Catherine saved some money and plans to add the same amount each week to her savings account. The table represents the number of weeks that she will save, x, and the total amount of money that she will have in her account, y.


Weeks, x
Dollars in account, y
4
74
6
86
9
104
11
116

Which linear equation represents Catherine’s situation?
y = one-sixth x + 70
y = 6 x + 50
y = StartFraction 1 Over 9 EndFraction x + 104
y = 11 x + 116

Answer

uhg k

Step-by-step explanation:

Answer:

0>32/3. no solution

Step-by-step explanation:

hopes this helps

Answer:

(A) $157.25

(B) $3,857.25

Step-by-step explanation:

The given values are:

Principle (P)

= $3700

Time (T)

= 6 months i.e., 1/2 years

Rate (R)

= 8.5%

(A)

As we know,

Simple Interest,

⇒  [tex]SI=\frac{P\times R\times T}{100}[/tex]

On putting the values, we get

⇒       [tex]=\frac{3700\times 8.5\times \frac{1}{2} }{100}[/tex]

⇒       [tex]=\frac{15,725}{100}[/tex]

⇒       [tex]=157.25[/tex] ($) (he paid for the use of money)

(B)

Amount he paid to the bank will be:

⇒  [tex]P+SI[/tex]

⇒  [tex]3700+157.25[/tex]

⇒  [tex]3,857.25[/tex] ($)

Answer:

A and D

Step-by-step explanation:

[tex]A)3\frac{2}{3} +\sqrt\frac{36}{4} \\=3\frac{2}{3} + \frac{6}{2} \\=\frac{11}{3} +\frac{6}{2} \\=\frac{22+18}{6} \\=\frac{40}{6} \\\\D)3\frac{2}{3} * \sqrt\frac{36}{4} \\=\frac{11}{3} *\frac{6}{2} \\=11[/tex]

As 40/6 form a ratio and can be expressed in a p/q form where p=40 and q=6, it is rational

As 11 forms a ratio(11:1) and can be expressed in a p/q form where p=11 and q=1, it too is rational

Answer:

Step-by-step explanation:

6 x 8 = 48

11,04 x 6 = 66,24

66,24/48 = 1,38$

Answer:

x = 11/5

Step-by-step explanation:

Step 1: Write equation

5x + 1 = 12

Step 2: Solve for x

Answer:

x = 11 / 5 or 2 ¹/₅

Step-by-step explanation:

5x + 1 = 12

5x = 12 - 1

x = 11 / 5 or 2 ¹/₅

Answer:

1 3/4

Step-by-step explanation:

Convert all the time listed to decimal number, let 9 1/4 (or 9.25hr subtract all of them) and divide by 2. Final answer is ~1.75 which is 1 3/4

The number of hours Sandy practices on Saturday is [tex]3\frac{1}{2}[/tex] hours. Therefore, option C is the correct answer.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Sandy is required to practice her clarinet for a total of [tex]9\frac{1}{4}[/tex] hours in one week.

Let the number of hours Sandy practices on Saturday be x.

Now, [tex]\frac{3}{4}+1\frac{1}{6}+\frac{1}{2}+1\frac{1}{3}+2+x=9\frac{1}{4}[/tex]

3/4 +7/6 +1/2 +4/3+2+x= 37/4

9/12 +14/12+6/12 +16/13+24/12+x=37/4

(9+14+6+16+24)/12 +x=37/4

69/12 +x=37/4

x=37/4 -69/12

x= 111/12 -69/12

x= (111-69)/12

x= 42/12

x= 7/2

x= [tex]3\frac{1}{2}[/tex] hours

Therefore, option C is the correct answer.

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Answer:

we have

speed <=35 miles per hour.

Answer: 4

Step-by-step explanation:

1. Subtract 2 from both sides.

5y=22 -2

This equals 5y=20

2.Divide by 5 on each side. That gets 4.

Hope it helped :)

The probability that the experiment results in an outcome less than 40 is 0.25.

