At the inflection points, f''(x) = 0, which implies that x = μ ± σ. Therefore the probability density function has inflection points at x = μ ± σ.
The probability density function (PDF) of a normally distributed random variable is defined as:
f(x) = 1/(σ√2π) e-(x - μ)²/2σ²
where μ is the mean,
σ is the standard deviation.
This equation has two inflection points at x = μ ± σ. To show this, we differentiate the equation twice with respect to x.
f'(x) = -(x - μ) / σ² e-(x - μ)²/2σ²
f''(x) = [-(x - μ)² / σ³ - 1] e-(x - μ)²/2σ²
At the inflection points, f''(x) = 0, which implies that x = μ ± σ. Thus, we have proved that the PDF of a normally distributed random variable has inflection points at x = μ ± σ.
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From her eye, which stands 1.69 meters above the ground, Sadie measures the angle of elevation to the top of a prominent skyscraper to be 36 ∘ ∘ . If she is standing at a horizontal distance of 275 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.
We can use the tangent function to solve this problem. Let h be the height of the skyscraper.
First, we need to find the length of the adjacent side of the right triangle formed by Sadie, the base of the skyscraper, and the point where she is standing. This length is the horizontal distance between Sadie and the base of the skyscraper, which is 275 meters.
Next, we can use the tangent of the angle of elevation to find the ratio of the opposite side (the height of the skyscraper) to the adjacent side:
tan(36°) = h/275
Solving for h, we get:
h = 275 tan(36°)
Using a calculator, we find:
h ≈ 198.64 meters
Therefore, the height of the skyscraper is approximately 198.64 meters.
Answer: 201.49
Step-by-step explanation:
Write the following inequality in slope-intercept form. 5x - y _> -6
Answer: y < 5x+6
Step-by-step explanation:
Chicken costs $3. 40 per pound and beef costs $4. 30 per pound. What is the cost of 3 pounds of chicken
If Beef costs $4.30 per pound and chicken costs $3.40 per pound then the three pounds of chicken costs $10.20.
The cost of chicken is $3.40 per pound. To find the cost of 3 pounds of chicken, we can multiply the price per pound by the number of pounds:
Cost of 3 pounds of chicken = 3 pounds × $3.40/pound
Cost of 3 pounds of chicken = $10.20
Therefore, the cost of 3 pounds of chicken is $10.20.
Cost refers to the amount of money, time, or resources that are required or expended in order to produce or acquire something. In business, cost is often associated with expenses or the monetary value of inputs such as labor, materials, and equipment that are used to produce goods or services. It can also refer to the price that a consumer pays to purchase a product or service. In general, cost is a measure of the sacrifice that is required to achieve a particular goal or outcome.
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IV. Suggested Enrichment Reinforcement Activitylies
A. Give the measures of the other three angles of parallelogram MAKE,
1. If m LM = 105°
M
А
2. If m LA = 70°
3. If m LK = 120°
E
K
Х
B. In parallelogram AXEL, diagonals XL and EA bisect each other at o
1. If XE = 12 cm, how long is AL?
A
2. If AX = 15 cm, how long is LE ?
3. If XO = 5 cm, and EO = 6 cm, what is the length
of XL ? of EA?
O
E
Please pa help po
If m LM = 105°, then m KL = 75° because opposite angles in a parallelogram are congruent.
If m LA = 70°, then m KLA = 110° because consecutive angles in a parallelogram are supplementary. Therefore, m ALK = 70°.
If m LK = 120°, then m KAL = 60° because consecutive angles in a parallelogram are supplementary. Therefore, m ALM = 120°.
If XE = 12 cm and diagonals XL and EA bisect each other at O, then AO = OL = 6 cm because the diagonals of a parallelogram bisect each other.
Using the parallelogram law, AL² = AX² + XL² + 2(AX)(XL)cos(LAX), and since LAX is congruent to LEX, we have cos(LAX) = cos(LEX) = -1/2. Substituting the given values and solving for AL, we get AL = sqrt(421) cm.
