To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350
Solving for W, we get:
W = 350 - 2L
Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:
L = x + y + z
Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:
Area = Length x Width
Therefore, the total area of the fenced-in region is:
Area = (xW) + (yW) + (zW)
Substituting W = 350 - 2L and L = x + y + z, we get:
Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))
Simplifying this equation, we get:
Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)
To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.
After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:
W = 350 - 2L
L = x + y + z
With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.
In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.
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At what values of x does f(x)= 3x^5 - 5x^3 +15 have a relative maximum?a) -1 onlyb) 0 onlyc) 1 onlyd) -1 and 1 onlye) -1, 0 and 1
The function f(x) = 3x⁵ - 5x³ + 15 has relative maxima at x = -1 and relative minima at x = 1, so the answer is (d) -1 and 1 only.
To find the relative maximum of the function f(x) = 3x⁵ - 5x³ + 15, we need to find the critical points and then determine whether they correspond to a maximum or minimum.
To find the critical points, we need to find where the derivative of the function is equal to zero
f'(x) = 15x⁴ - 15x²
f'(x) = 15x²(x² - 1)
Setting f'(x) equal to zero, we get
x²(x² - 1) = 0
This equation is true when x = 0, x = 1, and x = -1.
Now we need to determine whether these points correspond to a relative maximum or minimum. To do this, we can use the second derivative test.
f''(x) = 60x³ - 30x
Plugging in x = -1, we get
f''(-1) = -30 < 0
This means that x = -1 corresponds to a relative maximum.
Plugging in x = 0, we get
f''(0) = 0
This test is inconclusive, so we need to use another method to determine the nature of the critical point at x = 0.
Plugging in x = 1, we get
f''(1) = 30 > 0
This means that x = 1 corresponds to a relative minimum.
Therefore, the correct option is (d) -1 and 1 only
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Suppose that you are headed toward a plateau 40 m high. If the angle of elevation to the top of the plateau is 20 degrees, how far are you from the base of the plateau?
We are approximately 17.88 meters from the base of the plateau.
What is an angle of elevation?An angle of elevation is the angle formed between a horizontal line and a line of sight that is directed upward to an object or point above the horizontal level. It is commonly used in trigonometry and geometry to determine the height or distance of an object, such as a building, tower, or mountain.
We can use trigonometry to solve this problem. Let's call the distance we are from the base of the plateau "x".
From the problem, we know that the height of the plateau (the opposite side) is 40m and the angle of elevation (the angle between the horizontal and the line of sight to the top of the plateau) is 20 degrees.
Using the tan function, we get,
tan(20) = 40/x
To solve for x, we can cross-multiply:
x * tan(20) = 40
Then, we can divide both sides by tan(20):
x = 40 / tan(20)
Using a calculator, we get:
x ≈ 17.8798 meters
Therefore, we are approximately 17.88 meters from the base of the plateau.
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what is 6 and 2/5 times 1/6
Answer: [tex]\frac{16}{15}[/tex]
Step-by-step explanation:
First, we will turn 6 and 2/5 into a single improper fraction.
6 * 5 = 30
30 + 2 = 32
6 and 2/5 = 32/5
Next, we will multiply across:
[tex]\displaystyle \frac{32}{5} *\frac{1}{6} =\frac{32}{30}[/tex]
Lastly, we will simplify by dividing both the numerator and the denominator by 2:
[tex]\displaystyle \frac{16}{15}[/tex]
Help me show my work for any of the answers , I’ll mark brainliest
Answer:
Set your calculator to degree mode.
