Thus, the amount after the compounding is found to be $14,683.82.
Explain about the compound interest:Compound interest is, to put it simply, interest that is earned on interest. Compound interest is interest that is earned on both the initial principal and interest that builds up over time in a savings account.
There may be a difference in the timing of when interest is paid out and compounded. For instance, interest on a savings account may be paid monthly but compounded daily.
Given data:
principal P: $5,000,
annual interest r: 6%,
n interest periods: 12,
number of years t : 18
Formula:
A = P[tex](1 + r/n)^{nt}[/tex]
Put the values:
A = 5000[tex](1 + 0.06/12)^{12*18}[/tex]
A = 5000*2.93
A = 14,683.82
Thus, the amount after the compounding is found to be $14,683.82.
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Complete question:
principal: $5,000, annual interest: 6%, interest periods: 12, number of years: 18
After 18 years, the investment compounded what will be worth $___.?
Leland wants to paint a portrait for his parents using a photograph of them that is 5 inches wide by 8 inches high. He wants the portrait to be proportional to the photograph and 42 inches high. Which proportion can Leland use to find , the width he needs to use to make the portrait proportional?
The ratio to make the portrait proportional is width/42 = 5/8
Which proportion can Leland use to find , the width he needs to useFrom the question, we have the following parameters that can be used in our computation:
Photograph that is 5 inches wide by 8 inches high.
This means that
Ratio = width/height
Substitute the known values in the above equation, so, we have the following representation
Ratio = 5/8
Given that he wants the portrait to be proportional to the photograph and 42 inches high.
Then, we have
width/42 = 5/8
Hence, the ratio to make the portrait proportional is width/42 = 5/8
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What occurs when a white dwarf in a binary star system if it gains mass beyond the chandrasekhar limit?.
If a white dwarf in a binary star system gains mass beyond the Chandrasekhar limit (approximately 1.4 solar masses), it undergoes a runaway nuclear reaction, causing it to collapse and explode in a Type Ia supernova.
A white dwarf is a dense stellar remnant that is left behind after a star has exhausted all its nuclear fuel and has shed its outer layers. In a binary star system, the white dwarf may gain mass from its companion star, either through accretion or a merger. If the mass of the white dwarf exceeds the Chandrasekhar limit, the gravitational forces become so strong that the electrons in the atoms are forced to combine with the atomic nuclei, forming neutrons. This process is called electron capture, and it releases a tremendous amount of energy.
The energy released is enough to ignite a runaway nuclear reaction, causing the white dwarf to collapse and explode in a Type Ia supernova. Type Ia supernovae are important cosmic events because they are used as standard candles to measure the distance to distant galaxies. These explosions are also believed to play a significant role in the chemical evolution of the universe, as they produce heavy elements such as iron and nickel that are scattered into the interstellar medium.
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What is the height, to the nearest tenth of a foot, of a tree that creates a 35-foot shadow when the sun is at an angle of elevation of 35⁰? (do NOT type in units, just the value)
The height of the tree is approximately 20.1 feet.
What is the height of a tree that produces a 35-foot shadow when the sun is at an angle of 35 degrees?To determine the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the length of the shadow) of a right triangle.
tan(35°) = height of tree / 35 feet shadow
Rearranging this formula, we get:
height of tree = 35 feet shadow x tan(35°)
Plugging in the given values and using a calculator, we get:
height of tree = 35 x tan(35°) ≈ 20.1 feet
Therefore, the height of the tree is approximately 20.1 feet.
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If the smith children are served randomly how likely is it that the two oldest smith children are served before the others ?
The probability of the two oldest Smith children being served first is 2/4 or 50%.
How likely is it for the two oldest Smith children to be served first?Assuming that all the children have an equal chance of being served first, there are a total of 4 possibilities for the order in which the two oldest Smith children can be served:
Oldest served first, followed by second oldestSecond oldest served first, followed by oldestOldest served first, followed by one of the younger children, then second oldestSecond oldest served first, followed by one of the younger children, then oldestOut of these 4 possibilities, only the first 2 would satisfy the condition that the two oldest Smith children are served before the others. So the probability that the two oldest Smith children are served first is 2/4 or 50%.
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the aspect ratio of a wide screen tv is 2.39:1. what is the length of the diagonal of a wide screen tv screen with an area of 150 in??