If AX = 15 cm, then LX = EA = 15/2 = 7.5 cm because the diagonals of a parallelogram bisect each other. Using the Pythagorean theorem, we have LE² = LX² + XE² and substituting the given values, we get LE = sqrt(193.5) cm.
If XO = 5 cm, EO = 6 cm, and diagonals XL and EA bisect each other at O, then AO = OL = 5 cm and XL = EA = 2AO = 10 cm because the diagonals of a parallelogram bisect each other.
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Complete Question:
A. Find the measures of the other three angles of parallelogram MAKE if:
m LM = 105°
m LA = 70°
m LK = 120°
B. In parallelogram AXEL, diagonals XL and EA bisect each other at point O. Find:
The length of AL if XE = 12 cm
The length of LE if AX = 15 cm
The length of XL and EA if XO = 5 cm and EO = 6 cm.
What is an equation of the line that passes through the points (−2,4) and (3,−6)?
Answer:
y=10x+24
Step-by-step explanation:
y-4=10(x-(-2))
y-4=10(x+2)
y-4=10x+20
y=10x+24
Answer:
y= -2x
Step-by-step explanation:
m=y2-y1/x2-x1
m=-6-4/3-(-2)
m=-2
y= mx+q
y= -2x+q
-6= -2(3)+q
-6+6= q
q= 0
Therefore y= -2x
Janie graduates from high school in 2019 and enrolls in college in the fall. Her parents (who file a joint return) pay $11,100 for her tuition and fees.
If required, round your computations to the nearest whole value.
a. Assuming Janie's parents have AGI of $177,600, what is the American Opportunity tax credit they can claim for Janie?
Assuming Janie's parents have AGI of $177,600, the American Opportunity Tax Credit that Janie's parents can claim for her is $2,500.
The American Opportunity Tax Credit (AOTC) is a tax credit that allows taxpayers to reduce their federal income tax liability for qualified education expenses paid for an eligible student.
To calculate the AOTC, the following formula can be used:
AOTC = 100% of the first $2,000 of qualified education expenses + 25% of the next $2,000 of qualified education expenses
The maximum amount of AOTC that can be claimed per eligible student is $2,500.
To determine the AOTC that Janie's parents can claim, we first need to calculate their Modified Adjusted Gross Income (MAGI). MAGI is calculated by adding certain deductions back to their AGI. Assuming they have no deductions, their MAGI would be the same as their AGI, which is $177,600.
Since the tuition and fees paid by Janie's parents ($11,100) are less than $4,000, they can claim the full AOTC of $2,500.
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find the slope-intercept form of this table
Answer:
y = 3x - 10
Step-by-step explanation:
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is zero).
See the attached worksheet. Let's calculate slope, m. Slope is defined as the Rise/Run, or change in y over the change in x. Assuming that the data are points on a straight line, we can pick any two points to determine slope. Let's use (25,65) and (28,74). See the worksheet. The slope,m, is shown to be 3. Now we can write:
y = 3x + b
To find b, the y-intercept, we can use the above expression and substitue any of the given points for x and y, leaving b as the only unknown. Let's use point (25.65):
y = 3x + b
65 = 3*(25) + b [for point (25,65)]
65 = 75 + b
b = - 10
The equation is therefore y = 3x - 10
Kevin has a bottle that contains 4. 5 liters of sparkling water. He pours 400 milliliters of the water into a glass. How many milliliters of water are left in the bottle? 1 liter= milliliters
The quantity of water in milliliters left in the water bottle after pouring 400 milliliters of water in glass is 4100 milliliters.
Milliliter is the smaller unit of quantity in the SI unit. One liter is equal to thousand times of one milliliter. It is given that the bottle contains 4.5 liters of water which means there is 4500 milliliters of water in it. Since Kevin pours 400 milliliters of water in the glass, this means 400 milliliters was emptied from the water bottle and hence the remaining amount can be calculated by subtracting the amount of water taken out from the bottle from the total amount.
