the hands do form a right angle during Mario's math class, at 2:35:17.5 p.m. (rounded to the nearest half-second).
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
During the class from 2:00 p.m. to 2:50 p.m.,
the hour hand will move from the 2 to the 3 and will be halfway between the 2 and 3 at 2:30 p.m. The minute hand will make one full revolution around the clock face, from the 12 to the 12, during this time.
Let's calculate the positions of the hour and minute hands at 2:30 p.m.:
The hour hand moves 1/12 of the way around the clock face for each hour or 30 degrees for each hour. At 2:30 p.m.,
it will have moved 2.5 hours, so it will be 2.5 * 30 = 75 degrees past the 2 o'clock mark.
The minute hand moves 360 degrees in 60 minutes or 6 degrees per minute. At 2:30 p.m.,
it will have moved 30 minutes, so it will be 30 * 6 = 180 degrees past the 12 o'clock mark.
To determine if the hands form a right angle, we need to calculate the angle between them. Let's call this angle "A".
The angle between the hour and minute hands is the absolute difference between their positions, which is 105 degrees in this case (180 degrees - 75 degrees).
If the minute hand is ahead of the hour hand by exactly a quarter of a revolution or 90 degrees, then the hands will form a right angle.
So, we need to check whether angle A is equal to 90 degrees. If A = 90 degrees, then the hands form a right angle, and we can calculate the time when this happens by finding the time at which the minute hand is exactly 90 degrees ahead of the hour hand.
Let's set up an equation to solve for the time t:
A = 90 = 180 - 75 - 6t
Solving for t, we get:
t = 17.5
Therefore, the hands do form a right angle during Mario's math class, at 2:35:17.5 p.m. (rounded to the nearest half-second).
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Design n activity to teach Grade R learners about sharing with remainders. Indicate theme in which your activity will be based on
Use the cookies to teach basic fractions, such as one-half or one-third of a cookie.
What is Activity ?
An activity is a task, exercise, or action that is carried out for a specific purpose or goal. It can be an organized event or a spontaneous action that requires some level of effort or engagement from participants.
Begin by gathering the Grade R learners together and introduce the theme "Sharing Treats with Friends" and the concept of sharing with remainders. Explain to the learners that sometimes when we share treats with our friends, we might not have enough for everyone to have an equal amount.
Place the bag of cookies on the plate and ask the learners to estimate how many cookies are in the bag. Write their guesses on the board or chart paper.
Open the bag of cookies and count how many there are. Record the actual number of cookies on the board or chart paper.
Explain that the learners will be sharing the cookies with their friends, but they must make sure that everyone gets the same number of cookies. Divide the class into small groups of three or four learners.
Instruct each group to count the number of cookies in the bag and divide them equally among the members of the group. If there are any remaining cookies, they should be placed on the plate.
Ask the learners to share their results with the class. Some groups may have exactly the same number of cookies, while others may have remainders. Write their results on the board or chart paper.
Discuss with the learners how they can share the remaining cookies equally among their group members. For example, they could break the remaining cookies into smaller pieces or take turns sharing the last cookie.
Give the learners a chance to practice sharing with remainders by repeating the activity with different amounts of cookies and different group sizes.
As a conclusion, ask the learners to reflect on the activity and discuss how it felt to share with their friends. Encourage them to think about why sharing is important and how it can make everyone feel happy.
Optional extension activities:
Have the learners draw pictures or write stories about sharing treats with their friends.
Therefore, Use the cookies to teach basic fractions, such as one-half or one-third of a cookie.
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The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 2/ t^2 , where t is measured in seconds. Find the velocity (in m/s) of the particle at times t = a, t = 1, t = 2, and t = 3.
As a result, the particle's velocity changes as time passes. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3.
What about the equation's meaning?A mathematical equation, such as 6 x 4 = 12 x 2, states that two numbers or values are equivalent. a meaningful noun. When several or even more components need to be taken into account simultaneously in order to comprehend or describe the entire situation, an equation is used.
The derivatives of the displacing equation with time as a parameter is the particle's velocity.
v = ds/dt = d/dt (2/t²) = -4/t³
As a result, the particle's velocity at times t = a, t = 1, t = 2, and t = 3 is as follows:
v(a) = -4/a³
v(1) = -4/1³ = -4 m/s
v(2) = -4/2³ = -0.5 m/s
v(3) = -4/3³ = -0.15 m/s
The particle's velocity consequently varies over time. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3. Due to the fact also that velocity is negative for any and all values of t, the particle is travelling in the reverse way (i.e., to the left).
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(04.01 LC)
Which of the following sequences represents an arithmetic sequence with a common difference d = -3?