The length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.
Aspect ratio refers to the proportional relationship between the width and height of an image or screen. In the case of a wide screen TV, the aspect ratio is 2.39:1, which means that for every 2.39 units of width, there is 1 unit of height.
To find the length of the diagonal of a wide screen TV with an area of 150 inches, we need to use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the width and height.
First, we need to find the width and height of the TV screen. We can do this by setting up the equation:
2.39x^2 = 150
where x is the width of the screen. Solving for x, we get:
x = √(150/2.39) = 10.87 inches
Now we can find the height by dividing the width by the aspect ratio:
h = 10.87 / 2.39 = 4.55 inches
Using the Pythagorean theorem, we can find the length of the diagonal:
d^2 = 10.87^2 + 4.55^2 = 126.68
d = √126.68 = 11.25 inches
Therefore, the length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.
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can someone please help will give brain
Answer:
y = 9
Step-by-step explanation:
• Parallel lines have equal slopes
calculate the slope m of TU using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = T(- 7, 4 ) and (x₂, y₂ ) = U(- 2, - 6 )
[tex]m_{TU}[/tex] = [tex]\frac{-6-4}{-2-(-7)}[/tex] = [tex]\frac{-10}{-2+7}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2
now calculate the slope of VW and equate to - 2
with (x₁, y₁ ) = V(8, 7 ) and (x₂, y₂ ) = W(7, y )
[tex]m_{VW}[/tex] = [tex]\frac{y-7}{7-8}[/tex] = [tex]\frac{y-7}{-1}[/tex]
now equating gives
[tex]\frac{y-7}{-1}[/tex] = - 2 ( multiply both sides by - 1 to clear the fraction )
y - 7 = 2 ( add 7 to both sides )
y = 9
Para el periódico mural, los alumnos decidieron representar un pino por medio de un triángulo que tiene una superficie de 1. 5m si la base mide 1. 5 m ¿cuanto mide la altura? 
La fórmula para calcular el área de un triángulo es:
área = base * altura / 2
Podemos despejar la altura de esta fórmula y sustituir los valores que conocemos:
área * 2 / base = altura
1.5 * 2 / 1.5 = 2
Por lo tanto, la altura del triángulo es de 2 metros.
3. the sketch shows three adjacent angles. please write an equation that can be
used to determine the value of y?
28
36
please help
The value of y is 116°.
Three given Adjacent angles are 28°, 36° and y°.
When two angles are adjacent, they have a common side between them and share a common vertex where the two sides meet. The angles are said to be adjacent because they are next to each other.
We know that if a ray stands on a straight line, then the sum of adjacent angles is 180°.
So, 28° + y° + 36° = 180°
y° + 64° = 180°
Subtracting 64° from both sides.
y°- 64° = 180° - 64°
y° = 116°
Hence, the value of y is 116°.
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You spin the spinner, flip a coin, then spin the spinner again. Find the probability of not spinning a 5. Flipping tails, then spinning a 5. Write your answer as a traction in simplest form
The probability of not spinning 5 is 81/200.
What is the probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: You spin the spinner, flip a coin, then spin the spinner again.
We have to find the probability of not spinning a 5. Flipping tails, then spinning a 5.
P(not spinning a 5) = 9/10
P(heads)= 1/2 because there is an equal chance to get heads or tails
P(not spinning a 5)= same as before, 9/10 (independent events).
= [tex]\frac{9}{10}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{10}[/tex]
= [tex]\frac{81}{200}[/tex]
Hence, the probability of not spinning 5 is 81/200.
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En una imprenta, 4 impresoras tardan 3 horas en imprimir 5000 hojas, ¿cuánto tiempo tardarán en imprimir 6000? escribe el resultado en horas con decimales
Tardarán aproximadamente 3.6 horas.
How long to print 6000 sheets?Para resolver este problema, podemos establecer una relación proporcional entre el número de hojas impresas y el tiempo requerido. Si 4 impresoras tardan 3 horas en imprimir 5000 hojas, podemos establecer la proporción
4 impresoras / 3 horas = 5000 hojas / x horas
Donde x representa el tiempo que tardarán en imprimir 6000 hojas. Podemos resolver esta proporción utilizando regla de tres:
4 / 3 = 5000 / x
Multiplicando en cruz, obtenemos:
4x = 3 * 5000
4x = 15000
x = 15000 / 4
x = 3750
Por lo tanto, tardarán aproximadamente 3750 horas en imprimir 6000 hojas.
