a) The determination of the dividends per share for the cumulative preferred and common stock for each year is as follows:
Preferred StockDividends per share
2011 $3.00
2012 $1.20
2013 $4.80
Common StockDividends per share
2011 $1.50
2012 $0
2013 $2.10
b) The determination of the amount of current dividends that preferred stock should receive per year is $75,000.
What is cumulative preferred stock?Cumulative preferred stock is a special class of preferred stock that enjoys cumulative dividends.
Cumulative dividends imply that any year when sufficient dividends are not declared, the arrears are carried forward to subsequent years.
It is the opposite of non-cumulative preferred stock.
On the other hand, the common stockholders can only receive dividends after the preferred stockholders have been paid, including their cumulative dividends.
Cumulative Preferred Stock:Number of shares = 25,000
Dividend rate = 2%
Par value = $150
Total cumulative preferred stock = $3,750,000 (25,000 x $150)
Annual dividend = $75,000 ($3,750,000 x 2%)
Common Stock:Number of shares = 50,000
Par value = $15
Total common stock = $750,000 (50,000 x $15)
Preferred StockDividends Due (Dividends per share)
2011 $75,000 $3 ($75,000/25,000)
2012 $30,000 $1.2 ($30,000/25,000)
2013 $120,000 $4.8 ($120,000/25,000)
Common StockDividends Available (Dividends per share)
2011 $75,000 ($150,000 - $75,000) $1.50 ($75,000/50,000)
2012 $0 ($30,000 - $30,000) $0
2013 $105,000 ($225,000 - 120,000) $2.10 ($105,000/50,000)
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Calculate the area of each triangle using two different methods. Figures are not drawn to scale.
Who ever give me the answer gets extra points
The areas of the triangles are as follows:
1. 52.5 ft²
2. 369 inches²
How to find the area of a triangle?The area of a triangle can be represented as follows:
area of a triangle = 1 / 2 bh
where
b = base of the triangleh = height of the triangleTherefore, let's find the areas of the triangle using the formula as follows:
1.
area of the triangle = 1 / 2 × 15 × 7
area of the triangle = 1 / 2 × 105
area of the triangle = 52.5 ft²
2.
area of the triangle = 1 / 2 × 41 × 18
area of the triangle = 1 / 2 × 738
area of the triangle = 369 inches²
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Richard used a radius measure of a circle to be 3.6 inches when he calculated the area of a circle. The correct radius measure was actually 3.5 inches. What is the difference between Richard’s measured area of the circle and the actual area of the circle?
a. 0.1π square inches
b. 0.71π square inches
c. π square inches
d. 0 square inches
e. 2.4 square inches
As a result, the answer is (e) 2.4 square inches, which is the difference between Richard's measured and real circle area.
What is area?In mathematics, area is a measure of the amount of space occupied by a two-dimensional object, such as a rectangle, triangle, circle, or any other shape. It's a scalar quantity that describes the size of a region in two-dimensional space. The units of area are typically square units, such as square inches, square centimeters, square meters, etc. In general, the area of a shape is a measure of how much space it occupies, and it is an important concept in geometry, engineering, and many other fields.
Here,
The formula for the area of a circle is given by:
A = πr²
Where r is the radius of the circle.
Using the incorrect radius of 3.6 inches, the calculated area would be:
A = π * (3.6 inches)² = 40.44 square inches
Using the correct radius of 3.5 inches, the actual area would be:
A = π * (3.5 inches)² = 38.5 square inches
So, the difference between Richard's measured area of the circle and the actual area of the circle would be:
40.44 square inches - 38.5 square inches = 1.94 square inches
Therefore, the answer is (e) 2.4 square inches that is the difference between Richard’s measured area of the circle and the actual area of the circle.
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given the following data, find the weight that represents the 45th percentile. weights of newborn babies 7.8 5.5 7.6 8.3 7.1 7.3 8.6 7.4 8.5 7.7 6.5 9.4 8.4 8.1 6.5
The 45th Percentile from the data is 7.65
Percentiles are a method for dividing data into 100 equal parts. So, there are 99 percentile values.
single data percentile formula is
Px = [tex]\frac{x (y+1)}{100}[/tex]
Px = Percentile x
y = lots of data
How to find the 45th percentile weight of newborn babies?
first, we must be sorted from the smallest to the largest.