1) sin(X)/x = sin(Z)/z
sin(57.5°)/15 = sin(Z)/13
sin(Z) = 13sin(57.5°)/15
Z = 47.0°
2) sin(M)/m = sin(L)/l
sin(32°)/9 = sin(L)/12
sin(L) = 12sin(32°)/9
L = 45.0°, so N = 180° - (32° + 45°)
= 103.0°
3) sin(Q)/q = sin(P)/p
sin(48°)/19 = sin(P)/17
sin(P) = 17sin(48°)/19
P = 41.7°, so R = 180° - (48° + 41.7°)
= 90.3°
4) sin(A)/a = sin(B)/b
sin(85°)/8 = sin(B)/7
sin(B) = 7sin(85°)/8
B = 60.7°
5) sin(D)/d = sin(F)/f
sin(D)/24 = sin(56°)/23
sin(D) = 24sin(56°)/23
D = 59.9°
6) sin(U)/u = sin(V)/v
sin(U)/30 = sin(130°)/45
sin(U) = 30sin(130°)/45
U = 30.7°
In 9-11,use the dot plot at the right.
A dot plot is a simple type of graph that represents data using dots. It is a one-dimensional display of data where each dot represents a single data point. Dot plots are useful for showing the distribution of a set of values, particularly when the data set is small.
What is a dot plot?To create a dot plot, you simply draw a horizontal or vertical line and plot a dot above or beside the line for each data point. The dots are usually stacked vertically or horizontally if there are multiple data points with the same value.
| x
8 | x
7 | x x x
6 | x x x x
5 | x x x x
4 | x x x x x
3 | x x x x x
2 | x x x x x x
1 | x x x x x x x
---------------
1 2 3 4 5 6 7
In this example, the dot plot shows the number of times a dice roll resulted in a particular value. The x's represent the data points, and the numbers on the left indicate the frequency of each value.
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4. Patel has 5 less than 4 times as many trophies as Horatio. He has 19 trophies in all. How many trophies does Horatio have?
Answers:
A. 3
B. 6
C. 71
D. 91
Horatio has 6 trophies by equating the resultant linear equation in one variable.
Hence option b is the correct option.
Patel has 19 trophies in total.
Its is said that Patel has five less than four times as many trophies as Horatio has.
Let the number of trophies Horatio has be x and that of Patel be y.
From the given relation of trophies of Patel and Horatio we get,
y = 4x - 5
This forms a linear equation.
We have y = 19.
Thus y = 4x - 5 can be written as,
19 = 4x - 5
Thus we have the equation in the form of a linear equation in one variable.
Simplifying the linear equation in one variable we get,
19 = 4x - 5
⇒ 19 + 5 = 4x
⇒ 24 = 4x
or, 4x = 24
⇒ x = 24/4
⇒ x = 6
Hence, Horatio has x = 6 trophies in total.
Hence option b is correct option.
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question 1 help me asap
Answer:
-1 = (-1/2)(6) + b
-1 = -3 + b, so b = 2
y = -(1/2)x + 2, so m = -1/2 and b = 2
You invest $5,000 into a CD that is compounded every month. The interest rate is
1.25% and you leave the money in the CD for 5 years. How much money do you
have in your CD at the end of the 5 years?
You will have $5,333.85 in your CD at the end of the 5 years.
The formulation for the future value of an investment with monthly compounding is:
[tex]CD = P(1 + \frac{r}{n} )^{(nt)}[/tex]
Wherein:
CD = final amountP = primary amountr = annual interest charge (as a decimal)n = number of times the interest is compounded in step with 12 monthst = time (in years)Plugging in the given values:
[tex]CD= 5000(1 + \frac{0.0125}{12} )^{(12*5)}[/tex]
[tex]CD = 5000(1.00104)^{60}[/tex]
CD = 5000(1.06677)
CD = $5,333.85
Consequently, you will have $5,333.85 in your CD at the end of the 5 years.
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I need some help please
Answer:
x+2
hope this helps ;)
and cute pfp
Answer:
Step-by-step explanation:
x-1, because 3 fits the criteria, x>=1
The angle of depression from the top of a lighthouse to a boat in the ocean is 44°. If the lighthouse
is 245 feet tall, how far is the boat from the base of the lighthouse? Round to the nearest tenth.
The angle of depression is always measured from the horizontal.