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Jack is making $9.50 per hour at his job re-stocking grocery shelves. His supervisor is impressed with his good work and gives him a 10% raise. How much per hour is Jack making now?
PLS HELP I WILL MARK YOU BRAINLIEST
Answer:
Jack now makes $10.45
Step-by-step explanation:
First, we need to find 10% of 9.50. To do that we must divide 9.50 by 10 or simply move the decimal one place to the left to get 0.95. 0.95 is 10% of 9.50. Now we must ADD 0.95 to 9.50 because Jack is getting a 10% raise. 0.95 + 9.50 = 10.45. Therefore Jack makes $10.45 per hour at his job.
WILL GIVE BRAINLIEST!!!
1.)
A composite figure is composed of a semicircle whose radius measures 4 inches added to a square whose side measures 11 inches. A point within the figure is randomly chosen.
What is the probability that the randomly selected point is in the semicircular region?
Enter your answer rounded to the nearest tenth in the box.
2.)
A circular spinner has a radius of 6 inches. The spinner is divided into three sections of unequal area. The sector labeled green has a central angle of 90°. A point on the spinner is randomly selected.
What is the probability that the randomly selected point falls in the green sector?
1/90
1/9
1/4
1/3
3.)
Question
A spinner is divided into 10 equally sized sectors. The sectors are numbered 1 to 10. A randomly selected point is chosen.
What is the probability that the randomly selected point lies in a sector that is a multiple of 3?
Enter your answer in the box.
4.)
Question
Two concentric circles form a target. The radii of the two circles measure 8 cm and 4 cm. The inner circle is the bullseye of the target. A point on the target is randomly selected.
What is the probability that the randomly selected point is in the bullseye?
Enter your answer as a simplified fraction in the boxes.
Answer:
1. 17.2
2. 1/4 or 0.25
3. 3/10 or 30%
4. 15/16
I hope this helped
Step-by-step explanation:
A closed rigid system has a volume of 85 litres contains steam at 2 bar and dryness fraction of 0.9. calculate the quantity of heat which must be removed from the system in order to reduce the pressure to 1.6 bar. also determine the change in enthalpy and entropy per unit mass of the system
The quantity of heat which must be removed from the system in order to reduce the pressure from 2 bar to 1.6 bar is 4.23 kJ. The change in enthalpy per unit mass of the system is -123 kJ/kg, and the change in entropy per unit mass of the system is 0.134 kJ/kg-K.
To solve this problem, we need to use the steam tables to determine the properties of the steam at the initial and final conditions. We will assume that the system is undergoing a reversible, adiabatic process, so there is no heat transfer into or out of the system.
First, we determine the specific volume and enthalpy of the steam at the initial conditions of 2 bar and 0.9 dryness fraction. From the steam tables, we find that the specific volume is 0.4019 m^3/kg and the specific enthalpy is 2895.5 kJ/kg.
Next, we use the steam tables to find the specific volume and enthalpy of the steam at the final conditions of 1.6 bar. We find that the specific volume is 0.5059 m^3/kg and the specific enthalpy is 2772.5 kJ/kg.
The change in specific enthalpy per unit mass of the system is then given by:
Δh = h2 - h1 = 2772.5 - 2895.5 = -123 kJ/kg
The change in specific entropy per unit mass of the system is given by:
Δs = s2 - s1 = s2 - s1 = s2 - sf - x2*(sg - sf)
where sf and sg are the specific entropy of saturated liquid and saturated vapor at the final pressure of 1.6 bar, and x2 is the final dryness fraction. From the steam tables, we find that sf = 7.4332 kJ/kg-K, sg = 8.1248 kJ/kg-K, and x2 = 0.714.