5.5 6.5 6.5 7.1 7.3 7.4 7.6 7.7 7.8 8.1 8.3 8.4 8.5 8.6 9.4
After sorting the data, we can plug it into a single data percentile formula
Px = P45
x = 45
y = 15
P45 = [tex]\frac{45 (15+1)}{100}[/tex]
P45 = [tex]\frac{36}{5}[/tex]
P45 = 7.2
The 45th percentile is in the order of the 7th & 8th digits
the order of the 7th & 8th numbers is 7.6 & 7.7
after that we average the 7th & 8th numbers to find out the 45th percentile value
[tex]\frac{7.6 + 7.7}{2}[/tex] = [tex]\frac{15.3}{2}[/tex] = 7.65
the 45th percentile of newborn weight data is 7.65
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My sister is buying new carpet for her bedroom floor. The length of the bedroom is 13 feet. The area of the bedroom is 175.5 square feet. How wide is my sister's bedroom?
Solve the system of equations using elimination: 5 � + 4 � = − 4 5x+4y=−4 and 4 � + 4 � = 4 4x+4y=4.
The solution to the system of equations is x = -8, y = 9.
To solve the system of equations by elimination, we must manipulate the two equations so that when the equations are added or subtracted, one of the variables is eliminated.
One method is to multiply one or both equations by a constant, resulting in opposite coefficients for one of the variables. In this case, we can multiply the first equation by 4 and the second equation by -5, yielding the following y coefficients:
code :
(4)(5x + 4y = -4) => 20x + 16y = -16 (-5)
(4x + 4y = 4) => -20x - 20y = -20
We can now combine the two equations to eliminate y:
code :
20x + 16y = -16 \s-20x - 20y = -20 \s———————
0x - 4y = -36
When we simplify the result, we get:
code :
-4y = -36 y = 9
Now we can plug y = 9 back into one of the original equations to find x. Let's look at the first equation:
code :
5x+4y = -4 5x+4(9) = -4 5x+36 = -4 5x = -40 x = -8
As a result, the system of equations solution is x = -8, y = 9.
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Neda sells televisions. She earns a fixed amount for each television and an additional $25 if the buyer gets an extended warranty. If Neda sells 17 televisions with extended warranties, she earns $1,445. How much is the fixed amount Neda earns for each television?
Answer:
$60 per TV sold
Step-by-step explanation:
Multiply $25 by 17 to find out how much she earned from the extended warranties
so 25 x 17 = 425
1445-425= 1020
now divide 1020 by 17 to find out how much neda earned from each TV
1020/17 = 60
According to AAA ('Triple' A), the median amount that Americans spent over the 2012 Labor Day Holiday was $761.00. Consider the pie chart below.
A -- Fuel Transportation
B -- Other Transportation
C -- Food and Beverage
D -- Shopping
E -- Entertainment/Recreation
F -- Hotel
G -- Other
Express your answers rounded to the nearest cent.
a). How much money did the average American spend on Food & Beverage over the 2012 Labor Day Holiday?
b). How much money did the average American spend on Entertainment/Recreation over the 2012 Labor Day Holiday?
c). How much more money did the average American spend on Food & Beverage than on Entertainment/Recreation over the 2012 Labor Day Holiday?
a. The average American spend on Food & Beverage is $152.2. b. The average American spend on Entertainment/Recreation is $98.93. c. They spent $53.27 more on food than on entertainment.
What is pie chart?In order to show mathematical issues, the "pie chart," often referred to as a "circle chart," divides the circular statistical visual into sectors or portions. A proportionate amount of the entire is indicated by each sector. The Pie-chart is now the most effective method for determining the composition of something. Pie charts typically take the role of other graphs, such as bar graphs, line plots, histograms, etc.
Given that, the average American spent $761.00.
a. Money spent on Food and Beverages is:
F = 761(20/100) = $152.2
b. Money spent on Entertainment is:
E = 761(13/100) = $98.93
c. The money spent on food is more than entertainment by:
A = 152.2 - 98.93 = $53.27
Hence, a. The average American spend on Food & Beverage is $152.2. b. The average American spend on Entertainment/Recreation is $98.93. c. They spent $53.27 more on food than on entertainment.
