What is an equation of the line that passes through the point (5, 1) and is parallel to
the line x + y = 9?

Answer:

Angle BFC.

Step-by-step explanation:

Because angle BFD is a right angle because angle AFE is equal to BFD because of vertical angles

Joe's goal to earn 1 sticker every two weeks is a reasonable and achievable target. By setting a specific goal, Joe can work towards earning stickers through consistent good behavior over time.

Having a goal provides Joe with motivation and a clear objective to strive for. It also allows him to track his progress and see the tangible results of his efforts. By earning stickers, Joe not only receives a physical reward but also reinforces positive behavior and builds a sense of accomplishment.

Earning 1 sticker every two weeks also sets a manageable pace for Joe. It allows him to focus on consistent good behavior over a reasonable timeframe without feeling overwhelmed or discouraged. This approach encourages him to maintain his efforts consistently rather than relying on sporadic bursts of good behavior.

Moreover, the process of earning stickers every two weeks helps Joe develop discipline and self-control. It teaches him the value of delayed gratification and the importance of consistent effort towards his goals. It also instills a sense of responsibility and accountability as he actively works towards achieving his target.

Overall, Joe's goal of earning 1 sticker every two weeks provides him with a structured approach to improve his behavior and work towards a reward. It encourages consistency, discipline, and personal growth while reinforcing positive habits and values.

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To construct a 90% confidence interval for the average speed of cars on the highway with a margin of error no more than ±0.5 mph and a standard deviation of 7 mph, you must clock at least 339 cars.

Step 1: Identify the critical value (z-score) for a 90% confidence interval. This can be found in a standard z-table or using a calculator. The critical value for a 90% confidence interval is 1.645.

Step 2: Use the margin of error (E) formula to calculate the sample size (n):
E = (z * σ) / √n

Where E is the margin of error (0.5 mph), z is the critical value (1.645), σ is the standard deviation (7 mph), and n is the sample size.

Step 3: Rearrange the formula to solve for n:
n = (z * σ / E)^2

Step 4: Plug in the values and calculate the sample size:
n = (1.645 * 7 / 0.5)^2
n ≈ 338.89

Since the sample size must be a whole number, round up to the nearest whole number.

To construct a 90% confidence interval for the average speed of cars on the highway with a margin of error no more than ±0.5 mph and a standard deviation of 7 mph, you must clock at least 339 cars.

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Answer:

well we know that top and botton are 12 and the sides are 5. there are 4 sides soo thats 4 times 5. so basically its 12x12x5x5x5x5 whick is 90000.

Step-by-step explanation:

sorry for the wait!

hope this helps!

please mark brainliest!

have a good day!

:) ;)

(if this is wrong im so sorry, i tried .;(

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

According to the statement seen in this question, the line segments RT and  ST are collinear to each other. Mathematically speaking, the length of the line segment ST can be found by using the following formula:

RT = RS + ST

ST = RT - RS

ST = 19 - 6

ST = 13

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

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From the figure,

∠6 and ∠3 are adjacent angles because they form supplementary angles.

∠3 and ∠2 are opposite angles so they form equal angles.

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides. The opposing or confronting sides and the opposing angles in a parallelogram are of equal length. The Euclidean parallel postulate, or one of its equivalent formulations, is a necessary precondition for both the congruence of opposite sides and opposite angles, and neither condition can be demonstrated without using it.

In contrast, a quadrilateral with just one set of parallel sides is referred to as a trapezoid or trapezium in British or American English.

A parallelepiped is the parallelogram's three-dimensional counterpart.

From the figure,

∠6 and ∠3 are adjacent angles because they form supplementary angles.

∠3 and ∠2 are opposite angles so they form equal angles.

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(a) To find the inverse Laplace transform of F(s) = (s²+1) / [(s-2)(s-1)s(s+1)], we can use partial fraction decomposition.

First, factorize the denominator: (s-2)(s-1)s(s+1) = s^4 - 2s^3 - s^2 + 2s^3 - 4s^2 + 2s + s^2 - 2s - s + 1 = s^4 - 4s^2 + 1.

Now, we can rewrite F(s) as: F(s) = (s²+1) / (s^4 - 4s^2 + 1).

Next, we need to express F(s) in terms of partial fractions. Let's assume the decomposition is: F(s) = A/(s-2) + B/(s-1) + C/s + D/(s+1).

By equating the numerators, we can solve for the unknown coefficients A, B, C, and D.

Once we have the partial fraction decomposition, we can use the Laplace transform table to find the inverse Laplace transform of each term.