Thus, we have:
Δs = s2 - s1 = s2 - sf - x2*(sg - sf) = (7.9757 - 7.4332) - 0.714*(8.1248 - 7.4332) = 0.134 kJ/kg-K
Finally, we can calculate the quantity of heat that must be removed from the system using the first law of thermodynamics:
Q = m*(h1 - h2) = m*Δh
where m is the mass of the steam in the system. To determine the mass of the steam, we use the specific volume at the initial conditions:
V = m/v1
where V is the volume of the system and v1 is the specific volume at the initial conditions. Substituting the given values, we have:
V = 85 L = 0.085 [tex]m^3[/tex]
m = Vv1 = 0.0850.4019 = 0.0344 kg
Substituting this value into the equation for Q, we obtain:
Q = mΔh = 0.0344(-123) = -4.23 kJ
Therefore, the quantity of heat which must be removed from the system in order to reduce the pressure from 2 bar to 1.6 bar is 4.23 kJ.
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Un Jardinero usa un total de 61. 5 galones de gasolina en un mes. De la cantidad total
3/5
de gasolina, se usaron en sus cortadoras de césped. ¿Cuántos galones de gasolina usa
el jardinero en sus cortadoras de césped en ese mes? Me ayudan plis
The gardener used 36.9 gallons of gasoline in the lawnmowers in that month.
What are proportions?In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:
a/b = c/d
We know that the gardener used a total of 61.5 gallons of gasoline in a month and that 3/5 of that total was used in the lawnmowers.
To find out how much gasoline the gardener used in the lawnmowers, we need to multiply the total amount of gasoline by 3/5:
61.5 gallons x 3/5 = 36.9 gallons
Therefore, the gardener used 36.9 gallons of gasoline in the lawnmowers in that month.
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Help a man out. Its due tomorrow need to get it done.
Answer:
A≈166.28
Step-by-step explanation:
Answer:
A≈166.28
Step-by-step explanation:
The owner of a company asks a manager, "How many hours does an employee work each week?" a. Is this a statistical question? Explain. The question a statistical question because there. Question 2 b. The manager records the number of hours worked each week by several employees. Display the data in a dot plot. Identify any clusters, peaks, or gaps in the data. Hours worked 40 39 40 39 47 38 41 37 40 41 40 43 40 41 40 38 40 42 40 42 Most of the data are clustered around. There is a peak at and a gap between. Question 3 c. Use the distribution of the data to answer the question. Most employees work about hours each week
This is a statistical question because it involves collecting data. Most employees work around 40 hours each week.
a. This is a statistical question because it involves collecting data on the number of hours worked by employees each week and analyzing the distribution or pattern of the data.
b. Here's a dot plot of the data provided:
37: •
38: ••
39: ••
40: ••••••••
41: •••
42: ••
43: •
47: •
The distribution of the data in the dot plot shows that the majority of employees worked around 40 hours each week, as this is where the data is most heavily clustered. Most of the data are clustered around 40 hours, with a peak at 40 hours. There is a gap between 43 and 47 hours.
c. Based on the distribution of the data, most employees work about 40 hours each week.
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Calculate the partial derivative, using implicit differentiation of e⁷xy + sin (5xz) + 4y = 0. (Use symbolic notation and fractions/where needed.) dz/dy
The partial derivative using implicit differentiation is:
[tex]dz/dy = (-7x * e^(7xy) * (dx/dy) - 4) / (5x * cos(5xz))[/tex]
To calculate the partial derivative of the given equation with respect to y (dz/dy), we'll use implicit differentiation. The given equation is:
[tex]e^(7xy) + sin(5xz) + 4y = 0[/tex]
First, differentiate both sides of the equation with respect to y:
[tex]d(e^(7xy))/dy + d(sin(5xz))/dy + d(4y)/dy = 0[/tex]
Apply the chain rule for the first and second terms:
[tex](7x * e^(7xy)) * (dx/dy) + (5x * cos(5xz)) * (dz/dy) + 4 = 0[/tex]
Now, we are interested in finding dz/dy. To solve for it, rearrange the equation:
[tex](5x * cos(5xz)) * (dz/dy) = -7x * e^(7xy) * (dx/dy) - 4Finally, divide by (5x * cos(5xz)) to isolate dz/dy:dz/dy = (-7x * e^(7xy) * (dx/dy) - 4) / (5x * cos(5xz))[/tex]
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Which algebraic expression is equivalent to the expression below? 25/4(5x-4/5)+29 A. 125/4x + 24 B.125/4x + 34 C. 125/4x - 24 D.125/4x - 34
The algebraic expression is equivalent to the expression is 125/4x + 34. Option B
What are algebraic expressions?Algebraic expressions are simply defined as expressions that are composed of terms, variables, constants, coefficients and factors.