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find the exact value of all six trigonometric functions of an acute angle, in standard position if the radius is 6 and the x coordinate is 5
The exact value of all six trigonometric functions:
sin(θ) = 0.55
cos(θ) = 0.83
tan(θ) = 0.66
cot(θ) = 1.51
sec(θ) = 1.2
cosec(θ) = 1.81
Let us assume that x represents the horizontal distance(x-axis), y represents the vertical distance and r be the radius.
here, r = 6 units and x = 5 units
Using Pythagoras theorem,
y = [tex]\sqrt{r^2-x^2}[/tex]
y = [tex]\sqrt{6^2-5^2}[/tex]
y = 3.32 units
Now we find the exact value of all six trigonometric functions.
Let us assume that θ be an angle made by radius with positive x-axis.
sin(θ) = y/r
sin(θ) = 3.32 / 6
sin(θ) = 0.55
cos(θ) = x/r
cos(θ) = 5/6
cos(θ) = 0.83
tan(θ) = y/x
tan(θ) = 3.32 / 5
tan(θ) = 0.66
cot(θ) = x/y
cot(θ) = 5/3.32
cot(θ) = 1.51
sec(θ) = r/x
sec(θ) = 6/5
sec(θ) = 1.2
cosec(θ) = r/y
cosec(θ) = 6/3.32
cosec(θ) = 1.81
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Translate this sentence into an equation.
Chau's savings increased by 17 is 54.
Answer: 17x = 54
x represents chau's savings before it increased
For a certain company, the cost function for producing a items is C (a) = 50 x + 150 and the revenue function for selling a items is R (a) = -0.5(⅜ - 110)2 + 6,050. The maximum capacity of the company is 150 items.
Since the optimal production level is within the company's maximum capacity of 150 items, the company should produce and sell 75 items to maximize profit.
What are functions?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
According to question:To find the optimal production level a that maximizes profit, we need to determine the point at which marginal revenue equals marginal cost.
The marginal cost function is the derivative of the cost function, which is C'(a) = 50.
The marginal revenue function is the derivative of the revenue function, which is R'(a) = -0.5(3/8 - 110).
Setting these two equal and solving for a gives:
50 = -0.5(3/8 - 110)
a = 75
Since the optimal production level is within the company's maximum capacity of 150 items, the company should produce and sell 75 items to maximize profit.
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Pet shelters typically have special adoption events for black cats and dogs, since their adoption rate is lower. One specific pet shelter (which has only cats and dogs) has 40% cats and 60% dogs. Twenty percent of the cats are black, and 10% of the dogs are black. The adoption percentage for black cats is 5%, and for black dogs is 10%. Cats that are not black are equally likely to be adopted as not adopted, and this is the same for dogs that are not black. For (b)-(f), write the probability statement and then calculate your answer.
a) Draw the probability tree and label all events and probabilities in it.
b) What is the probability that a randomly chosen animal is not black, a dog, and is adopted?
c) What is the probability that a randomly chosen animal is black, a cat, and is not adopted?
d) What is the probability that a randomly chosen animal is adopted?
e) Suppose a randomly chosen animal is a cat, what is the probability that it is adopted?
f) Suppose a randomly chosen animal is adopted, what is the probability that it is a cat?
a) The pet shelter has 40% cats (20% black, 5% adopted), and 60% dogs (10% black, 10% adopted). 50% are adopted in non-black cats and dogs, b) 0.45, c) 0.19, d) 0.15, e) 0.375, f) 0.6.
a) The probability tree would seem like this:
P(Cat) = 40%
P(Black Cat) = 20%
P(Adopted Black Cat) = 5%
P(Not Adopted Black Cat) = 95%
P(Not Black Cat) = 80%
P(Adopted Not Black Cat) = 50%
P(Not Adopted Not Black Cat) = 50%
P(Dog) = 60%
P(Black Dog) = 10%
P(Adopted Black Dog) = 10%
P(Not Adopted Black Dog) = 90%
P(Not Black Dog) = 90%
P(Adopted Not Black Dog) = 50%
P(Not Adopted Not Black Dog) = 50%
b) P ( Adopted & Not Black Dog ) = P(Not Black Dog) x P(Adopted | Not Black Dog) = 0.90 * 0.50 = 0.45
c) P(Not Adopted & Black Cat) = P(Black Cat) x P(Not Adopted | Black Cat) = 0.20 * 0.95 = 0.19
d) P(Adopted) = P(Adopted Black Cat) + P(Adopted Not Black Cat) + P(Adopted Black Dog) + P(Adopted Not Black Dog) = 0.05 + 0.50 + 0.10 + 0.50 = 0.15
e) P(Adopted | Cat) = P(Adopted & Cat) / P(Cat) = (0.05 + 0.50) / 0.40 = 0.375
f) P(Cat | Adopted) = P(Cat & Adopted) / P(Adopted) = (0.05 + 0.50) / 0.15 = 0.6.