To calculate the probability, we need to determine the range of outcomes that are less than 40 out of the total range of 30 to 80. The total range is 80 - 30 = 50. The range of outcomes less than 40 is 40 - 30 = 10.

To find the probability, we divide the range of outcomes less than 40 by the total range:

Probability = (Range of outcomes less than 40) / (Total range)

          = 10 / 50

          = 0.2

Therefore, the probability that the experiment results in an outcome less than 40 is 0.2 or **20%**.

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Answer:

[tex](\frac{1}{14} ,-\frac{7}{6})[/tex]

Step-by-step explanation:

You can use the midpoint formula: [tex]\frac{ChangeInX}{2} ,\frac{ChangeInY}{2}[/tex]

So, the Change In X is: [tex]\frac{4}{7} -\frac{3}{7} = \frac{1}{7}[/tex]

And the Change in Y is: [tex]-\frac{5}{3} - \frac{2}{3} = -\frac{7}{3}[/tex]

Once you divide both of the changes by 2, you get

X: [tex]\frac{1}{14}[/tex]

Y: [tex]-\frac{7}{6}[/tex]

So the midpoint is: [tex](\frac{1}{14} ,-\frac{7}{6})[/tex]

Answer:

a) [tex]p\rightarrow \neg q \wedge \neg r[/tex]

b) [tex]r\vee q \iff \neg p[/tex]

Step-by-step explanation:

Given statements:

[tex]p:[/tex] It is raining

[tex]q:[/tex] Sam is wearing a hat

[tex]r:[/tex] It is winter

To find:

The symbolic forms for the following:

a) If it is raining then Sam is not wearing a hat, and it is not winter.

b) It is winter or Sam is wearing a hat, if and only if it is not raining.

Solution:

a) The statement followed by 'if ' is written on the left hand side and the statement followed by 'then' is written after the symbol [tex]\rightarrow .[/tex]

Not of a statement [tex]s[/tex] is represented as [tex]\neg s[/tex].

And is represented by [tex]\wedge[/tex] symbol.

Therefore, the statement in symbolic form becomes:

[tex]p\rightarrow \neg q \wedge \neg r[/tex]

b) Not of a statement [tex]s[/tex] is represented as [tex]\neg s[/tex].

Or is represented by [tex]\vee[/tex] symbol.

If and only if is represented by the symbol [tex]\iff.[/tex]

Therefore, the statement in the symbolic form becomes:

[tex]r\vee q \iff \neg p[/tex]

Answer:

Step-by-step explanation:

xy is the coefficient of 6m, mxy is the coefficient of 6 and so on……. Note: In the term 'm', the coefficient of m is 1 since 1 times m is equal to m. Similarly, in the term '-m' the coefficient of m is -1 since -1 times m is equal to -m.

Answer:

Should be D

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Subtract the 15 and the 2(they are the y-values) to get the length of one of the legs

Answer:

6

Step-by-step explanation:

5^24 = 5^30/5^x subtract x from 30

5^24 = 5^30-x since the bottom numbers are equal the powers must be equal as well

24 = 30 - x

x = 6

To determine whether an equation defines y as a function of x, we need to check if, for each value of x, there is a unique corresponding value of y. If there is more than one value of y for a particular x, the equation does not define y as a function of x. Based on the given equations, 2x + 3y = 4 and 4x + y = 0 define y as a function of x, while 2x + y = 16 and √√(x-1) = 0 do not define y as a function of x.

The equation 2x + 3y = 4 can be rearranged to solve for y as follows: 3y = 4 - 2x, y = (4 - 2x)/3. For each value of x, there is a unique corresponding value of y, so this equation defines y as a function of x.

Similarly, the equation 4x + y = 0 can be rearranged to solve for y: y = -4x. Again, for each value of x, there is a unique corresponding value of y, so this equation defines y as a function of x.

On the other hand, the equation 2x + y = 16 cannot be rearranged to solve for y in terms of x. There are infinitely many solutions for y for a given value of x, such as y = 16 - 2x, y = 16 - 2x + 5, y = 16 - 2x - 10, etc. Therefore, this equation does not define y as a function of x.