These algebraic expressions are also composed of mathematical operations, such as;
AdditionsubtractioMultiplicationDivisionBracketParenthesesFrom the information given, we have;
25/4(5x-4/5)+29
expand the bracket, we get;
125x - 100/5 + 29
Find the LCM, we get;
125x - 100 + 145/5
Divide the values
125/4x + 34
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what are 2, 3, and 4
1. The area of square C is 625 ft². 2. The perimeter of square C is 46 ft. 3. The area of square B is 1456 ft². 4. The length of square A is 4√15 ft.
What is Pythagoras theorem?A key idea in geometry that connects the lengths of a right triangle's sides is known as the Pythagorean Theorem. It says that the hypotenuse's square length, which is the side that faces the right angle, is equal to the sum of the squares of the lengths of the other two sides in a right triangle. It has the following mathematical expression:
a² + b² = c²
1. The area of square C can be found using the Pythagorean Theorem:
a² + b² = c²
Using the area the side is calculates as follows:
Side length of A = √225 = 15 ft
Side length of B = √400 = 20 ft
Now,
15² + 20² = c²
225 + 400 = c²
625 = c²
c = √625 = 25 ft
So the area of square C is:
Area of C = 25² = 625 ft²
2. The perimeter of square C can be found by adding up the side lengths of all three squares:
Perimeter of A = 36 ft, so each side length of A is 9 ft.
Perimeter of B = 48 ft, so each side length of B is 12 ft.
Perimeter of C = Side length of A + Side length of B + Side length of C
Perimeter of C = 9 + 12 + c
We found earlier that c = 25 ft, so we can substitute that in:
Perimeter of C = 9 + 12 + 25 = 46 ft
3. The area of square B can be found using the fact that the areas of squares A, B, and C are related by the equation:
Area of A + Area of B = Area of C
We know the area of A and the area of C, so we can solve for the area of B:
Area of A = 15² = 225 ft²
Area of C = 1681 ft²
Area of A + Area of B = Area of C
225 + Area of B = 1681
Area of B = 1456 ft²
4. Perimeter of B = 64 ft
Side length of B = 64 / 4 = 16 ft
Now we can use the Pythagorean Theorem to find the side length of C:
a² + b² = c²
a = 15 ft (side length of A)
b = 16 ft (side length of B)
c = √(a² + b²) = √(15² + 16²) = √481 = 22 ft
Finally, we can use the Pythagorean Theorem again to find the side length of A:
a² + b² = c²
b = 16 ft (side length of B)
c = 22 ft (side length of C)
a = √(c² - b²) = √(22² - 16²) = √240 = 4√15 ft
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What is 43% , 2/5 , 3/7 , and 0. 42 remaining in ascending order ?
Answer:
2/5 < 0.42 < 43% < 3/7
Step-by-step explanation:
Let's convert them all to decimals:
43% = 0.43
2/5 = 0.4
3/7 = 0.428571...
0.42 = 0.42
Now we can arrange them in ascending order:
0.4
0.42
0.43
0.428571...
Analyze the diagram below and answer the question that follows.
P
20
10
gg
70
110
A. ZVOU and ZUOS
B. ZROS and ZTOS
C. ZNOP and ZROS
D. ZNOP and ZPOQ
R
80
IN
Image by Scientif38
Name two angles with identical measures.
S
10 110 120
130
ΤΑ
140 150 160 170
30
10
U
By observing the given protractor we know that option (C) is correct which says ∠NOP = ∠ROS.
What is a protractor?An instrument for measuring angles is a protractor, which is often made of transparent plastic or glass.
Protractors might be straightforward half-discs or complete circles. Protractors with more complex features, like the bevel protractor, include one or two swinging arms that can be used to measure angles.
To draw arcs or circles, use a compass.
To measure angles, one uses a protractor.
So, we need to observe the given image of the protractor:
We will easily find that ∠NOP = ∠ROS
Therefore, by observing the given protractor we know that option (C) is correct which says ∠NOP = ∠ROS.
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PLEASE URGENTLY HELP!!!!!!!!!!!
LOOK AT SCREENSHOT!!!