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Problem 6. Determine if the pair of planes is parallel or intersecting. If they are parallel, find the distance between them. If they intersect, find a parametrization for the line of intersection. 1. 3.x + 2y +z = 8 and x + 3y – z = 5. 2. 2.c – y +z = 4 and 4.0 – 2y + 2z = 3.
1. To determine if the pair of planes 3x + 2y + z = 8 and x + 3y – z = 5 are parallel or intersecting, we can check if their normal vectors are parallel or not.
The normal vector of the first plane is <3, 2, 1>, and the normal vector of the second plane is <1, 3, -1>. These normal vectors are not parallel, so the planes intersect at a line.
To find a parametrization for the line of intersection, we can set one of the variables to be a parameter and solve for the other two. Let's choose z as the parameter.
From the second plane equation, we have z = x + 3y - 5. Substituting this into the first plane equation, we get: 3x + 2y + (x + 3y - 5) = 8
Simplifying, we get: 4x + 5y = 13
Solving for y in terms of x, we get: y = (13 - 4x) / 5
So a parametrization for the line of intersection is: x = t
y = (13 - 4t) / 5, z = t + 3((13 - 4t) / 5) - 5 = (2t + 2) / 5
2. To determine if the pair of planes 2c – y + z = 4 and 4c – 2y + 2z = 3 are parallel or intersecting, we can again check if their normal vectors are parallel or not.
The normal vector of the first plane is <2, -1, 1>, and the normal vector of the second plane is <4, -2, 2>. These normal vectors are parallel (in fact, they are scalar multiples of each other), so the planes are parallel.
To find the distance between the two parallel planes, we can take any point on one plane and find its distance to the other plane. Let's choose the point (0, 0, 4) on the first plane. The distance between this point and the second plane is: |4c - 2(0) + 2(4) - 3| / sqrt(4^2 + (-2)^2 + 2^2) = |4c - 5| / 2sqrt(6)
So the distance between the two parallel planes is |4c - 5| / 2sqrt(6).
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Enter the correct answer in the box. The graph of a quadratic function is represented by the table. x f(x) 6 -2 7 4 8 6 9 4 10 -2 What is the equation of the function in vertex form? Substitute numerical values for a, h, and k.
The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
The given values are
x, f(x)
6, -2
7, 4
8, 6
9, 4
10, -2
The equation of the function in vertex form is given as follows;
f(x) = a × (x - h)² + k
To find the values of a, h, and k, we proceed as follows;
When x = 6, f(x) = -2
We have;
-2 = a × (6 - h)² + k = (h²-12·h+36)·a + k.............(1)
When x = 7, f(x) = 4
We have;
4 = a × ( 7- h)² + k = (h²-14·h+49)·a + k...........(2)
When x = 8, f(x) = 6...........(3)
We have;
6 = a × ( 8- h)² + k
When x = 9, f(x) = 4.
We have;
4 = a × ( 9- h)² + k ..........(4)
When x = 10, f(x) = -2...........(5)
We have;
-2 = a × ( 10- h)² + k
Subtract equation (1) from (2)
4-2 = a × ( 7- h)² + k - (a × (6 - h)² + k ) = 13·a - 2·a·h........(6)
Subtract equation (4) from (2)
a × ( 9- h)² + k - a × ( 7- h)² + k
32a -4ah = 0
4h = 32
h = 32/4
= 8
From equation (6) we have;
13·a - 2·a·8 = 6
-3a = 6
a = -2
From equation (1), we have;
-2 = -2 × ( 10- 8)² + k
-2 = -8 + k
k = 6
The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6
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Find each value or measure. Assume that segments that appear to be tangent are tangent.
The measure of arc AD is 25°.
AC and BD are chords of the circle. The two chords intersect at the point E which makes an angle 93°. The measure of arc BC is 161°. To find the measure of arc AD:
The measure of arc AD by using the property that "if two chords intersect in the interior of the circle, then the measure of each angle is half the sum of the arcs intercepted by the angles and its vertical angle".