Similarly, the equation √√(x-1) = 0 does not define y as a function of x. This equation represents a square-root operation, and for a given value of x, there can be two possible values of y, one positive and one negative, that satisfy the equation. Hence, it does not define y as a function of x.

Finally, the equation y = 0 is a horizontal line where y is constantly zero, regardless of the value of x. Therefore, it does define y as a function of x.

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Answer:

57

Step-by-step explanation:

Answer:

its either c or b I'm pretty sure its b

Answer:

3(k+4)

Step-by-step explanation:

3k and 12 have a common factor of 3

factor 3 out of the two values

3(k+4)

you can check by multiplying everything in the brackets by 3

3xk =3k

3x4=12

Answer:

3(k+4)

Step-by-step explanation:

As the common factor between 3k and 12 is 3.

so 3 goes infront of the open bracket. 3×K =3K and 3×4=12

so k+4 goes inside the brackets.

The present value of the loan, rounded to the nearest cent, is $37,196.88.

To calculate the present value of a loan, we can use the formula for the present value of an ordinary annuity:

PV = PMT * ((1 - (1 + r)^(-n)) / r),

where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is $3,400, the interest rate is 5.19% compounded semi-annually, and the loan term is 7 years, which is equivalent to 14 semi-annual periods.

First, let's convert the interest rate to its semi-annual equivalent by dividing it by 2. So, the interest rate per semi-annual period is 5.19% / 2 = 2.595%.

Now, we can plug these values into the formula:

PV = $3,400 * ((1 - (1 + 0.02595)^(-14)) / 0.02595).

Calculating this equation, we find that the present value of the loan is approximately $37,196.88 when rounded to the nearest cent.

Therefore, the present value of the loan, rounded to the nearest cent, is $37,196.88.

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A)The expression for the value of the bulldozer in terms of how many years old it is, t, is: V = $134,350 - ($5,530.95 * t) B) The value of the bulldozer after 5 years is $106,695.25.

To express the value of the bulldozer, V, in terms of how many years old it is, t, we can use the concept of linear depreciation. Linear depreciation assumes that the value decreases at a constant rate over time. In this case, the initial value of the bulldozer is $134,350, and it depreciates over 21 years.

The depreciation per year can be calculated by subtracting the salvage value ($11,500) from the initial value and dividing it by the useful life of the bulldozer:

Depreciation per year = (Initial value - Salvage value) / Useful life

Depreciation per year = ($134,350 - $11,500) / 21

Now, we can express the value of the bulldozer, V, in terms of the number of years, t, using the depreciation per year:

V = Initial value - (Depreciation per year * t)

V = $134,350 - ([$134,350 - $11,500] / 21) * t

B) To find the value of the bulldozer after 5 years, we substitute t = 5 into the expression:

V = $134,350 - ($5,530.95 * 5)

V = $134,350 - $27,654.75

V = $106,695.25

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In the given problem, we need to determine the linear independence of the vectors (2 + x, e*) and the set S = {(1,0,1,0), (0,2,0,2), (2,6,2,6)}. To show that (2 + x, e*) is linearly independent, we need to demonstrate that the only solution to the equation a(2 + x) + be* = 0 is a = b = 0. For the set S, we can determine linear dependence by checking if there exist scalars a, b, and c, not all zero, such that a(1,0,1,0) + b(0,2,0,2) + c(2,6,2,6) = 0.

To show that (2 + x, e*) is linearly independent, we assume that a(2 + x) + be* = 0 for some scalars a and b. Expanding this equation, we get 2a + ax + be* = 0. Since e* is a nonzero vector, the only way for this equation to hold is if a = b = 0. Thus, (2 + x, e*) is linearly independent.