Therefore the arithmetic equation will be as follows:
Amount of water left in bottle = Total quantity of water in the bottle - Water emptied out
Amount of water left in bottle = 4500 - 400 = 4100 milliliters
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The area (in square meters) of the surface of an artificial lake is represented by x2. Three ways to modify the dimensions of the lake are listed. Match the change in dimensions with the special product that represents the new area A of the lake.
Increase both dimensions by 2 meters:
Decrease both dimensions by 2 meters:
Increase one dimension by 2 meters and decrease the other dimension by 2 meters:
Answer:
Increase both dimensions by 2 meters: (x+2)^2
Decrease both dimensions by 2 meters: (x-2)^2
Increase one dimension by 2 meters and decrease the other dimension by 2 meters: (x+2)(x-2)
Step-by-step explanation:
Write each expression as a multiple of a power of 10: A 43,200
B 4,000
C. 2,800,000
D. Five thousand
E 60 million
F 45 billion
G. 0.00000123
H. 0.00038
I 0.002
A. 43,200 can be written as multiple of a power of 10 as 4.32 x 10⁴.
B. 4,000 can be written as 4 x 10³
C. 2,800,000 can be written as 2.8 x 10⁶.
What is expression pοwer?In mathematics, an expressiοn in pοwer refers tο a mathematical expressiοn that includes a base raised tο an expοnent. The base is the number οr variable being raised tο a pοwer, and the expοnent is the superscript number indicating hοw many times the base is being multiplied by itself.
Fοr example, in the expressiοn 2³, the base is 2 and the expοnent is 3. This means that we multiply 2 by itself 3 times, which gives us a value οf 8. Similarly, in the expressiοn x⁴, the base is x and the expοnent is 4. This means that we multiply x by itself 4 times, which gives us a value οf x multiplied by x multiplied by x multiplied by x.
Expressiοns in pοwer can be used in variοus mathematical οperatiοns, such as multiplicatiοn, divisiοn, additiοn, and subtractiοn . They are alsο cοmmοnly used in algebraic equatiοns and in scientific nοtatiοn tο represent very large οr very small numbers.
A. 43,200 can be written as 4.32 x 10⁴. This means that the number is equal to 4.32 times 10,000.
B. 4,000 can be written as 4 x 10³. This means that the number is equal to 4 times 1,000.
C. 2,800,000 can be written as 2.8 x 10⁶. This means that the number is equal to 2.8 times 1,000,000.
D. Five thousand can be written as 5 x 10³. This means that the number is equal to 5 times 1,000.
E. 60 million can be written as 6 x 10⁷. This means that the number is equal to 6 times 10,000,000.
F. 45 billion can be written as 4.5 x 10¹⁰. This means that the number is equal to 4.5 times 10,000,000,000.
G. 0.00000123 can be written as 1.23 x 10⁻⁶. This means that the number is equal to 1.23 divided by 1,000,000.
H. 0.00038 can be written as 3.8 x 10⁻⁴. This means that the number is equal to 3.8 divided by 10,000.
I. 0.002 can be written as 2 x 10⁻³. This means that the number is equal to 2 divided by 1,000.
In summary, by expressing each of these numbers as a multiple of a power of 10, we can better understand the magnitude of the number and compare it to other numbers more easily.
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Your complete question is :-
Write each expression as a multiple of a power of 10:
A 43,200
B 4,000
C. 2,800,000
D. Five thousand
E 60 million
F 45 billion
G. 0.00000123
H. 0.00038
I 0.002
An entomologist has an insect colony for an experiment. The
population of insects is increasing at a
continuous rate of 5.6 percent per week. The
initial population of the insect colony was 100.