Thus, applying the above theorem:
93° = 1 /2 (arcBC + arcAD)
Here, measure of angle E is 93°.
93° = 1 / 2( 161 + AD)
93 = 161 / 2 + AD / 2
93 = 161/ 2 + AD/2
solving further ( multiplying equation by 2 on both sides)
186 = AD + 161
AD = 186 - 161
arc AD = 25°
So, the measure of arc AD is 25°.
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____The given question is incomplete, the complete question is given below:
Find each value or measure. Assume that segments that appear to be tangent are tangent. Find arc AD.
SH . Given f(x)=x²-3x and g(x)=2x-5, find each value. a. f(-4) b. g(1)-f(-3) c. f(g(-4))
a. To find f(-4), we simply substitute -4 for x in the function f(x):
f(-4) = (-4)² - 3(-4) = 16 + 12 = 28
Therefore, f(-4) = 28.
b. To find g(1)-f(-3), we first need to find g(1) and f(-3) separately.
g(1) = 2(1) - 5 = -3
f(-3) = (-3)² - 3(-3) = 9 + 9 = 18
Then, we can substitute these values into the expression:
g(1)-f(-3) = -3 - 18 = -21
Therefore, g(1)-f(-3) = -21.
c. To find f(g(-4)), we first need to find g(-4) and then substitute this value into f(x).
g(-4) = 2(-4) - 5 = -8 - 5 = -13
Then, we can substitute -13 for x in the function f(x):
f(g(-4)) = (-13)² - 3(-13) = 169 + 39 = 208
Therefore, f(g(-4)) = 208.
A bakery sold 105 cupcakes in one day. The head baker predicted he would sell 85 cupcakes that day. What was the percent error of the baker's prediction?
There was 19% percent error of the baker's prediction.
What is a percent error?Percent error is the difference between the estimated value and the actual value in comparison to the actual value and is expressed as a percentage.
Given that, a bakery sold 105 cupcakes in one day, the head baker predicted he would sell 85 cupcakes that day.
We are asked to find the percent error of the baker's prediction,
Percent error = |expected value - exact value| / exact value × 100 %
The expected value is the prediction of the Chef = 85
The exact value = 105
Percent error = |85-105| / 105 × 100 %
= 20/105 × 100 %
= 19%
Hence, there was 19% percent error of the baker's prediction.
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An airplane on a transatlantic flight took 2 hours 30 minutes to get form New York to its destination, a distance of 3,000 miles. To avoid a storm, however, the pilot went off his course, adding a distance of 600 miles to the flight. How fast did the plane travel?
A) 1440mph
B) 1461mph
C) 1480mph
D) 1466mph
E) 1380mph
Please Help
Answer:
We can use the formula:
distance = rate x time
The total distance traveled by the plane is 3,000 + 600 = 3,600 miles. The time it took to cover this distance is 2 hours and 30 minutes, or 2.5 hours. So we have:
3,600 = rate x 2.5
Solving for the rate, we get:
rate = 3,600 / 2.5 = 1440 mph
Therefore, the answer is (A) 1440mph
What is the slope of the line?
Answer:
The slope is 3.
Step-by-step explanation:
You can find this by using rise/run.
The line goes from (1,2) to (2,5).
The rise for this is 3 and the run is 1.
3/1 is 3, therefore the slope is 3
Andre said he is thinking of a 2-digit number. He makes the number from tens and ones in 8 different ways. In one way, there is 1 more ten than there are ones. What is Andre's number? Show your thinking using drawings, numbers, or words.
Andre's number is 43.
What is Andre's number?Generally, Let's call the tens digit of Andre's number "t" and the ones digit "o".
We know that Andre can make the number in 8 different ways. This means that there are 8 different combinations of t and o that can make up the number.
One of these ways has 1 more ten than ones, which means that the number is 10 more than the sum of the digits. In other words:
t + o + 10 = 10t + o + 1
Simplifying this equation, we get:
9t = 9o + 9
Dividing both sides by 9, we get:
t = o + 1
This means that the tens digit is 1 more than the ones digit, which narrows down our possibilities.
Since the number is a 2-digit number, the tens digit must be between 1 and 9 (inclusive), and the ones digit must be between 0 and 9 (inclusive). We also know that the tens digit is 1 more than the ones digit.