144, 48, 18, 6, 2
24, 21, 18, 15.5
3,-9, 27. -81, 243
43,40,37,34,31
An arithmetic sequence with a common difference d = -3 include the following: D. 43,40,37,34,31.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 40 - 43
Common difference, d = -3
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Which of the following would not be a possible function for f (x) and g(x)
The following function won't produce the intended composite function:
f(x) = 8/x + 4
g(x) = 1/x²
What are functions?A method or connection known as a function connects each element of a non-empty set A to at least one element of a second non-empty set B. A function in mathematics is a relation f between a set A (the function's domain) and a different set B (the function's co-domain).
In the given question,
When f(x) = 8/x + 4 and g(x) = 1/x²
Then (f o g(x)) = 8/1/x² + 4
= 8x² + 4
As a result, the following function would not produce the intended composite function:
f(x) = 8/x + 4
g(x) = 1/x²
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express in exponential form (-2.5 + i4.2)
Answer:
The given complex number is (-2.5 + i4.2).
To express it in exponential form, we need to find the modulus (r) and argument (θ) of the complex number.
The modulus is given by:
|r| = √((-2.5)^2 + (4.2)^2) = √(6.25 + 17.64) = √23.89 ≈ 4.888
The argument is given by:
θ = tan⁻¹(4.2/(-2.5)) = tan⁻¹(-1.68) ≈ -1.03 radians
Therefore, the exponential form of the complex number is:
(-2.5 + i4.2) = 4.888e^(-i1.03)
What transformation is happening? (x,y) —> (2x, 3y)
The scaling factors need not be the same, and this transformation scales the x-axis by a different factor than the y-axis, resulting in a non-uniform scaling.
What is Transformation axes ?
Transformation axes refer to the new coordinate axes after a transformation is applied to a given set of coordinates or points.
The transformation (x, y) → (2x, 3y) is a linear transformation that stretches the x-coordinate by a factor of 2 and the y-coordinate by a factor of 3, while keeping the origin fixed.
This transformation is an example of a scaling transformation, where the scale factor along the x-axis is 2 and along the y-axis is 3.
Visually, this transformation will stretch out the graph horizontally and vertically, making objects appear larger or smaller depending on their position relative to the x and y axes.
Therefore, The scaling factors need not be the same, and this transformation scales the x-axis by a different factor than the y-axis, resulting in a non-uniform scaling.
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Help. Marked most brainlliest
Answer:
Incorrect
Step-by-step explanation:
In step one, when they multiplied exponents, they added them which is correct
Step two, they divided exponents, which means they should have subtracted. if they subtracted 6/5 and 2/5, it would have been
[tex]( {x}^{ \frac{4}{5} } )^{ \frac{1}{2} } [/tex]
HELP ME!!!!!!!!!!!!!!!!!!!
The required number line shows that the four numbers between 10 and 20 that have a remainder of 2 when divided by 3.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
To show the numbers between 10 and 20 that have a remainder of 2 when divided by 3, we need to start with the first number in that range that has a remainder of 2 when divided by 3, which is 11. Then, we can add 3 to that number to get the next number that has a remainder of 2 when divided by 3, which is 14.
We can continue adding 3 to each previous number to get the rest of the numbers that meet this condition:
11, 14, 17, 20
So, these are the four numbers between 10 and 20 that have a remainder of 2 when divided by 3. We can plot them on the number line as shown.
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Use Pattern blocks to represent each multiplication equation. recall that a hexagon represents 1 whole.
Pattern blocks are shapes that are used to illustrate math equations. They can be used to represent addition, subtraction, multiplication and division. If five hexagons are stacked on top of each other, then the equation can be read as 5 x 1.
What are pattern blocks?Pattern blocks are a great visual tool for teaching younger children basic multiplication. They can help children understand the concept of multiplication better, as well as help them to remember the equation. Pattern blocks are also a great way to show the relationship between addition and multiplication, since both equations can be represented using the same shapes. By using pattern blocks to illustrate multiplication equations, children can have a more concrete understanding of the concept.
For multiplication, there are two different ways to use pattern blocks. The first way is to use the number of sides on a pattern block to represent the multiplication equation. For example, if two hexagons are used to represent 2 x 2, then the equation can be read as two times two. The second way is to simply stack the pattern blocks in order to represent the equation. For example, if five hexagons are stacked on top of each other, then the equation can be read as 5 x 1.
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Can you please solve? TKSSSSS
Answer:
18π or
Step-by-step explanation:
To find the area of a semicircle, use the formula of the area of a semicircle.
Area = [tex]\frac{1}{2}[/tex] π r^2
Radius = 6
Area = [tex]\frac{1}{2}[/tex] π 6^2
Area = [tex]\frac{1}{2}[/tex] (36π)
Area = 18π (in terms of π)
Area = 56.52 (in terms of 3.14)
How many 3cm cubes can be placed inside the box?
Answer: 36 cubes
Step-by-step explanation:
Length x Width x Height
18 x 6 x 9 = 972
3 x 3 x 3 = 27
972 / 27 = 36
Vehicle manufactures crash test their new vehicles and measure the impact force Subaru's Crosstrek impact force measurements are normally distributed with a mean of 30 metric tons and a standard deviation of 2 metric tons. Suppose Subaru tests a random sample of 9 cars and calculates the sample mean impact force.
a. What is the mean and standard deviation of the sampling distribution of the sample mean impact force?
b. What is the probability of a sample mean impact force being less than 28.7 metric tons?