A triangle is formed by the lighthouse, the ground and the boat. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the boat. (Alternate angles on parallel lines)
The angle at the top of the lighthouse, inside the triangle is:
[tex]90^\circ-27^\circ=63^\circ[/tex]
The distance to the boat is the side opposite the angle of 63° while the height of the lighthouse is the adjacent side.
[tex]\dfrac{\text{opposite}}{\text{adjacent}} =\text{tan 63}^\circ[/tex]
[tex]\dfrac{\text{distance}}{245} =\text{tan 63}^\circ[/tex]
[tex]\text{distance}=245\times \text{tan 63}^\circ[/tex]
[tex]=480.83=480.84\thickapprox\boxed{\bold{480.8}}[/tex]
Robert ate lunch at 11:am. He ate a snack4and a half hours later. What time did he eat his snack
If Robert ate lunch at 11:am and he ate a snack 4and a half hours later, Robert ate his snack at 3:30 pm
To find out what time Robert ate his snack, we need to add 4 and a half hours to the time he ate lunch.
Since he ate lunch at 11:00 am, we can convert this time to 24-hour format by adding 12 hours to get 11:00 + 12:00 = 23:00.
Next, we add 4 and a half hours to 23:00 by converting the half hour to minutes and adding it to the minutes portion of the time:
23:00 + 4 hours + 30 minutes = 27:30
However, since there are only 24 hours in a day, we need to convert this time back to 12-hour format. To do this, we subtract 12 hours from 27:30 to get 15:30.
Therefore, Robert ate his snack at 3:30 pm (or 15:30 in 24-hour format).
In summary, we added 4 and a half hours to the time Robert ate lunch, converted the resulting time to 24-hour format, subtracted 12 hours to account for the excess of 24 hours, and then converted the time back to 12-hour format to obtain the time Robert ate his snack.
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a. ( 24 – 59 ) – ( 48:2 -60)
Answer:
Step-by-step explanation:
Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carson sisters to divide evenly among themselves. There are 5 Carson sisters. How many pieces of jewelry did each sister recive
As per the given Equation Each sister received 1 piece of jewelry.
Let's the number of pieces of jewelry that each sister received "x". Since there are 5 sisters, the total number of pieces of jewelry that the sisters received is 5x.
We can then set up an equation to represent the total number of pieces of jewelry that the sisters received from both grandmothers:
13 + y = 5x
This equation says that the total number of pieces of jewelry the sisters received is equal to the sum of 13 pieces from Grandma Gertrude and y pieces from Grandma Fien, and this total is also equal to the number of sisters (5) times the number of pieces each sister received (x).
To solve for x, we can first simplify the equation:
y = 5x - 13
Now we can substitute this expression for "y" into the original equation:
13 + (5x - 13) = 5x
5x = 5x
This equation is true for any value of x, which means that x can be any number. However, we are looking for the number of pieces of jewelry that each sister received, so we need to find a specific value of x.
Dividing both sides of the equation by 5, we get:
x = 1
This means that each sister received 1 piece of jewelry.
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most people complain that they gain weight during the december holidays. to find out how much, we sample the weights of 23 adults in mid-november and again in early to mid-january. the mean weight change for the sample was a gain of 0.11 lbs., with a standard deviation of the differences of 5.25 lbs. find a 82% confidence level for the average weight gain.
With 82% confidence that the true average weight gain during the December holidays for the sampled adult population is between -1.25 pounds. and 1.47 pounds.
To find the 82% confidence interval for the mean weight gain over the holidays in December, you can use the following formula:
[tex]CI = xd ± t*(SDd/sqrt(n))[/tex]
where:
xd = average weight change of sample (0.11 lb increase)
SDd = standard deviation of weight difference (5.25 lbs)
n = sample size (23)
t = the critical value of the t distribution with n-1 degrees of freedom and the desired confidence level (82% in this case)
You can use a t-table or a calculator to find the critical value of the t-distribution. With 22 degrees of freedom (n-1) and an 82% confidence level, the critical value is approximately 1.319.