Using these constraints, we can create a table of all the possible combinations of t and o that satisfy these conditions:( table attached below)
Out of these 8 numbers, only one of them can be made in a way where there is 1 more ten than ones. Looking at the table, we can see that the number is 43, since it is the only number where the tens digit is 1 more than the ones digit, and it can be made by combining the digits in a way where there is 1 more ten than ones (i.e., 3 tens and 4 ones).
Therefore, Andre's number is 43.
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Which properties are true for all parallelograms?
The requried properties are true for all the parallelograms are,
1. Opposite sides are parallel 2. Opposite sides are congruent
A parallelogram is a quadrilateral consisting of pairs of parallel sides.
The following properties are true for all parallelograms,
The opposite sides are parallel.
The Opposite sides are congruent.
All parallelograms have four congruent sides (property 1), four right angles (property 2), or exactly one pair of parallel sides (property 3). These properties only apply to specific types of parallelograms, such as rectangles or squares.
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Jacy keeps track of the amount of average monthly rainfall in her hometown. She determines that the average monthly rainfall can be modeled by the function ...where ...represents the average monthly rainfall in centimeters and ... represents how many months have passed. If ... represents the average rainfall in July, in which months does Jacy’s hometown get at least 10.5 centimeters of rainfall? Show all of your algebraic reasoning to support your final answer.
Answer:
September, October, November
Step-by-step explanation:
When monthly rainfall in centimeters is represented by A(t) = 2.3sin(πt/6)+9.25 and A(0) represents July's rainfall, you want to know the months in which average rainfall is at least 10.5 cm.
InequalityWe want to find the values of t that make A(t) ≥ 10.5:
2.3sin(πt/6) +9.25 ≥ 10.5
2.3sin(πt/6) ≥ 1.25 . . . . . . subtract 9.25
sin(πt/6) ≥ 0.543478 . . . . divide by 2.3
πt/6 ≥ 0.574575 . . . . . . . take inverse sine
t ≥ 1.097
The sine function is symmetrical about π/2, so this also means solutions will be of the form ...
πt/6 ≤ π -0.574575
t ≤ 6 -1.097 ≈ 4.903
MonthsThe month numbers that will have rainfall at least 10.5 cm will fall in the range ...
1.097 ≤ t ≤ 4.903
t ∈ {2, 3, 4}
If July is month 0, then these months are September, October, November.
Jacy's hometown will get at least 10.5 cm of rain in September, October, and November.
__
Additional comment
The attachment confirms this result. We have shifted the rainfall function so it can use conventional month numbers. It shows months 9, 10, 11 have rainfall above 10.5 cm.
<95141404393>
can you please solve?
The equation of the line is y = (2/3)x + 20/3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation has:
Slope = 2/3
Passes through the line (-4, 4).
Now,
The equation of the line is y = mx + c.
m = 2/3
Consider (-4, 4) = (x, y)
So,
4 = (2/3)(-4) + c
4 = -8/3 + c
c = 4 + 8/3
c = (12 + 8) / 3
c = 20/3
Now,
y = (2/3)x + 20/3
Thus,
The equation of the line is y = (2/3)x + 20/3.
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HELP PLEASE! Find the surface area of the composite shape. Round to the nearest tenth.
The surface area of the composite figure is 415. 25 in²
How to determine the surface area of the composite structureFrom the image shown, we can see that the figure is made up of a cuboid and a semicircle.
The formula for calculating the surface area of a cuboid is given as;
Surface area =2lw+2lh+2hw
Given that, l is the length, h is the height and w, the width.
Surface area = 2(6×10) + 2(6×8) + 2(8 × 10)
expand the brakect
Surface area = 120 + 96+ 160
Surface area = 376 in²
Surface area of a semicircle = 1/2(πr2 ),
Substitute the values
Surface area = 1/2 ×22/7 ×5² = 39.25 in²
Hence, the value is the sum of the surface areas
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find the derivative of the following function using the definition. no credit will be given for using derivative rules. f(x)= 1/ (1+x^2). please solve and explain
Strictly using the limit definition of the derivative to find the derivative of the function:
The limit definition of the derivative looks like this:
[tex]\lim_{h \to \zero} \frac{f(x+h) - f(x) }{h}[/tex]
If we replace f(x) with −3x, we get:
[tex]\lim_{h \to \zero} \frac{-3(h+x) - 3x }{h}\\\\\lim_{h \to \zero} \frac{-3h-3x) - (-3x) }{h}\\[/tex]
Simplifying, we get:
[tex]\lim_{h \to \zero} \frac{-3h }{h}\\[/tex]
So, the derivative of −3x must be −3.
