The area of a rectangular wall of a barn is 24 square feet. Its length is 8 feet longer than twice it’s width. Find the length and width of the wall of the barn

Answer:

m = 5/4

Y-intercept: (0,0)

Step-by-step explanation:

The equation is in slope-intercept form y = mx + b

m = the slope

b = y-intercept

Our equation y = 5/4x

m = 5/4

Y-intercept is located at (0,0)

Answer:

the slope is 5/4 and the y-intercept is 0

Step-by-step explanation:

The slope is the number before x.

The y intercept is the constant term in the equation.

Info related to the question

The equation I just worked with was given in slope intercept form :

Where the slope is defined as m and the intercept is defined as b.

Answer: Therefore, the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches is 0.884. Rounded to 3 decimal places, the answer is 0.884.

Step-by-step explanation:We can use the standard normal distribution to find the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches.

First, we need to standardize the values using the formula:

z = (x - mu) / sigma

where:

x = 52.2 and 60.6 (the values we want to find the probability between)

mu = 55.7 (the mean)

sigma = 2.6 (the standard deviation)

For x = 52.2:

z = (52.2 - 55.7) / 2.6 = -1.346

For x = 60.6:

z = (60.6 - 55.7) / 2.6 = 1.885

Next, we use a standard normal distribution table or calculator to find the area between these two z-scores:

P(-1.346 < z < 1.885) = 0.884

Therefore, the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches is 0.884. Rounded to 3 decimal places, the answer is 0.884.

Answer:

View explanation

Step-by-step explanation:

The highlighted arc from D to O

Brynen will use 7.71 gallons of gas driving to and from work this week.

To calculate the gallons of gas Brynen will use driving to and from work this week, we need to consider the round trip distance and the car's fuel efficiency.

Given:

Brynen drives 27 miles each way to work.

His car gets 35 miles per gallon of gas.

To find the total distance Brynen will travel in a week, we need to calculate the round trip distance for each workday and multiply it by the number of workdays (five days).

Round trip distance = 27 miles (one-way distance) * 2 = 54 miles (round trip distance)

Total distance traveled in a week = 54 miles (round trip distance) * 5 days = 270 miles

Next, we can determine the total gallons of gas Brynen will use using his car's fuel efficiency.

Gallons of gas used = Total distance / Fuel efficiency

Gallons of gas used = 270 miles / 35 miles per gallon

Gallons of gas used ≈ 7.71 gallons (rounded to the nearest tenth)

Therefore, Brynen will use approximately 7.71 gallons of gas driving to and from work this week.

It's important to note that this calculation assumes that Brynen's car maintains a consistent fuel efficiency of 35 miles per gallon throughout the entire week and that no additional driving outside of the work commute is considered. Factors such as traffic, variations in fuel efficiency, or additional trips would affect the actual gas consumption.

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Answer:

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The segment GI contains both GH and HI.

Using the segment addition postulate we set up an equation:

Substitute to get:

So the value of x is 9.

It means that the domain of the relation [tex]R[/tex] is the set of such elements [tex]u[/tex] for which there exists such an element [tex]v[/tex] that [tex]u[/tex] and [tex]v[/tex] are related.

The reason of discontinuity of the given function is described below.

Since we know that,

A continuous function, as the name implies, is one whose graph is continuous with no breaks or jumps. In other words, if we can draw the curve (graph) of a function without ever raising a pencil, we may claim that the function is continuous. The study of a function's continuity is critical in calculus because a function cannot be differentiable unless it is continuous.

A function is considered continuous if its graph is an uninterrupted curve with no holes, gaps, or breaks.

Now by mathematical definition of continuity

Left hand limit of a function at any point = right hand limit of function at that point = value of function at that point

Now from the graph we can see that,

At point point 3

The left hand limit and right hand limit are not equal and also the curve is discontinuous.

Hence, the given function is discontinuous function.

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Answer:

0.5ml/hr

Step-by-step explanation:

Given:

Infusion rate: 0.002 units/min

To convert the infusion rate from units/min to ml/hr, we need to know the flow rate conversion factor specific to the medication and solution being administered.

In this case, we have the information that the patient is receiving 10 units of oxytocin (Pictocin) in 250 ml of D5W solution.

To calculate the ml/hr rate, we can use the following formula:

ml/hr = (Infusion rate in units/min * Volume in ml) / Time in min

ml/hr = (0.002 units/min * 250 ml) / 1 min

ml/hr = 0.5 ml/min

Therefore, the infusion rate of 0.002 units/min is equivalent to 0.5 ml/hr.