Plugging in the given values gives:
[tex]CI = 0.11 ± (1.319*(5.25/sqrt(23))) = (-1.25, 1.47)[/tex]
Therefore, we can say with 82% confidence that the true average weight gain during the December holidays for the sampled adult population is between -1.25 pounds. and 1.47 pounds.
Note that the confidence intervals include zero. This means that we cannot reject the null hypothesis that there is no significant difference in weight between mid-November and he early-to-mid-January.
However, this does not necessarily mean no weight gain during his December vacation, as there is individual variation in weight change within the sample.
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if tan A=4/3 and tan B=3/5 calculate and simplify the following
the value of the expression sin A cos B - cos A sin B is √34/5. use the trigonometric identities
what is expression ?
Trigonometric identities are mathematical equations that relate the values of trigonometric functions to one another. They are true for all possible values of the variables involved, and can be used to simplify and solve trigonometric equations.
In the given question,
To solve this problem, we need to use the properties of trigonometric functions to find the values of other trigonometric functions for angles A and B.
We know that:
tan A = opposite/adjacent = 4/3
tan B = opposite/adjacent = 3/5
Using the Pythagorean theorem, we can find the hypotenuse of the right triangles for angles A and B:
For angle A: hypotenuse = √(opposite² + adjacent²) = √(4² + 3²) = 5
For angle B: hypotenuse = √(opposite² + adjacent²) = √(3² + 5²) = √34
Now, we can use the definitions of sine, cosine, and tangent to find their values for angles A and B:
sin A = opposite/hypotenuse = 4/5
cos A = adjacent/hypotenuse = 3/5
sin B = opposite/hypotenuse = 3/√34
cos B = adjacent/hypotenuse = 5/√34
We can simplify these values by rationalizing the denominators:
sin B = 3√34/34
cos B = 5√34/34
Finally, we can use the trigonometric identities to find the value of the expression:
sin A cos B - cos A sin B
Substituting the values we found:
sin A cos B - cos A sin B = (4/5)(5√34/34) - (3/5)(3√34/34)
Simplifying:
sin A cos B - cos A sin B = √34/5
Therefore, the value of the expression sin A cos B - cos A sin B is √34/5.
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if tan A=4/3 and tan B=3/5 calculate and simplify the following expression sin A cos B - cos A sin B ?
find the sum of the first 6 terms of the finite geometric series 18, -54, 162
The sum of the first 6 terms of the given sequence is -1350.
What is sum?
In mathematics, the term "sum" refers to the result of adding two or more numbers or quantities together. The sum of two numbers a and b is denoted by a + b. Similarly, the sum of three numbers a, b, and c is denoted by a + b + c.
The given sequence is a finite geometric sequence with a common ratio of -3. To find the sum of the first 6 terms of this sequence, we can use the formula for the sum of a finite geometric series:
[tex]S_n = a(1 - r^n) / (1 - r)[/tex]
where S_n is the sum of the first n terms of the sequence, a is the first term of the sequence, r is the common ratio, and n is the number of terms in the sequence.
Substituting the given values, we get:
[tex]S_6 = 18(1 - (-3)^6) / (1 - (-3))\\\\S_6 = 18(1 - 729) / 4\\\\S_6 = -1350[/tex]
Therefore, the sum of the first 6 terms of the given sequence is -1350.
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Answer:
Step-by-step explanation:
-1,092
7. The formula for the volume of
a cone is given by V=1/3 pi r²h,
where r is the radius of the base
and h is the height of the cone.
Solve the formula for h. Then find
the height of a cone with a volume
of 48 cm³ and a base with a radius
of 4 cm.
The height of the cone is approximately 1.5 cm.
What is a cone?Both a cone and a cylinder have circular bottoms and are three-dimensional shapes. The lateral surfaces of the two shapes differ most noticeably from one another. A cone has a lateral surface that tapers from a point at the apex to a circular base, whereas a cylinder has a curved lateral surface that is parallel to its base. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height, whereas the volume of a cone is calculated using V = (1/3)πr²h.