We know that the secondary means the rate of change of the function. Graphically, this means that the outgrowth is the pitch of the graph of that function.
Since −3x is a first degree polynomial, we know that it'll always have the same pitch, and therefor the same outgrowth. We can also corroborate this by looking at the graph, noticing that it's a straight line:
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photo attacthed! please help quick!
The missing values in the table are
3/2, 4/3 and 4/9
How to find the missing valuesThe table shows a proportion of
oats = flours * 4/9
the proportion was gotten from
1/3 / 3/4 = 4/9
The missing parts are
let the missing value be x
x * 4/9 = 2/3
x = 2/3 / 4/9
x = 3/2
3 * 4/9 = x
x = 4/3
1 * 4/9 = x
x = 4/9
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For each value of y, determine whether it is a solution to 22 ≤-7y+1
A.-3 B. 4 C. 9 D. -9
The solution of the inequality is -3.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
22 ≤-7y+1
Solving the inequality
22 ≤-7y+1
22 - 1 ≤-7y
21 ≤-7y
21/7 ≤-y
3 ≤-y
y≤ -3.
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El agua de un recipiente varía su temperatura de 12 °C a 38°C, cuando se le transfieren 205 calorías. ¿Cuál es la masa de agua en el recipiente?
The mass of the water is 7880.1 grams.
What is specific heat capacity?Specific heat capacity is the amount of heat energy required to raise the temperature of a substance per unit of mass.
Mathematically -
Q = mcΔT
where -
{Q} = heat energy
{m} = mass
{c} = specific heat capacity
{ΔT} =change in temperature
Given is the water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it.
Specific heat capacity of water = 4.186 J/g°C
205 calories = 857720 Joules
We can write -
Q = mcΔT
857720 = m x 4.186 x (38 - 12)
857720 = 108.836 x m
m = 857720/108.836
m = 7880.1 grams
Therefore, the mass of the water is 7880.1 grams.
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{QUESTION IN ENGLISH -
The water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it. What is the mass of water in the container?}
point B is 2 root 5 units from A and is on the intersection of two gridlines write the co-ordniates of both positions of point B
The coordinates of both positions of point B is (2√5,0) and B2: (0,2√5).
What is y-intercept of a function?The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.
Assume that we've got: y = f(x)
At y-axis, we've got x = 0, so putting it will give us the y-intercept.
Thus, y-intercept of y = f(x) is y = f(0)
We are given that;
Point b= 2 root 5 units
Now,
Since point B is 2√5 units away from point A, we can draw two circles with radius 2√5 centered at point A. The two intersections of these circles with the gridlines will give us the two possible positions of point B.
For example, if point A has coordinates (0,0) and the gridlines are the x-axis and y-axis, then the two possible positions of point B are:
B1: (2√5,0) - the intersection of the circle with the positive x-axis
B2: (0,2√5) - the intersection of the circle with the positive y-axis
If the gridlines are different, then the positions of point B will be different.
Therefore, by the intercept the answer will be (2√5,0) and B2: (0,2√5).
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what is 2/3 of 3/7 in math
Answer:
(2x3) / (3x7) = 6/21
We simplify to get 2/7
Answer: 5/21 ?
im not 100% sure this is correct but I think so. sorry if its wrong
Un cubo tiene un volumen de 8 Metro cúbicos .¿cual es la longitud de una arista del cubo ? Muestra cómo hallasteis tu respuesta
The edge of the cube is equal to 2 m³.
QuadrilateralsThere are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a square, all angles are 90° and all sides present the same value.
A square is a 2D figure, when the square is associated with a 3D figure, the figure is called a cube.
The cube presents 6 faces with length (l), height (h) and width (w) equal. Thus, the cube presents congruent edges. The volume is given from the formula V=a³, where a is a congruent edge.
The exercise gives the volume of the cube 8m³. As presented previously, the edges of the cube are congruent and the formula by the volume is V=a³. Thus,
V=a³
8=a³
[tex]\sqrt[3]{a^3}[/tex]=[tex]\sqrt[3]{8}[/tex]
a=[tex]\sqrt[3]{2^3}[/tex]
a=2 m
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