What is the value of x in degrees?
Please show work if you can!
Answer: 72
Step-by-step explanation:
Q is same as M = 72
N=36
L=x
All 3 angles of a triangle add to 180
72+36+x=180
x=72
Pentagon A'B'C'D'E'A
′
B
′
C
′
D
′
E
′
A, prime, B, prime, C, prime, D, prime, E, prime is the image of pentagon ABCDEABCDEA, B, C, D, E under a dilation with a scale factor of \dfrac{1}{2}
2
1
start fraction, 1, divided by, 2, end fraction.
The length of segment C'D' is given as follows:
C'D' = 2.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The length of segment CD is given as follows:
CD = 4. (4 vertical units of difference).
The scale factor is given as follows:
k = 1/2.
Hence the length of segment C'D' is given as follows:
C'D' = 1/2 x 4 = 2.
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subtract -10x+3 from -7x^2 +5x +10
Answer:
-7x^2 + 15x +7
Step-by-step explanation:
-7x^2 + 5x + 10 - (-10x + 3)
-7x^2 + 5x + 10 + 10x -3.......when u distribute it multiple by -1
-7x^2 + 15x +7 ...... simplify by collecting like term.
answer this geometry question and show work!!
Answer:
x = 58°
Step-by-step explanation:
Label the point where the diagonals cross as T
Diagonals always meet at right angles
m∠SRT = 32
Sum of interior angles of ΔSRT = 180
x = 180 - 90 - 32 = 58
Select the statement that best describes how pollination begins.
The statement that best describes how pollination begins is that it starts when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower. Pollination is an essential step in the reproduction of plants, and it allows for the exchange of genetic material between different plants.
Pollination can occur through various methods, including wind, water, and animals such as bees, butterflies, and birds. Once the pollen is transferred, it begins to grow and develop, ultimately leading to the formation of a seed and the growth of a new plant.
Pollination is vital to the continuation of plant life, and without it, many plant species would not be able to survive. It is essential for plant breeders to understand the pollination process, as they can use it to cross different plant varieties and produce new and improved plants.
In conclusion, pollination begins when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower, allowing for the exchange of genetic material and the growth and development of new plants.
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Find the value of b. Round your answer to the nearest hundredth.
Image may not
be drawn to scale.
The value of the tangent segment b is 20.15.
What is the value of side b?The secant-tangent power theorem, also known as the tangent-secant theorem, states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.
It is expressed as:
( tangent segment )² = External part of the secant segment + Secant segment.
From the diagram:
Tangent segment = WX = b
External part of the secant segment = YX = 14
Secant segment = ZX = 15 + 14 = 29
Plug these values into the above formula and solve for b.
( tangent segment )² = External part of the secant segment + Secant segment.
b² = 14 × 29
b² = 406
b = √406
b = 20.15
Therefore, the value of b is 20.15.
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Si 12kg de papas y seis kg de arroz cuentan 102. 00 mientras que 9 kg de papas y 13 kilogramos de arroz cuestan 153. 00¿cuanto cuesta cada producto?
Entonces, concluimos que las papas cuestan 4 pesos por kilogramo y el arroz cuesta 9 pesos por kilogramo.
Para resolver este problema, necesitamos plantear un sistema de ecuaciones lineales con dos incógnitas: el precio por kilogramo de papas y el precio por kilogramo de arroz. Podemos escribir:
12p + 6r = 102
9p + 13r = 153
Donde p es el precio por kilogramo de papas y r es el precio por kilogramo de arroz. Podemos resolver este sistema de ecuaciones usando el método de eliminación. Multiplicando la primera ecuación por 13 y la segunda ecuación por -6, obtenemos:
156p + 78r = 1326
-54p - 78r = -918
Sumando estas ecuaciones, obtenemos: 102p = 408
Dividiendo ambos lados por 102, encontramos que p = 4. Por lo tanto, el precio por kilogramo de papas es de 4 pesos.
Para encontrar el precio por kilogramo de arroz, podemos sustituir p = 4 en una de las ecuaciones originales y resolver para r. Por ejemplo, usando la primera ecuación:
12(4) + 6r = 102
48 + 6r = 102
6r = 54
r = 9
Por lo tanto, el precio por kilogramo de arroz es de 9 pesos.