The volume of the cone is given as:
V = (1/3)πr²h
Rearranging the equation to isolate h we get:
3V = πr²h
h = (3V)/(πr²)
Now, for volume
of 48 cm³ and a base with a radius of 4 cm we have:
h = (3(48))/(π(4)²)
h ≈ 1.5 cm
Hence, the height of the cone is approximately 1.5 cm.
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What is the volume of the composite shape?
A rectangle has a perimeter of
90" and an area of 200" squared.
What are the dimensions of the
rectangle?
The dimensions of the rectangle are either 25" by 8" or 20" by 10".
What is perimeter and area?The perimeter of a two-dimensional shape is the space surrounding it. It is calculated using length units like inches or metres. The lengths of all the sides of a rectangle are added up to determine its perimeter.
Area is a unit used to describe how much room there is inside a two-dimensional form. It is calculated using area units like square inches or square metres. A rectangle's area is calculated by multiplying its length by its width.
The perimeter of the rectangle is given as:
Perimeter = 2(length + width)
Substituting the value we have:
90 = 2(L + W)
45 = L + W
Now, the area is given as:
Area = length × width
Substituting the values we have:
200 = L × W
The above equation can be written as:
W = 200/L
Substituting the value of W in the first equation we have:
45 = L + 200/L
45L = L² + 200
L² - 45L + 200 = 0
L = (45 ± √(45² - 4×1×200)) / (2×1)
L = (45 ± 5) / 2
L = 25 or L = 20
Now, for L = 25 the value of W is:
W = 200 / 25 = 8
For L = 20:
W = 200 / 20 = 10
Hence, the dimensions of the rectangle are either 25" by 8" or 20" by 10".
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HELP ME PLEASE!!!!! I NEED IT
Based on the information we can infer that the area of the figure is 464 ² units.
How to calculate the area of this figure?To calculate the area of this figure we must assume that it is a complete square and find its area as shown below:
basis = 24side = 2424 * 24 =576 units ²Now we must find the area of the non-grid regions and subtract them from the area we found previously:
4 * 12 = 48 units ²8 * 8 = 64 units ²64 + 48 = 112 units ²576 - 112 = 464 units ²
According to the above, the area of the figure is 464 units ²
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The rectangle below is dilated by a scale factor of 5. Find the perimeter and area of
the rectangle below, as well as the perimeter and area of the dilated rectangle. Figures
are not necessarily drawn to scale.
10
Perimeter of given rectangle
Area of given rectangle
Submit Answer
units
units²
Perimeter of dilated rectangle
Area of dilated rectangle
units
units2
Area of rectangle = 50 [tex]unit^2[/tex].
Perimeter of rectangle =30 unit.
Area of dilated rectangle = 1250 [tex]unit^2[/tex].
Perimeter of dilated rectangle = 150 unit.
What is dilation?
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size.
Here the given rectangle length l = 10 unit and width = 5 unit.
Now using formulas,
Area of rectangle = lw square unit.
=> A = 10*5 = 50 [tex]unit^2[/tex].
Perimeter of rectangle = 2(l+w) unit
=> P =2(10+5) = 2(15) = 30 unit.
Here scale factor= 5
The dilated rectangle length [tex]l_1[/tex]= 10*5 = 50 unit and
width [tex]w_1 = 5\times5 = 25[/tex] unit
Now area of dilated rectangle [tex]A_1[/tex]= [tex]l_1w_1[/tex] square unit.
=> [tex]A_1[/tex]= 50*25 = 1250 [tex]unit^2[/tex].
Perimeter of dilated rectangle [tex]P__1[/tex] = 2([tex]l_1+w_1)[/tex] unit.
=> [tex]P__1[/tex] = = 2(50+25) = 2(75) = 150 unit.
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The table shows the number of runs earned by two baseball players.
Player A Player B
2, 1, 3, 8, 2, 3, 4, 3, 2 2, 3, 1, 4, 2, 2, 1, 4, 6
Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with an IQR of 1.5.