(b) For F(s) = e^-s / [(s-1)(s² + 4s + 8)], we can also use partial fraction decomposition.

First, factorize the denominator: (s-1)(s² + 4s + 8) = s³ + 4s² + 8s - s² - 4s - 8 = s³ + 3s² + 4s - 8.

Now, we can rewrite F(s) as: F(s) = e^-s / (s³ + 3s² + 4s - 8).

Next, express F(s) in terms of partial fractions: F(s) = A/(s-1) + (Bs + C)/(s² + 4s - 8).

By equating the numerators, solve for the unknown coefficients A, B, and C.

Then, use the Laplace transform table to find the inverse Laplace transform of each term.

(c) For F(s) = (2s² + 3s - 1) / [(s-1)³ e^(-3s+2)], we can use the properties of Laplace transforms.

First, apply the shifting property of the Laplace transform to the denominator: F(s) = (2s² + 3s - 1) / (s-1)³ e^(-3s) e^2.

Now, we have F(s) = (2s² + 3s - 1) / (s-1)³ e^(-3s) e^2.

We can use the Laplace transform table to find the inverse Laplace transform of each term separately, considering the shifting property and the transforms of powers of s.

Overall, the process involves decomposing the functions into partial fractions, applying the shifting property if necessary, and utilizing the Laplace transform table to find the inverse Laplace transforms of each term.

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Answer:

0.000018, 2.5 x 10(-6), 7.5 x 10(-6)

Step-by-step explanation:

To calculate the charge flowing through the gold film, we'll use the formula Q = I × t, where Q is the charge, I is the current, and t is the time. First, we need to find the current (I) using the given current density.

The current density (J) is 7.3 × 10^5 A/m^2. The film's cross-sectional area (A) can be calculated by multiplying its thickness and width, which is 3.0 μm × 70 μm = 210 μm^2. To convert this to square meters, multiply by 10^-12: 210 × 10^-12 m^2.

Now we can find the current (I) by dividing the current density (J) by the area (A): I = J × A = 7.3 × 10^5 A/m^2 × 210 × 10^-12 m^2 = 0.1533 A.

Next, we need to find the time in seconds: 15 min × 60 s/min = 900 s.

Finally, calculate the charge (Q) using the formula Q = I × t: Q = 0.1533 A × 900 s = 137.97 C.

So, the charge that flows through the gold film in 15 minutes is approximately 137.97 Coulombs.

To calculate the amount of charge that flows through the gold film in 15 minutes, we need to use the formula:

Q = I x t

Where Q is the charge, I is the current density, and t is the time.

First, we need to calculate the total area of the gold film:

A = thickness x width
A = 3.0 μm x 70 μm
A = 210 μm2

Next, we need to calculate the total current that flows through the gold film:

I = current density x area
I = 7.3×105 Am2 x 210 μm2
I = 1.533×10-2 A

Finally, we can calculate the amount of charge that flows through the gold film in 15 minutes:

Q = I x t
Q = 1.533×10-2 A x 15 min x 60 s/min
Q = 13.80 C
Therefore, the amount of charge that flows through the gold film in 15 minutes is 13.80 coulombs.

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The relationship between a prism and a pyramid is the volume of a rectangular prism is 3 times the volume of a rectangular pyramid. The volume of the rectangular prism is 648 in3.

A rectangular prism is a 3-dimensional object. It has six rectangular faces .  It has 8 vertices, 6 faces, and 12 edges. The volume of a rectangular prism = width x height x length

A rectangular pyramid is a three-dimensional object. It is made up of a rectangular base and a triangular face.  The volume of a rectangular pyramid = 1/3(width x height x length )

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Answer:

It  is C

Step-by-step explanation:I Have the exact answer on my test

Answer:

Step-by-step explanation:

your gay

First, add to find how much he spent.

15 - 2.59 = $12.41

Second, divide to find how many gallons of gas he can buy.

12.41 / 3.39 ≈ 3.7

Therefore, he can roughly buy 3.7 gallons of gas.

Best of Luck!