Answer:

(a) To find the probability that a household views television between 3 and 11 hours a day, we need to calculate the z-scores for 3 and 11 hours using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. The z-score for 3 hours is (3 - 8.35) / 2.5 = -2.14 and the z-score for 11 hours is (11 - 8.35) / 2.5 = 1.06. Using a standard normal distribution table, we find that the probability of a z-score being between -2.14 and 1.06 is approximately 0.8209.

(b) To find how many hours of television viewing a household must have in order to be in the top 3% of all television viewing households, we need to find the z-score that corresponds to the top 3% of the standard normal distribution. Using a standard normal distribution table, we find that this z-score is approximately 1.88. Using the formula x = μ + zσ, we can calculate that a household must view television for approximately 8.35 + (1.88 * 2.5) = 12.75 hours to be in the top 3% of all television viewing households.

(c) To find the probability that a household views television more than 5 hours a day, we need to calculate the z-score for 5 hours using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. The z-score for 5 hours is (5 - 8.35) / 2.5 = -1.34. Using a standard normal distribution table, we find that the probability of a z-score being greater than -1.34 is approximately 0.9099.

Answer:

Step-by-step explanation:

The mean daily viewing time of television is 8.35 hours and the standard deviation is 2.5 hours. We can use a normal probability distribution to answer the following questions about daily television viewing per household:

(a) The probability that a household views television between 3 and 11 hours a day is 0.9772 (rounded to four decimal places).

(b) To be in the top 3% of all television viewing households, a household must have 15.68 hours of television viewing per day (rounded to two decimal places).

The probability that a household views television more than 5 hours a day is 0.8944 (rounded to four decimal places).

I hope this helps! Let me know if you have any other questions.

Answer:

The area bounded by the two functions f(x) and g(x) on the interval [0, 2π] is 6π.

Step-by-step explanation:

The range of y = sin(2x) is [-1, 1].

As function f(x) = sin(2x) + 1 has been translated 1 unit up, the range of f(x) is [0, 2].

The range of y = cos(x) is [-1, 1].

As function g(x) = cos(x) - 2 has been translated 2 units down, the range of g(x) is [-3, -1].

As ranges of the functions do not overlap, the two functions do not intersect.

As the curve of f(x) is above the x-axis, and the curve of g(x) is below the x-axis, we can integrate to find the area between the curve and the x-axis for each function in the given interval, then add them together.

Note: As g(x) is below the x-axis, the evaluation of the integral will return a negative area. Therefore, we need to negate the integral so we have a positive area (since area cannot be negative).

[tex]\begin{aligned}A_1=\displaystyle \int^{2\pi}_{0} (\sin(2x)+1)\; \text{d}x&=\left[-\dfrac{1}{2}\cos(2x)+x \right]^{2\pi}_{0}\\\\&=\left(-\dfrac{1}{2}\cos(2(2\pi))+2\pi\right)-\left(-\dfrac{1}{2}\cos(2(0))+0\right)\\\\&=\left(-\dfrac{1}{2}+2\pi\right)-\left(-\dfrac{1}{2}\right)\\\\&=2\pi\end{aligned}[/tex]

As the curve is below the x-axis, remember that we need to negate the integral to find the area.

[tex]\begin{aligned}A_2=-\displaystyle \int^{2\pi}_{0} (\cos(x)-2)\; \text{d}x&=-\left[\vphantom{\dfrac12}\sin(x)-2x \right]^{2\pi}_{0}\\\\&=-\left[(\sin(2\pi)-2(2\pi))-(\sin(0)-2(0))\right]\\\\&=-\left[(0-4\pi)-(0-0)\right]\\\\&=-\left[-4\pi\right]\\\\&=4\pi\end{aligned}[/tex]

[tex]\begin{aligned}A_1+A_2&=2\pi+4\pi\\&=6\pi\end{aligned}[/tex]

Therefore, the area bounded by the two functions f(x) and g(x) on the interval [0, 2π] is 6π.

The height of the cylinder is 25.

Option C is the correct answer.

We have,

To find the height of the right cylinder, we need to use the given information of the diagonal length and the total surface area.