The function that models the insect population after tt weeks is
P(t)=
Using the function from part (a) we can estimate that the insect population after 16 weeks is
___
(round your answer to the nearest whole number)
After how many weeks will the population reach 3800 insects?
weeks
___
(round your answer to one decimal place)
16 weeks is 277
3800 insects in about 27.4 weeks
The answer to the question is given below.An entomologist has an insect colony for an experiment. The population of insects is increasing at a continuous rate of 5.6 percent per week. The initial population of the insect colony was 100.The formula that represents the insect colony population after tt weeks is P(t) = 100 (1 + 0.056)^tUsing the formula from section (a), we can calculate that the insect population after 16 weeks is 277. The nearest whole number is 277.After how many weeks would the population of insects reach 3800?Let’s apply the formula P(t) = 100 (1 + 0.056)^t3800 = 100 (1 + 0.056)^t(1 + 0.056)^t = 38(1.056)^t = 38log 1.056^t = log 38t log 1.056 = log 38t = log 38 / log 1.056t ≈ 27.4 weeksThe insect population will reach 3800 insects in about 27.4 weeks. We rounded the answer to one decimal place.
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There is a bag filled with 6 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 red?
The prοbability οf getting at least 1 red marble is 85/121.
What is prοbability?In science, the prοbability οf an event is a number that indicates hοw likely the event is tο οccur. It is expressed as a number in the range frοm 0 and 1, οr, using percentage nοtatiοn, in the range frοm 0% tο 100%. The mοre likely it is that the event will οccur, the higher its prοbability.
The prοbability οf nοt getting a red marble in the first draw is 6/11. The prοbability οf nοt getting a red marble in the secοnd draw is alsο 6/11. Therefοre, the prοbability οf getting nο red marbles in twο draws is (6/11) x (6/11) = 36/121.
The prοbability οf getting at least οne red marble in twο draws is 1 - the prοbability οf getting nο red marbles. Sο, the prοbability οf getting at least οne red marble is: 1 - 36/121 = 85/121
Therefοre, the prοbability οf getting at least 1 red marble is 85/121.
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Clara poured 650 milliliters of milk out of a bottle that originally held three and a half liters. How many milliliters of milk were left in the bottle?
There are 2850 milliliters of milk left in the bottle after Clara poured 650 milliliters of milk from the bottle
How to calculate the milliliters of milk left in the bottle?Clara poured 650 milliliters of milk out of a bottle
The bottle originally held 3 1/2 litres of milk
Convert 3 1/2 to decimal
= 3 + 1/2
= 3 + 0.5
= 3.5
The first step is to convert the original volume to milliliters
Multiply the value in liters by 1000
= 3.5 × 1000
= 3500 milliliters
The next step is to subtract 650 from 3500
= 3500 - 650
= 2850
Hence the amount of milk left in the bottle is 2850 milliliters
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Use a Double- or Half-Angle Formula to solve the equation in the interval \( [0,2 \pi \) ). (Enter your answers as a comma-separated list.) \[ \cos (\theta)-\sin (\theta)=\sqrt{2} \cdot \sin \left(\fr
The solution for the given equation isθ = π/2, 5π/6, 13π/6.
The given equation is cos(θ) - sin(θ) = √2sin(θ/2)cos(θ/2).Use double-angle formula for sin to write sin(θ) in terms of cosθ as follows:sin(θ) = 2sin(θ/2)cos(θ/2).Substitute sin(θ) with the above equation. We have,cos(θ) - 2sin(θ/2)cos(θ/2) = √2sin(θ/2)cos(θ/2)cos(θ) - 3sin(θ/2)cos(θ/2) = 0(cosθ - 3sin(θ/2) = 0 or cosθ/3 = sin(θ/2)Squaring both sides of the equation gives us:cos2θ/9 = 1 - cos2(θ/2)cos2(θ/2) = (1 - cos2θ/9) / 2cos2(θ/2) = (9 - cos2θ) / 18sin2(θ/2) = 1 - cos2(θ/2)sin2(θ/2) = 1 - ((9 - cos2θ) / 18)sin2(θ/2) = (9 + cos2θ) / 18Therefore, the solution for the given equation isθ = π/2, 5π/6, 13π/6.