Player B is the most consistent, with an IQR of 2.5.
Player A is the most consistent, with a range of 7.
Player B is the most consistent, with a range of 5.
From the given table, Player A is the most consistent, with an IQR of 1.5. So, correct option is A.
To find the best measure of variability for this data, we need to consider a measure that is robust and resistant to outliers. The interquartile range (IQR) is a good choice as it is calculated based on the range of values that fall within the middle 50% of the data and is therefore less affected by extreme values.
To calculate the IQR, we first need to find the median, which is the middle value in the dataset. For Player A, the median is 3 and for Player B, the median is 2.5.
Next, we calculate the first quartile (Q₁) and the third quartile (Q₃) which represent the 25th and 75th percentiles of the data, respectively. For Player A, Q₁ is 2 and Q₃ is 3.5, while for Player B, Q₁ is 2 and Q₃ is 4.5.
The IQR is the difference between Q₃ and Q₁. For Player A, the IQR is 1.5 (3.5 - 2) and for Player B, the IQR is 2.5 (4.5 - 2). Therefore, Player A is more consistent as their IQR is smaller, indicating that their runs earned are more tightly clustered around the median.
The range, which is the difference between the largest and smallest values in the dataset, is also a measure of variability, but it is sensitive to extreme values. In this case, the range for Player A is 7 (8 - 1) and for Player B is 5 (6 - 1), but these values do not provide as accurate an indication of consistency as the IQR.
So, correct option is A.
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Complete question is:
The table shows the number of runs earned by two baseball players.
Player A
2, 1, 3, 8, 2, 3, 4, 3, 2
Player B
2, 3, 1, 4, 2, 2, 1, 4, 6
Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with an IQR of 1.5.
Player B is the most consistent, with an IQR of 2.5.
Player A is the most consistent, with a range of 7.
Player B is the most consistent, with a range of 5.
Phoenix Corp. reported the following information for 2013 and 2014.Interest payable, December 31, 2013 $5,700Interest payable, December 31, 2014 6,200Interest expense--2014 12,250How much cash was paid for interest during 2014?A. $11,750B. $12,250C. $12,500D. $12,750
Cash paid for interest during 2014 was $12,750. Based on the provided Phoenix Corp. information, the question requires you to calculate the cash paid for interest throughout the 2014 calendar year.
Also provided are the amounts for the year's interest expenditure and the balance of interest payable as of December 31, 2013 and 2014.
These are the formulas that can be used to determine the cash paid in interest in 2014:
Interest paid in 2014 minus any increases in interest due equals the cash paid in interest.
The difference between the balance of interest payable as of December 31, 2014, and as of December 31, 2013, can be used to compute the increase in interest payable:
Interest payable at December 31, 2014 minus interest payable at December 31, 2013 equals $6,200 minus $5,700, which equals $500 in
additional interest.
This signifies that the corporation incurred more interest expense than it paid during the year Since the balance of interest payable increased from 2013 to 2014, the corporation incurred more interest expense than it paid in that period. As a result, the money used to pay interest in 2014 is:
Interest paid in 2014 plus the increase in interest due is $12,250 plus $500.= $12,750
Thus, $12,750 is the correct response (D).
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How many miles go into 10,000 kilometers
Answer:
Step-by-step explanation:
6213.712
Answer:
10,000 Kilometers = 6,213.7119 Miles
Step-by-step explanation:
the table shows the number of people who rode two different carnival rides during the first hour of the fair on opening day. ferris wheel swing ride total children 72 24 96 adults 126 42 168 total 198 66 264 based on the data in the table, what is the approximate value of p(adult|rode a ferris wheel)?
The approximate value of P(adult ∣ rode a ferris wheel) is 0.6364, which is approximately 63.64%.