The diagonal length of a right cylinder can be found using the formula:

diagonal = √(height² + radius²)

Given that the diagonal length is 37, we can set up the equation:

37 = √(height² + radius²)

We also know that the total surface area of a right cylinder is given by:

surface area = 2πrh + 2πr²

Given that the total surface area is 492π, we can set up the equation:

492π = 2πrh + 2πr²

Simplifying the surface area equation, we have:

246 = rh + r²

Now we have a system of equations:

37 = √(height² + radius²)

246 = rh + r²

Since we only need to find the height of the cylinder, we can focus on the first equation:

37 = √(height² + radius²)

Squaring both sides of the equation, we get:

37² = height² + radius²

1369 = height² + radius²

Substituting the second equation (246 = rh + r²) into the equation above, we have:

1369 = height² + (246 - rh)

Simplifying further, we get:

1369 = height² + 246 - rh

Now, let's analyze the answer options:

a. 35

b. 42

c. 25

d. 17

e. 32

We need to substitute each value into the equation and check if it satisfies the equation.

After checking each option, we find that the height that satisfies the equation is:

c. 25

Therefore,

The height of the cylinder is 25.

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Answer:

C.

Step-by-step explanation:

A chord has two endpoints on the circle. A diameter is a special chord bc it also goes through the center.

RT is the diameter and the rest of answer A are radii (plural of radius)

answer B is a chord, the diameter, but thats not the only chord.

answer D are chords but they forgot RT.



So, C. is the best answer.

The linear program shows that there are different attainable arrangements that accomplish the same ideal objective function value..

Based on the given data, since the objective function values at the five corner points are diverse, able to conclude that there's no one-of-a-kind ideal arrangement for this linear program.

The reality that there are numerous distinctive objective function values at the corner points suggests that there are numerous ideal arrangements or that the objective work isn't maximized or minimized at any of the corner points.

In this case, the linear program may have numerous ideal arrangements, showing that there are different attainable arrangements that accomplish the same ideal objective function value.

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a. Shape 1 = 24cm²

Shape 2 = 14.1cm²]

Total area = 38.1cm²

b. Shape 1 = 50ft²

Shape 2 = 24ft²

Total area =  74ft²

The formula for calculating area of a triangle is;

A = 1/2bh

Substitute the values

A = 1/2 × 8 × 6

Multiply the values

A = 24cm²

Area of a semicircle =3. 14 × 3²/2 = 14.1cm²

Total area = 38.1cm²

2. Area of the trapezoid is;

A = a +b/2h

A = 20/2(5) = 50ft²

Area of the triangle;

A = 1/2 × 6 × 8

A = 24ft²

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The statement about the graph of y = tan x that is true is A The period is 2pi.

In the graph of y = tan x, the function has vertical asymptotes at x = (2n + 1)π/2, where n is an integer. At these points, the value of cos x becomes zero, causing the tangent function to approach positive or negative infinity.

The period of a function is the smallest positive number such that the graph of the function repeats itself after being shifted that number of units to the right or left. In the case of y=tanx, the graph repeats itself after being shifted π units to the right.

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Which statement about the graph of y = tan x is true?

A The period is 2pi.

B The function has horizontal asymptotes whenever cos x = 0.

C The function has zeros whenever csc x = 0.

D The function is increasing everywhere in its domain

The coordinates of point M are (1, 2).

The gradient of CB is 5.

The equation of line AD in the form y = mx + c is: y = (-1/5)x + 37/5.

To solve the given problem, we can follow these steps:

1. Calculate the coordinates of point M:

Since the diagonals of a rhombus bisect each other, the midpoint of the diagonal AC will give us the coordinates of point M.

Midpoint formula:

x-coordinate of M = (x-coordinate of A + x-coordinate of C) / 2

                 = (-3 + 5) / 2

                 = 2 / 2

                 = 1

y-coordinate of M = (y-coordinate of A + y-coordinate of C) / 2

                 = (8 - 4) / 2

                 = 4 / 2

                 = 2

Therefore, the coordinates of point M are (1, 2).

2. The gradient (slope) of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the formula:

Gradient (m) = (-4 - 1) / (5 - 6)

            = -5 / -1

            = 5

Therefore, the gradient of CB is 5.

3. To find the equation of line AD, we need to calculate the gradient (m) of AD and the y-intercept (c).

Gradient of CB = 5

Gradient of AD = -1/5 (negative reciprocal of 5)

To find the y-intercept (c), we can substitute the coordinates of point A (-3, 8) into the equation y = mx + c and solve for c:

8 = (-1/5)(-3) + c

8 = 3/5 + c

c = 8 - 3/5

c = 40/5 - 3/5

c = 37/5

Therefore, the equation of line AD in the form y = mx + c is:

y = (-1/5)x + 37/5.