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express each of the following as a single fraction 5y/2-2y/3
Answer:
Use a calculator for you to get an answer
Please help!! answers needed now-- work only NEEDS to be shown for question 2
use the triangle to answer the questions:
1. What is the exact height of the triangle, x?
2. What is the exact area of the triangle? Leave your answer in radical terms.
Show your work
3. What is the area of the triangle to the nearest hundredth of a square in?
Answer:
1. 5√3
2. (25√3)/2
3. 21.65
Step-by-step explanation:
1. x = 10 * cos(30 degree) = 5√3
2. area = x * y = (10 * sin(30 degree)) * (10 * cos(30 degree)) = 25/2 * √3
3. Use calculator
2x +5y +1=0
3x + 7y= 1
Answer:
We can solve this system of equations using substitution or elimination.
Using substitution, we can solve for one variable in terms of the other in one equation and substitute that expression into the other equation. For example, we can solve the first equation for x in terms of y:
2x + 5y + 1 = 0
2x = -5y - 1
x = (-5/2)y - 1/2
Now we can substitute this expression for x into the second equation:
3x + 7y = 1
3((-5/2)y - 1/2) + 7y = 1
-15/2 y - 3/2 + 7y = 1
9.5y = 5
y = 5/9.5 = 1/1.9
Now we can substitute this value of y back into either equation to solve for x:
x = (-5/2)y - 1/2
x = (-5/2)(1/1.9) - 1/2
x = -2.632
So the solution to the system of equations is x = -2.632 and y = 1/1.9.
At December 31, bonds payable of $119,588,000 are outstanding the bonds pay 12% interest every September 30th in mature and installment of 29 million 897,000 every September 30th beginning 30th 2026 Bond payable (09/30/2026 installment) _________________ Bond payable (other than 09/30/2026 installment) ________________ Interest payable ___________________
The amounts due on December 31, 2026 are: Bond payable (09/30/2026 installment) = $29,897,000, Bond payable (other than 09/30/2026 installment) = $90,313,578.19,Interest payable = $622,578.19
We can break down the problem into two parts: first, calculating the amount of bonds payable that are due on September 30, 2026 (the first installment), and second, calculating the amount of bonds payable and interest payable that are due on any other date.
Bond payable due on September 30, 2026:
The total amount of bonds payable outstanding is $119,588,000. The installment due on September 30, 2026 is $29,897,000. Therefore, the amount of bonds payable that is due on September 30, 2026 is:
$29,897,000
Bond payable and interest payable due on any other date:
The total amount of bonds payable outstanding is $119,588,000. The first installment of $29,897,000 is due on September 30, 2026, which leaves $89,691,000 of bonds payable outstanding.
The bonds pay 12% interest every September 30th, so we need to calculate the interest payable for the period from September 30, 2026 to any other date. Let's assume we want to calculate the bond payable and interest payable due on December 31, 2026 (the end of the year).
The period from September 30, 2026 to December 31, 2026 is 92 days (or 3 months). The annual interest rate is 12%, so the daily interest rate is:
12% / 365 = 0.0328767%
The interest payable for 92 days is therefore:
$89,691,000 x 0.0328767% x 92/365 = $622,578.19
Adding this to the outstanding bonds payable gives:
Bond payable (other than 09/30/2026 installment) = $89,691,000 + $622,578.19 = $90,313,578.19
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What is the correct answer
Answer:
248[tex]mm^{2}[/tex]
Step-by-step explanation:
Instead of calculating for the hexagon, divide it into 5 separate triangles with a 8mm base and 5.5mm height. Calculate using the "half base times height" formula and multiply it by five for the hexagon's area:
[tex]\frac{1}{2}((b)(h)) (5)\\\frac{1}{2}((8)(5.5)) (5)\\\\ \frac{1}{2}(44) (5)\\\\(22)(5)\\110[/tex]
This is the area of the pentagonal pyramid's base. Now for the sides calculate the area of an individual side (triangle with base 8mm and height 6.9mm) then multiply by 5 for the area of all the sides:
[tex]\frac{1}{2}((b)(h)) (5)\\\\\frac{1}{2}((8)(6.9)) (5)\\\\\frac{1}{2}(55.2) (5)\\\\(27.6) (5)\\\\138\\[/tex]
For the total surface area of this shape add these values together for 110+138=248mm[tex]mm^{2}[/tex]
I hope that this helps :)
PLEASE HELPPP
(a) Write an expression for the total by both the bedrooms and the kitchen.