Multiply and simplify the expression assume variable are positive is is \(\sqrt[3]{42x^{15} }\)

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

applying the law of indices

Index laws are the rules for simplifying expressions involving powers of the same base number

\(\sqrt[3]{7}x^{7}. \sqrt[3]{6x^{8} }\)

Factor our the roots

\(\sqrt[3]{7x^{7}. 6x^{8} }\)

multiply the number

\(\sqrt[3]{42x^{15} }\)

Simplify further using law of indices we have:

\(\sqrt[3]{42x^{15} }\)

Therefore, the root of the variable is \(\sqrt[3]{42x^{15} }\)

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Answer:

1. 2 hours

2. 25cm

3. 6.84

Step-by-step explanation:

120÷3=40

4800÷40=120 so 2 hours

for the second one just divide 50 in half

for 3 just do $1.14×6

Answer:

1. 120 min

2. 25 cm

3. $6.84

Step-by-step explanation:

1. 120 words : 3min

multiply each side by 40 because 120 words times 4 is 4800 words

4800 words : 120min

2.   2 : 1 = length : width

multiply each side by 25 because 2 times 25 is 50 cm

50 cm : 25 cm

3. $1.14 : 100 grams

multiply each side by 6 because 100 grams times 6 is 600 grams

$6.84 : 600 grams

For quadratic equation f(x) = ax² + bx + c in given interval using mean value theorem answers of given questions are,

Value of z is 3 in ( 2,4).

Option1) z is independent of the values of a, b, and c.

value of z = 3  in [1,417]

Conjecture is tangent line at (z, f(z)) has same slope as line connecting the endpoints of the interval.

Quadratic function is,

f(x) = ax² + bx + c

Interval = (2, 4)

By the Mean Value Theorem,

There exists a number z between 2 and 4 such that,

f'(z) = (f(4) - f(2))/(4 - 2)

Taking the derivative of f(x), we get

f'(x) = 2ax + b

Substituting this into the above equation, we get,

2az + b = (f(4) - f(2))/2

We also know that,

f(2) = 4a + 2b + c

f(4) = 16a + 4b + c

Substituting these into the above equation,

⇒2az + b = (16a + 4b + c - 4a - 2b - c)/2

⇒2az + b = 6a + b

⇒ z = (6a)/(2a)

⇒ z = 3

Value of z depends only on the interval (2,4).

And not on the specific values of a, b, and c.

So the correct statement is

z is independent of the values of a, b, and c.

If the same function was defined on the interval [1, 417],

Find z by using the same formula,

z = (6a)/(2a)

  = 3

z is still 3.

Based on the Mean Value Theorem,

Conjecture that for any given interval, there exists a number z within the interval .

Such that the tangent line at (z, f(z)) has the same slope as the line connecting the endpoints of the interval.

This number z is independent of the specific values of a, b, and c.

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Answer:

3^3 = 27, so C

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The method of reduction of order is a technique used to find a second solution to a homogeneous linear differential equation when one solution is already known.

However, it cannot be directly used for nonhomogeneous linear differential equations. In nonhomogeneous equations, the method of undetermined coefficients or variation of parameters is typically used to find a particular solution.

Therefore, the statement "the method of reduction of order can also be used for the nonhomogeneous equation" is false. It is important to understand the different techniques for solving differential equations, and to choose the appropriate method based on the type of equation and boundary conditions given.

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The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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Answer:

C, D and E

Step-by-step explanation:

Given equation:

\(\dfrac35(30x-15)=72\)

Use the distributive law  \(a(b-c)=ab-ac\):

\(\implies \dfrac35\cdot30x- \dfrac35\cdot15=72\)

\(\implies \dfrac{3 \cdot30}5x- \dfrac{3 \cdot15}5=72\)

\(\implies \dfrac{90}5x- \dfrac{45}5=72\)

\(\implies 18x- 9=72\)  ←  option c

Factor out common term 3:

\(\implies 3(6x- 3)=72\)  ←  option d

Solve \(18x- 9=72\):

\(\implies 18x- 9+9=72+9\)

\(\implies 18x=81\)

\(\implies \dfrac{18x}{18}=\dfrac{81}{18}\)

\(\implies x=4.5\)  ←  option e

Answer:

£120

Step-by-step explanation:

Given that

The price after reduction = £78

So, 65% = £78.

We have to calculate 100 %

To do so, find 5% and multiply that by 20

65% = £78

5% = 78/13 = £6

So, 100% = 6 x 20 = £120

Hope this helps.

Good Luck

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The percent yield is calculated as the ratio of the actual yield to the theoretical yield, multiplied by 100.

Percent yield is a measure of how efficient a chemical reaction or process is in producing the desired product.

The formula for percent yield is:

Percent Yield = (Actual Yield / Theoretical Yield) * 100

The actual yield is the amount of product obtained from the reaction or process, typically measured in grams or moles. It represents the actual amount of product obtained in the laboratory.

The theoretical yield, on the other hand, is the maximum amount of product that can be obtained based on stoichiometry and other factors. It is calculated using balanced chemical equations and the starting amounts of reactants.