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To find the area of a sector, you can use the formula:

Area of Sector = (θ/360) * π * r^2

where θ is the central angle in degrees, r is the radius, and π is a mathematical constant approximately equal to 3.14159.

Let's calculate the areas for the given sectors:

r = 16 mi, θ = 150°

Area of Sector = (150/360) * π * (16 mi)^2

= (5/12) * π * 256 mi^2

≈ 334.930 mi^2

Therefore, the area of sector 16 is approximately 334.930 square miles.

Based on the LCM, Jaziel, Elisa, and Sofía will coincide again after 60 days.

From the information, in the family business, the siblings Jaziel Elisa and Sofía must help take care of it, so he comes every four days, Elisa every five days and Sofía that at six o'clock.

In order to determine when Jaziel, Elisa, and Sofía will coincide again, we need to find the least common multiple (LCM) of their visit intervals.

The intervals for Jaziel, Elisa, and Sofía are 4 days, 5 days, and 6 days, respectively. We need to find the smallest number that is divisible by all three of these intervals.

The LCM of 4, 5, and 6 is 60. Therefore, Jaziel, Elisa, and Sofía will coincide again after 60 days.

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In the family business, the siblings Jaziel Elisa and Sofía must help take care of it, so he comes every four days, Elisa every five days and Sofía that at six o'clock if the three have coincided on March 4 after how many days will they coincide again

Answer:

  tan(2x) = 2√2

Step-by-step explanation:

You want tan(2x) when tan(x) is -2/√2 and x is a 4th-quadrant angle.

The tangent double-angle identity is ...

  tan(2x) = 2tan(x)/(1 -tan(x)²)

For tan(x) = -2/√2, this gives ...

  tan(2x) = 2(-2/√2)/(1 -(-2/√2)²) = -2√2/(1 -2)

  tan(2x) = 2√2

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The measure of the ∠d is 65 degrees.

The measure of the ∠c is 89 degrees.

The measure of the arc a is 131 degrees.

The measure of arc b is 47 degrees.

The value of each variable. For the circle, the dot represents the center.

1. The measure of ∠d is;

∠d+ 115°= 180°

∠d= 180°-115°= 65°

The measure of the ∠d is 65 degrees.

2. The measure of ∠c is,

∠c+ 91°= 180°

∠c =180°-91° =89°

The measure of the ∠c is 89 degrees.

3. The measure of arc a is,

The inscribed angle measures half that of the arc comprising;

arc a = 230 - 90

arc a = 131 degrees

4. The measure of arc b is,

The inscribed angle measures half that of the arc comprising;

arc b = 178 - 131

arc b = 47 degrees

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Answer:

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The y-intercept of (0, 4) means the function has a value of 4 when x = 0.

Verify it with given functions:

A) y = 3x + 1

B) y = 4ˣ

C) y = 1ˣ

D) y = 2ˣ + 3

The step in which the subtraction property of equality was applied to solve the equation is given as follows:

D. The subtraction property of equality was not applied to solve this equation.

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality, and hence it is used to isolate a variable that is adding on a side of the expression.

For this problem, to remove the term -7, we add 7 to both sides of the expression, hence the addition property of equality was applied.

In the other step, the multiplication property was applied, hence option D is the correct option for this problem.

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The angles supplementary to ∠EOF are ∠FOB and ∠COE.

Supplementary angles are those angles that sum up to 180 degrees. In

other words, two angles are called supplementary when their measures

add up to 180 degrees.

Therefore, let's find the angles that are supplementary angles to ∠EOF.

Therefore, let's use the angle relationships in the line intersection to find

the angles that are supplementary to ∠EOF.

Hence, the angles supplementary to  ∠EOF are ∠FOB and ∠COE

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Answer:

10.33 square units

Step-by-step explanation:

Area of the sector:

     ∠JKL = Ф= 74°

      JK = r = 4

[tex]\boxed{\text{\bf Area of sector = $ \dfrac{\theta}{360}\pi r^2$}}[/tex]

  Ф is the central angle of the sector.

  r is the radius

[tex]\sf Area \ of \ the \ sector = \dfrac{74}{360}*3.14*4*4[/tex]

                            = 10.33 square units

The values of m and n are 15 and 19, respectively in the given data.

From the given values:

x: 1, 2, 7, 4, 9

y: 3, 5, 11, m, n

Looking at the x-values, we can observe that they are increasing by 1 each time.

Looking at the y-values, we can observe that they are increasing by 2 each time except for the last two values (m and n) which are unknown.

