children in a family and the number of pets in the family is determined by examining the relationship between the two variables. Positive Correlation, Negative Correlation, No Correlation

There are several possible ways that the data could be correlated:

Positive Correlation: This means that as the number of children in a family increases, the number of pets in the family also increases. In other words, as one variable increases, the other variable increases as well.

Negative Correlation: This means that as the number of children in a family increases, the number of pets in the family decreases. In other words, as one variable increases, the other variable decreases.

No Correlation: This means that there is no relationship between the number of children in a family and the number of pets in the family. In other words, a change in one variable does not affect the other variable.

Melanie would have to examine the data collected from her survey to determine the correlation between the number of children in a family and the number of pets in the family. For example, if the data shows a positive correlation, Melanie could conclude that families with more children tend to have more pets. However, if the data shows no correlation, Melanie could conclude that the number of children in a family does not have any effect on the number of pets in the family.

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A tudy how that the more exercie people had a day the more they lept at night which catter plot repreent the relationhip The overall pattern of the scatter plot would show that as the amount of exercise increases, the amount of sleep also increases.

A scatter plot would be used to represent the relationship between the amount of exercise people have per day and the hours of sleep they get at night. The scatter plot would show the number of hours of exercise on the x-axis and the number of hours of sleep on the y-axis. Each point on the scatter plot would represent an individual's exercise and sleep hours. The overall pattern of the scatter plot would show that as the amount of exercise increases, the amount of sleep also increases.

1. A scatter plot is used to represent the relationship between two variables.

2. In this case, the two variables are the amount of exercise people have per day and the hours of sleep they get at night.

3. The x-axis of the scatter plot would represent the amount of exercise, while the y-axis would represent the hours of sleep.

4. Each point on the scatter plot would represent an individual's exercise and sleep hours.

5. The overall pattern of the scatter plot should show that as the amount of exercise increases, the amount of sleep also increases.

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