(b) Write an expression to calculate the perimeter of the living room.
(c) If the cost of carpeting is 50 per m², write an expression for calculating the total cost of carpeting both the bedrooms and the living room.
(d) If the cost of tiling is 30 per m², write an expression for calculating that total cost of floor tiles used for the bathroom and kitchen floors.
(e) If the floor area of each bedroom is 35 m², then find x.
(a) (65+5x)m², (b) 15+2+x+5+(15−x)+5+2=44m is the perimeter, (c) Rs.250(x+21) , (d) Rs.150(15−x) (e) 5x=35 ⇒x=7m
Describe Algebraic Expression?In an algebraic expression, variables are represented by letters or symbols, and constants are represented by numerical values. The variables can be used to represent unknown values that need to be solved for, while the constants provide fixed values.
Algebraic expressions are used extensively in algebra and other mathematical fields to represent relationships between variables and to solve equations.
(a)
length of bedroom =x m
Breadth of bedroom =5 m
And, length of kitchen =15−(x+2)=13−x m
Breadth of kitchen =5 m
So, Area of both kitchen and bedrooms =2× times of area of bedroom + area of kitchen
=2(5×x)+(13−x)×5
=10x+(65−5x)
=(65+5x)m²
(b)
From figure,
Perimeter of the living room
=15+2+x+5+(15−x)+5+2=44m
(c)
From figure,
Total area of both living the room and the bedrooms =(5×x)+(7×15)=(5x+105)m²
The cost of carpeting is Rs. 50/m²
Therefore, total cost of carpeting
=(5x+105)×50=Rs.250(x+21)
(d)
Total area, bathroom and kitchen
=(15−x)×5m²
The cost of tiling is Rs. 30/m²
Therefore, total cost of tilling
=(15−x)×5×30=Rs.150(15−x)
(e)
Given, Area of floor of each bedroom 35 m²
So, Area of one bedroom
=5xSq.m
∴5x=35
⇒x=7m
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I need help
An airplane flies in the path shown by the vector CD
on the graph below. What is the magnitude and direction of CD
? (1 unit represents 1 mile)
26° north for 7 miles
42° south for 8 miles
53° east of south for 5 miles
72° south of west for 6 miles
Calculating the distance between locations C and D will provide us with the vector CD's magnitude, which we will then use to determine the vector CD's direction and magnitude. Thus, 5 miles in size, with a direction of roughly 53.13 degrees, is the CD.
What is meant by the magnitude and direction of the vector?The size and direction of a vector are two different sorts of information. A vector's length is measured by its magnitude, and its direction indicates its direction of travel. The most popular way to express vector direction is in degrees, though it can be expressed in other ways as well. Vector examples include acceleration and velocity. A vector's length is considered to be its magnitude.
The distance formula between the given two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)² + (y2 - y1)²)
Plugging in the values for points C and D, we get:
d = √((0 - (-4))² + (1 - 4)²)
= √(16 + 9)
= √(25)
= 5 miles
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Make d the subject of the formula h=d/3 +2
Answer:
d = 3h - 6
Step-by-step explanation:
h = d/3 + 2
Subtract 2 from both sides to isolate the term involving d:
h - 2 = d/3
Multiply both sides by 3 to eliminate the fraction:
3(h - 2) = d
Simplifying the right-hand side, we get:
d = 3h - 6
Therefore, the formula in terms of d is:
d = 3h - 6.
find the area of the given circle
Answer:
Area of white circle = 346.36 cm²
Step-by-step explanation:
Area of a circle = πr² where r is the radius
r = diameter/s
For the green circle, d = 42, r = 21
A = π(21)² = 1,385.44 cm²
The white circle has a diameter half of the green circle = 42/2 = 21 cm
So radius of white circle = 21/2 = 10.5 cm
Area of white circle = π (10.5)² = 346.36 cm²
Use the information given to answer the question
A pack of crayons costs 1. 25. If z packs of crayons are purchased, the total price, P, can be represented by the relation P = 1. 252.