Entonces, concluimos que las papas cuestan 4 pesos por kilogramo y el arroz cuesta 9 pesos por kilogramo.
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A glass prism on a chandelier is 93 millimeters long. A base of the prism is an equilateral triangle with side lengths of 7 millimeters and a height of about 6. 6 millimeters. What is the approximate surface area of the prism?
The approximate surface area of the glass prism is approximately 1986.66 square millimeters.
To find the surface area of the glass prism, we need to determine the area of each of its faces and then add them together. The prism consists of two congruent equilateral triangles and three rectangular faces.
The area of an equilateral triangle with side length s and height h is given by:
A = (√(3)/4) * s²
Using this formula, we can find the area of each of the two equilateral triangles in the prism:
A = (√(3)/4) * 7² ≈ 21.22 mm²
Next, we need to find the area of each of the three rectangular faces. The length of each rectangular face is equal to the side length of the equilateral triangle (7 mm), and the height is equal to the length of the prism (93 mm). Therefore, the area of each rectangular face is:
A = length x height = 7 mm x 93 mm = 651 mm²
To find the total surface area of the prism, we add the areas of the two equilateral triangles and the three rectangular faces:
Total surface area ≈ 2 x 21.22 mm² + 3 x 651 mm² ≈ 1986.66 mm²
Therefore, the approximate surface area of the glass prism is approximately 1986.66 square millimeters.
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Apple needs 12 ounces of a stir fry mix that is made up of rice and dehydrated veggies. The rice cost $1.73 per ounce and the veggies costs $3.38 per ounce. Apple has $28 to spend and plans to spend it all.
Let x = the amount of rice
Let y = the amount of veggies
Part 1: Create a system of equations to represent the scenario. (2 points)
Part 2: Solve your system using any method. Write your answer as an ordered Pair. (1 point)
Part 3: Interpret what your answer means (how much rice and how much veggies Apple buys) (1 point)
The system of equations to represent the scenario is 1.73x + 3.38y ≤ 28,
and the ordered pair is (8,4).
What is the Linear equation?
A linear equation is an algebraic equation that represents a straight line on a coordinate plane. A linear equation has the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).
What is a system of equations?
A system of equations is a set of two or more equations that involve the same variables. In a system of equations, the solution is a set of values for the variables that satisfy all the equations in the system simultaneously. For example, the system of equations:
2x + 3y = 7
x - 2y = 5
has two equations with two variables x and y. The solution to the system is the set of values for x and y that satisfy both equations simultaneously.
According to the given information:
Part 1:
We are given that Apple needs 12 ounces of the stir fry mix, which is made up of rice and dehydrated veggies. Let x be the amount of rice in ounces and y be the amount of dehydrated veggies in ounces.
The total amount of stir fry mix needed is 12 ounces, so we have:
x + y = 12
The cost of the rice is $1.73 per ounce and the cost of the dehydrated veggies is $3.38 per ounce. Apple has $28 to spend and plans to spend it all, so the cost of the stir fry mix must be less than or equal to $28:
1.73x + 3.38y ≤ 28
Part 2:
To solve the system of equations, we can use substitution or elimination. Here, we will use substitution to solve for one variable in terms of the other:
x + y = 12 --> y = 12 - x
Substituting y = 12 - x into the second equation, we get:
1.73x + 3.38(12 - x) ≤ 28
Simplifying and solving for x, we get:
1.73x + 40.56 - 3.38x ≤ 28
-1.65x ≤ -12.56
x ≥ 7.616
We round up to the nearest whole number since we cannot buy a fraction of an ounce of rice. Thus, x = 8 ounces.
Substituting x = 8 into the equation y = 12 - x, we get:
y = 12 - 8
y = 4 ounces
Therefore, Apple buys 8 ounces of rice and 4 ounces of dehydrated veggies. The ordered pair is (8,4).
Part 3:
Our solution (8, 4) means that Apple needs to buy 8 ounces of rice and 4 ounces of dehydrated veggies to make 12 ounces of stir fry mix. The cost of the stir fry mix can be calculated by substituting these values into the cost equation:
1.73(8) + 3.38(4) = $21.48
Since this is less than or equal to the $28 that Apple has to spend, they can afford to buy the necessary ingredients to make the stir fry mix.
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