To find the approximate value of P(adult|rode a ferris wheel), we can use the conditional probability formula:
[tex]\mathrm{P(adult | rode\ a\ ferris\ wheel) = \frac{P(adult \ and \ rode \ a \ ferris \ wheel)}{P(rode \ a \ ferris \ wheel)} }[/tex]
From the data given in the table, you can see that:
Total number of people who rode the ferris wheel: 198 (children + adults)
Number of adults who rode the ferris wheel: 126.
So, P(rode a ferris wheel) = 198/264
And, P(adult and rode a ferris wheel) = 126/264
Now plug these values into the conditional probability formula:
[tex]\mathrm{P(adult | rode\ a\ ferris\ wheel) = \frac{P(adult \ and \ rode \ a \ ferris \ wheel)}{P(rode \ a \ ferris \ wheel)} } \\\\= \frac{126/264}{198/264}[/tex]
[tex]\mathrm{P(adult | rode\ a\ ferris\ wheel) } = \frac{126}{198} \\\\ \approx 0.6364[/tex]
Rounded to four decimal places, the approximate value of P(adult ∣ rode a ferris wheel) is 0.6364, which is approximately 63.64%.
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The median of distribution A is 8. which of these could be the mean?
a. 7
b. 8
c. 9
d. It cant be determined
Answer:
Step-by-step explanation:
The mean of the distribution with a median of 8 could also be: Option B: 8
How to interpret the mean, median and mode?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is defined as the middle value when a data set is ordered from least to greatest.
The mode is defined as the number that occurs most often in a data set.
Now, one good relationship between the 3 measures is given as:
3(median) = mode +2(mean)
Thus, if our median is 8, then it is very possible that our means could also be 8
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The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 140, 220, 48, and 19. What is the median length of time required to review an application
The median length of time required to review an application is 105 minutes.
To find the median, the data needs to be arranged in order from least to greatest: 19, 48, 140, 220.
Since there is an even number of data points, the median is the average of the two middle values, which in this case are 48 and 140. Adding them together and dividing by 2 gives 94, which is less than the next highest value of 220.
Therefore, the median length of time required to review an application is 105 minutes.
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i will give first answer brainliest
4. Make Sense Rebecca and Brian each have 4 packs of batteries. Each pack has 10 batteries. How many batteries do Rebecca and Brian have in all?
Answer:
Rebecca and Brian each have 40 batteries, making a total of 80 batteries.
Step-by-step explanation:
Rebecca:
Rebecca has 4 packs of batteries, and if each one contains 10 batteries, then she has 40 batteries.
Brian:
Brian also has 4 packs of batteries, each one contains 10 batteries, so he also has 40 batteries.
In total, they have a combined 80 batteries. hope this helps ;)
Please solve this using a tree diagram
Bag X contains 9 blue balls and 18 red balls.
Bag Y contains 7 blue balls and 14 red balls.
Liz picks a ball at random from bag X.
She puts the ball into bag Y.
Mike now picks a ball at random from bag Y.
Show that
Probability (Liz picks a blue ball) = Probability (Mike picks a blue ball)
The probability of picking blue ball by Liz and Mike are equal =1/3
What about probability?Probability is a branch of mathematics that deals with the study of random events or experiments. It is concerned with quantifying the likelihood or chance of a particular event occurring, given certain assumptions or conditions.
The probability of an event is typically represented as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain. For example, if you flip a fair coin, the probability of getting heads is 0.5, and the probability of getting tails is also 0.5.
There are different methods for calculating probabilities, depending on the nature of the event or experiment being considered. Some of the most commonly used methods include the classical probability method, the empirical probability method, and the subjective probability method.
Probability has many applications in various fields, including statistics, finance, engineering, and science. It is used to model and analyze complex systems and to make predictions and decisions based on uncertain information.
According to the given information:Given : X contains 9 blue balls and 18 red balls.
Y contains 7 blue balls and 14 red balls.
Probability of picking blue ball is 9/9+18
=9/27=1/3
Now Mike pick ball from bag Y one ball not affect these pick ball
so, 7/7+14=7/21=1/3
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