Does P 1. 252 represent a function, and why?
The relation is a function because there is exactly 1 value of P for every value of 1.
The relation is a function because there is exactly 1. 25 value of P for every value of z.
The relation is not a function because there is exactly 1. 25 value of P for every value of 2.
The relation is not a function because there is not exactly 1 value of P for every value of z.
Sting
The right response is: Because there is precisely one value of P for every value of z, the relationship is a function. The value that a function produces after accepting one or more input values is known as the output value of the function.
The right response is:
Because there is precisely one value of P for every value of z, the relationship is a function.
Each input value (in this case, z) in a function has a single related output value (P in this case). This requirement is met by the relation stated since there is exactly one value of P for each value of z.
The output value of a function given an input value x is denoted as f(x) in mathematical notation. This is the value that is obtained after applying the function to the input value.
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The surface area of this rectangular prism is 236 square yards. What is the volume?
Seventy-Two Inc. , a developer of radiology equipment, has stock outstanding as follows: 80,000 shares of cumulative preferred 3% stock, $20 par and 410,000 shares of $25 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $33,000; second year, $72,000; third year, $100,000; fourth year, $100,000. Determine the dividends per share on each class of stock for each of the four years.
Preferred stock (dividends per share)
1st Year 2nd Year 3rd Year 4th Year
Common stock (dividends per share)
1st Year 2nd Year 3rd Year 4th Year
The dividends per share on preferred stock for four years is $0.12, $0.12, $0.12, $0.12 and for common stock is $0.057, $0.152, $0.220, $0.220.
To calculate the dividends per share for each class of stock, we need to first determine the total dividends paid in each year.
For the preferred stock, the dividends are cumulative, which means any unpaid dividends from previous years must be paid before any dividends can be paid to common stockholders. Therefore, we need to calculate the total amount of unpaid dividends for each year before we can determine the amount available for common stockholders.
To calculate the unpaid dividends for the preferred stock in each year, we need to multiply the number of shares of preferred stock by the dividend rate (3%) and subtract the dividends paid in that year.
Unpaid dividends for preferred stock:
1st year: (80,000 x $20 x 0.03) - $33,000 = $9,600
2nd year: (80,000 x $20 x 0.03) - $72,000 - $9,600 = $9,600
3rd year: (80,000 x $20 x 0.03) - $100,000 - $9,600 = $9,600
4th year: (80,000 x $20 x 0.03) - $100,000 - $9,600 = $9,600
Now we can calculate the total dividends available for common stockholders in each year by subtracting the unpaid dividends for preferred stock from the total dividends paid in that year.
Total dividends available for common stockholders:
1st year: $33,000 - $9,600 = $23,400
2nd year: $72,000 - $9,600 = $62,400
3rd year: $100,000 - $9,600 = $90,400
4th year: $100,000 - $9,600 = $90,400
Finally, we can calculate the dividends per share for each class of stock by dividing the total dividends by the number of shares outstanding.
Dividends per share:
Preferred stock:
1st year: $9,600 / 80,000 = $0.12 per share
2nd year: $9,600 / 80,000 = $0.12 per share
3rd year: $9,600 / 80,000 = $0.12 per share
4th year: $9,600 / 80,000 = $0.12 per share
Common stock:
1st year: $23,400 / 410,000 = $0.057 per share
2nd year: $62,400 / 410,000 = $0.152 per share
3rd year: $90,400 / 410,000 = $0.220 per share
4th year: $90,400 / 410,000 = $0.220 per share
Therefore, the dividends per share on each class of stock for each of the four years are as follows:
Preferred stock (dividends per share)
1st Year: $0.12 per share
2nd Year: $0.12 per share
3rd Year: $0.12 per share
4th Year: $0.12 per share
Common stock (dividends per share)
1st Year: $0.057 per share
2nd Year: $0.152 per share
3rd Year: $0.220 per share
4th Year: $0.220 per share
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5 shirts, 2 neckties, 4 pants, and 2 sweaters? Looks like the previous problem, but the dress-code has changed, and I am permitted to omit the tie, and if the weather is warm, omit the sweater
Thus, if the weather is warm, you can make a total of 20 combinations (5 shirts x 4 pants), and if the weather is cold, you can make a total of 40 combinations (5 shirts x 4 pants x 2 sweaters).