Based on this pattern, we can establish the following equation:

y = 2x + 1

Now, let's calculate the values of m and n using this equation:

For x = 7:

y = 2(7) + 1

y = 14 + 1

y = 15

Therefore, m = 15.

For x = 9:

y = 2(9) + 1

y = 18 + 1

y = 19

Therefore, n = 19.

Hence, the values of m and n are 15 and 19, respectively.

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Answer:

Q1: $1,360, Q2: $30.83, Q3: $325.50, Q4: $75

Step-by-step explanation:

QUESTION 1:

If the minimum payment is made and no additional charges are made, the balance next month should be $1,400 minus 3% of $1,400, which is $1,360.

QUESTION 2:

To calculate the interest charged for the month, we need to determine the average daily balance. Assuming no other transactions, the average daily balance would be (($2,500 * 20) + ($1,100 * 10)) / 31 = $2,032.26. Multiply this by the APR of 18% and divide by 365 to get the daily interest rate. The interest charged for the month would be approximately ($2,032.26 * 0.18) / 365 * 31 = $30.83.

QUESTION 3:

After making the first minimum pyment, the new balance would be $350 minus 7% of $350, which is $325.50.

To calculate the minimum payment due the next month, we take 7% of the new balance, which is 7% of $325.50, equal to $22.79 (rounded to the nearest cent).

QUESTION 4:

The minimum payment required on a balance of $2,500 would be 3% of $2,500, which is $75.

The translated coordinates are:

A: A'(-6, -5)  ⇒ A''(-3,-7)

B:  D'(2,-5)  ⇒  D''(8, -7)

C: C (2, 0)   ⇒ C'(5, -2)

D: D(5,-5)    ⇒ D'(8, -7)

E; C'(-1,0)     ⇒ C''(2, -2)

F: A (-3,-5)   ⇒ A'(0, -7)

G: B'(-5, 0 ) ⇒  B''(-2, -2)

H: B (-2, 0)  ⇒  B'(1, -2)

Here,

We have to apply a translation of 2 units down and 3 units right to these coordinates.

Translation means moving the entire polygon in a particular direction by a certain distance.

To apply the translation,

Add the same amount of distance to the x-coordinate of each vertex for the rightward motion, and subtract the same amount of distance from the y-coordinate of each vertex for the downward motion.

In this case,

the translation is 2 units down and 3 units right.

So the new coordinates will be:

A: A'(-6, -5) ⇒ A'( -6+ 3, -5-2)

              = A''(-3,-7)

B:  D'(2,-5)  ⇒ D'(5+3, -5 -2 )

                  = D''(8, -7)

Similarly apply for each coordinates we get,

C: C (2, 0)   ⇒ C'(5, -2)

D: D(5,-5)    ⇒ D'(8, -7)

E; C'(-1,0)     ⇒ C''(2, -2)

F: A (-3,-5)   ⇒ A'(0, -7)

G: B'(-5, 0 ) ⇒  B''(-2, -2)

H: B (-2, 0)  ⇒  B'(1, -2)

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Answer:

2/13

Step-by-step explanation:

To find the probability of drawing a 6 or a king from a standard deck of cards, we need to determine the number of favorable outcomes (cards that are either a 6 or a king) and the total number of possible outcomes (total number of cards in the deck).

There are 4 kings in a standard deck (one king in each suit: hearts, diamonds, clubs, and spades) and 4 6s (one 6 in each suit).

Total number of favorable outcomes = 4 (4 kings) + 4 (4 6s) = 8

Total number of possible outcomes = 52 (total number of cards in the deck)

Therefore, the probability of drawing a 6 or a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

= 8 / 52

= 2 / 13

So, the probability of drawing a 6 or a king from a standard deck of cards is 2/13.

To find the length of the third side of a right triangle when two sides are given, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's assume the two given sides are 'a' and 'b', and the unknown third side is 'c' (the hypotenuse).

Using the Pythagorean theorem:

c² = a² + b²

Substituting the given values:

c² = 4² + 5²

c² = 16 + 25

c² = 41

To find the length of 'c', we need to take the square root of both sides:

c = √41

So, the length of the third side is √41 (approximately 6.40) when rounded to two decimal places.

Therefore, the possible length of the third side of the right triangle is √41.

Step-by-step explanation:

We will use a phayragoras theorem

a^2 +b^2= c^2

let side1=4 be a

let side2=5 be b

let the 3rd side be the hypotnuous=c

therfore 4^2+5^2=c^2

=16+25=c^2

=41=c^2.

therfore c=√41