For the set S = {(1,0,1,0), (0,2,0,2), (2,6,2,6)}, we can determine linear dependence by checking if there exist scalars a, b, and c, not all zero, such that a(1,0,1,0) + b(0,2,0,2) + c(2,6,2,6) = 0. By performing the vector addition and scalar multiplication, we get (a + 2c, 2b + 6c, a + 2c, 2b + 6c) = (0, 0, 0, 0).

To determine if this equation has nontrivial solutions, we can set up a system of equations:

a + 2c = 0,

2b + 6c = 0,

a + 2c = 0,

2b + 6c = 0.

Simplifying these equations, we find that a = -2c and b = -3c. Since c can take any non-zero value, we have infinitely many solutions that satisfy the equation. Therefore, the set S is linearly dependent.

In conclusion, (2 + x, e*) is linearly independent, while the set S = {(1,0,1,0), (0,2,0,2), (2,6,2,6)} is linearly dependent.

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A.  The film's overall message seems to emphasize the importance of personal growth, self-discovery, and finding one's own path amidst societal and religious expectations.

B. Both films offer nuanced perspectives on the role of Islam in society, encouraging viewers to critically examine the complexities and implications of religious beliefs and practices.

Among the three films mentioned, "Year of the Elephant" and "Bab el-Oued City" feature representations of Islam. Let's discuss how Islam is portrayed in these two works, compare and contrast their depictions, and analyze how these representations contribute to the overall messages of the films.

"Year of the Elephant": "Year of the Elephant" is a Moroccan film directed by Hamid Bennani. It is based on a novella by renowned Moroccan author Tahar Ben Jelloun. The story revolves around Zahra, a young woman struggling with her faith and personal identity. Islam is a central theme in the film, explored through Zahra's spiritual journey.

Islam is portrayed as a deeply ingrained cultural and religious force in Zahra's life. Zahra grapples with societal expectations and norms associated with being a Muslim woman. The film highlights traditional interpretations of Islam that restrict women's freedom and agency. There is a focus on the pressures faced by Zahra, including her arranged marriage and adherence to conservative gender roles prescribed by her community.

The portrayal of Islam in "Year of the Elephant" raises questions about the intersection of religion, culture, and personal autonomy. It examines the tension between adhering to religious traditions and pursuing individual desires. The film's overall message seems to emphasize the importance of personal growth, self-discovery, and finding one's own path amidst societal and religious expectations.

"Bab el-Oued City": "Bab el-Oued City" is an Algerian film directed by Merzak Allouache. The narrative revolves around societal tensions and political unrest in Algeria during the 1990s. While Islam is not the primary focus of the film, it is depicted as an influential aspect of Algerian society, particularly within the context of political and ideological struggles.

In "Bab el-Oued City," Islam is portrayed through various characters representing different perspectives and interpretations. Some characters are depicted as devout Muslims, engaging in rituals and prayers, while others exploit religion for personal gain or political manipulation. There is a portrayal of religious fundamentalism and its impact on society, highlighting the extremist views held by certain individuals.

The film explores the complex relationship between Islam, politics, and social dynamics. It sheds light on how religious ideologies can be manipulated to serve political agendas, leading to division and conflict within communities. The representation of Islam in "Bab el-Oued City" serves to provoke thought about the consequences of radicalization and the need for societal unity amidst ideological differences.

While both films touch upon the theme of Islam, their portrayals differ in focus and approach. "Year of the Elephant" primarily explores the personal struggles and identity crisis of an individual Muslim woman within a traditionalist society. On the other hand, "Bab el-Oued City" delves into the broader socio-political implications of Islam within a country undergoing significant turmoil.

In terms of their overall messages, "Year of the Elephant" emphasizes individual liberty and self-discovery within the confines of religious and societal expectations. It encourages viewers to question and challenge prevailing norms to find personal fulfillment. Conversely, "Bab el-Oued City" draws attention to the dangers of extremism and manipulation of religious beliefs for political purposes. It underscores the importance of understanding and bridging ideological divides to foster harmony and progress.

Both films offer nuanced perspectives on the role of Islam in society, encouraging viewers to critically examine the complexities and implications of religious beliefs and practices.

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