The total combination of clothing items you can wear is 5 shirts, 4 pants, and either 2 neckties or 2 sweaters. If the weather is warm, you can opt to omit the sweater and keep the two neckties. If the weather is cold, then you can omit the neckties and wear the two sweaters. To calculate the total number of clothing combinations you can make, you need to multiply the items you are allowed to wear. For example, if you are wearing a shirt and a pair of pants, you can make 5 x 4 = 20 combinations. If you are wearing a shirt, pants, and either a necktie or a sweater, you can make 5 x 4 x 2 = 40 combinations.
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∠F and ∠U included sides and included angles?
given is ΔFUN
A triangle has three straight sides that meet at a point. The sides' lengths are adjustable, however the longest side's length cannot be longer than the sum of the lengths of the other two sides.
What method can be used to locate the triangle?A triangle has three straight sides that meet at a point. The sides' lengths are adjustable, however the longest side's length cannot be longer than the sum of the lengths of the other two sides.
In the triangle ΔFUN,
∠F is an angle formed by the vertices F, U, and N.
∠U is an angle formed by the vertices F, U, and N.
The included sides of ∠F and ∠U are:
The included side of ∠F is UN.
The included side of ∠U is FN.
The included angles of ∠F and ∠U are:
Therefore, The included angle of ∠ F is ∠FUN, which is formed by the sides FU and UN. The included angle of ∠U is ∠NUF, which is formed by the sides NU and UF.
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please help with the image.
Answer:2 hours 20 minutes
Step-by-step explanation:divide 60 by 3
Sorry, now you know that he spends 20 minutes a day combing his hair. You multiply 20 time 7( for the 7 days in a week) = 140. You want to convert minutes to hours and 2 hour is 120 minutes so the answer is 2 hours and 20 minutes
Answer: A) 20 minutes
B)2 and 1/3 hours
Step-by-step explanation:
A) 1/3 of an hour is 20 minuets because 60÷3=20
This means that 20 minutes are spent combing his hair each day
B) He spends 20 minutes combing his hair each day so 20×7=140
140÷60=2 and 1/3 hours per week
What advice would you give to students B and C to help them avoid factoring this
type of problem incorrectly in the future?
Correct solved problem
Student A factored
this expression correctly:
²-10x-24
(x-12)(x+2)
Factor: ²-10-24
Incorrect solved problem:
Sum of the integers does not
equal the middle term
Student B did not factor
this expression correctly.
²-10x-24
(x-4)(x+6)
Incorrect solved problem:
Sum of the integers does not
equal the middle term
Student C did not factor
this expression correctly:
-10-24
(r+12)(x-2)
**Day 4 will open once you post to the discussion board
Therefore , the solution of the given problem of expressions comes out to be students can develop their factoring abilities and avoid mistakes with practise and instruction.
What exactly is an expression?Estimates that combine joining, disabling, and rather than randomly divide should be produced when variables are shifting. If they got together, they could solve a mental puzzle, provide some data, and instead software. A declaration of truth contains formulas, components, and mathematical processes like combination, subtraction, omission, and grouping. Both phrases and words can be assessed and analysed.
Here,
are some pointers to assist students B and C prevent incorrect factoring in the future:
Regularly practise factoring: Since factoring is a talent that must be honed, students should make sure to factor problems frequently. They will be better able to understand the procedure and spot trends in the expressions they are factoring as a result of this.
Verify the indications again because they are prone to error when factoring. Students should double-check their distribution of the signs and make sure no negative indicators are being left out.
Students should double-check their work by multiplying the factors back together after factoring an equation. They'll be able to correct any errors they may have made thanks to this.
If students need assistance with factoring, they should ask an instructor or tutor for assistance. Although factoring can be a challenging ability to master, students can develop their factoring abilities and avoid mistakes with practise and instruction.
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