By dividing the actual yield by the theoretical yield and multiplying by 100, we get the percent yield, which is expressed as a percentage.

This value provides insight into the efficiency of the reaction or process, with a higher percent yield indicating a more efficient conversion of reactants into products.

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That means that each hour it drops about 0.0625 inches

Divide the decrease in water level by the length of the time interval.

decrease = 7/12 inches ≅ 0.583 inches

Time interval: From 11 pm to 8:20 am you have 9:20 hours = (9 + 20/60) hours ≅ 9.33 hours

So the water drops at a rate of about

0.583/9.33 inches/hour ≅ 0.0625 inches/hour

Therefore, each hour it drops about 0.0625 inches.

The rate constant, or the specific rate constant, is the proportionality constant in the equation that expresses the relationship between the rate of a chemical reaction and the concentrations of the reacting substances.The rate constant is a proportionality factor in the rate law of chemical kinetics that relates the molar concentration of reactants to reaction rate. It is also known as the reaction rate constant or reaction rate coefficient and is indicated in an equation by the letter k.

Rate constant is dependent on the temperature. For zero-order reaction, rate constant's unit is mol L - 1 s - 1 . For first-order reaction, rate constant's unit is . For second-order reaction, rate constant's unit is mol - 1 L s - 1 .

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Answer:

90-51 = 39 39°

Step-by-step explanation:

A

1) Let's solve this system graphically, by plotting each line.

I) y + 2x = -1 Let's rewrite it as the slope-intercept form

y = -2x -1

Writing a t -table for that:

x | y=-2x-1

0 | -1

1 | -3

2 | -5

II) 3y -x = 4 Let's rewrite it as the slope-intercept form

3y = 4 +x Divide both sides by 3

y = 4/3 + x/3

Writing a table for that:

x | y = 4/3 +x3

0 | 1.33

1 | 1.66

2 | 2

2) As we have three coordinate points for each equation, we can locate them in the Coordinate Plane:

Notice that, the common point to those lines (the red one: 3y-x =4) and (blue: y+2x=-1)

3) Hence, the answer is A

On Day 1, Jenna's original menu had 11 percentage of calories from saturated fat, while on Day 2, Jenna's modified menu had only 4% of calories from saturated fat.

To calculate the percentage of calories from saturated fat for both days, first locate the columns for saturated fat (Fat-S) and calories (Cals) on the spreadsheet report. Add the total number of calories for both days, then add the total number of saturated fat calories for both days. To calculate the percentage of calories from saturated fat for each day, divide the total number of saturated fat calories for each day by the total number of calories for each day and multiply by 100. On Day 1, Jenna's original menu had a total of 2,826 calories, with 317 saturated fat calories, meaning 11% of calories from saturated fat. On Day 2, Jenna's modified menu had a total of 2,839 calories, with 115 saturated fat calories, meaning 4% of calories from saturated fat. Therefore, Day 2 had a much lower percentage of calories from saturated fat when compared to Day 1.

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In the null hypothesis, "pB" is the true proportion of sunny days in City B, and "pA" is the proportion of sunny days in City A.

The null hypothesis and alternative hypothesis your friend would use to test his claim are:

Null hypothesis: The true proportion of sunny days in City B is equal to or less than the proportion of sunny days in City A. That is, H0: pB ≤ pA.

Alternative hypothesis: The true proportion of sunny days in City B is greater than the proportion of sunny days in City A. That is, Ha: pB > pA.

In the alternative hypothesis, "pB" is again the true proportion of sunny days in City B, and "pA" is again the proportion of sunny days in City A, and the ">" symbol indicates that the true proportion of sunny days in City B is greater than the proportion of sunny days in City A.

what is proportion?

In statistics, proportion refers to the fractional part of a sample or population that possesses a certain characteristic or trait. It is often expressed as a percentage or a ratio. For example, in a sample of 100 people, if 20 are males and 80 are females, the proportion of males is 0.2 or 20% and the proportion of females is 0.8 or 80%.

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On solving the provided question we can say that by property AAA both triangle EFG and CBE are similar and in the triangle UVT and QRS  all sides are not equal, so it is not similar to any.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

in the triangle UVT and QRS

all sides are not equal, so it is not similar to any.

in triangle EFG and CBE

angle EBC = angle EGF

angle BCE = angle GFE

angle BEC = angle FEG

so by property AAA both triangle EFG and CBE are similar

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Answer:

There is an x-intercept at x=2

Step-by-step explanation:

wait no, convert to y=2x-4. X itnercept is when it should be like (X,0), so Y should be 0 and solve for x. 4=2x, x=2