The standard deviation is 0.67 metric tonnes, and the mean of the sampling distribution of the sample mean impact force is 30 metric tonnes.
What is the mean and standard deviation of the sampling distribution of the sample mean impact force?
a. The following formulas can be used to determine the mean and standard deviation of the sampling distribution of the sample mean impact force:
30 metric tonnes are the population's mean and the sampling distribution's mean.
Standard deviation of the sample distribution is equal to the square root of the population's standard deviation.
= [tex]2 / sqrt(9) (9)[/tex]
= 0.67 tonnes in metric
As a result, the standard deviation is 0.67 metric tonnes, and the mean of the sampling distribution of the sample mean impact force is 30 metric tonnes.
What is the probability of a sample mean impact force being less than 28.7 metric tons?
b. Using the z-score calculation and common normal distribution tables, we can determine the likelihood that the sample mean impact force will be less than 28.7 metric tonnes. The z-score equation is:
(Sample Mean - Population Mean) = Z (standard deviation of sampling distribution)
= (28.7 - 30) / 0.67 = -2
We discover that the probability of a z-score less than -2 is 0.0228 using the usual normal distribution table. Consequently, 0.0228 or 2.28% of the time, the sample mean impact force will be less than 28.7 metric tonnes.
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Which part of a prism gives a prism its characteristic name?
Answer:
Bases
Step-by-step explanation:
Cómo convertir 3000m a km
Answer:
Step-by-step explanation:
1000m = 1km
So 3000m = 3km
Please help urgently! Find all the missing angles in the diagram below. Explain how you used two different angle theories to find at least two missing angles.
The requried measures of angles a, b, c, and d are 97°, 15°, 68°, and 68° respectively.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
From the figure,
The calculation of the unknown angles is as follows,
112° and ∠d are supplementary angles.
So,
112 + ∠d = 180
∠d = 180 - 112
∠d = 68°
97° and angle a are corresponding angles, so
∠a = 97°.
112 and ∠c are also supplementary angles.
112 + ∠c = 180
∠c = 68°
Now,
∠a + ∠b = 112
∠a + 97 = 112
∠a = 15°
Thus, the requried measure of angles a, b, c, and d are 97°, 15°, 68° and 68°.
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Can someone answer this just read the picture? Right answers only please!
The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.
What is temperature?Temperature is a unit of hotness and coldness that can be described in terms of any number of arbitrary scales. It also represents the direction wherein heat energy will naturally flow, from either a hotter (i.e., higher temperature) body to a colder body.
Temperature is not the same as the energy of such a thermodynamic system; for instance, an iceberg has a significantly larger total heat energy than a match, despite the fact that a match is burning at a significantly higher temperature. The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.
Therefore, the linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.
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Everything step by stepped
The number of touchdowns scored by this professional football team could be: C. 10.
What is a percentage?In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
In order to determine the number of points scored by the defense of this professional football team, we would use the following mathematical expression:
Number of points = 24/100 × 242
Number of points = 0.24 × 242
Number of points = 58.08
For the number of touchdowns, we have:
Number of touchdowns = 58.08/6
Number of touchdowns = 9.68 touchdowns.
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Ryan, a consumer electronics salesperson, earns a base salary of $1400 per month and a commission of 5% on the amount of sales he makes. One month Ryan received a $1710 paycheck. Find the amount
Answer:
Let x be the amount of sales Ryan made in that month.
Ryan's commission on the sales would be 5% of x, which is 0.05x.
Adding the commission to his base salary gives his total income for the month, which is $1400 + 0.05x.
Since his paycheck for the month was $1710, we can write the equation:
$1400 + 0.05x = $1710
To solve for x, we can first subtract $1400 from both sides:
0.05x = $310
Then divide both sides by 0.05:
x = $6200
Therefore, Ryan made $6200 in sales that month.
why is it not possible to form a right triangle with the lengths 4, 8, and 10? please explain!
Answer:
It is not possible to form a right triangle with the lengths 4, 8, and 10 because the longest side of the triangle must be shorter than the sum of the other two sides. This is known as the Pythagorean Theorem, which states that in a right triangle, the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides. Since 8² + 10² = 164, and 10 is greater than the sum of 4 + 8, it is not possible to form a right triangle with those three lengths.
In this case, assuming that 10 is the hypotenuse, we have:
10² = 4² + 8²
100 = 16 + 64
This equation is not true, as 100 is not equal to 80. Therefore, we cannot form a right triangle
increase 1352 by the sum of 897.23 and 39.89
Answer:
2289.12
Step-by-step explanation:
Answer:
2289.12
Step-by-step explanation:
the sum of 897.23 and 39.89 is 937.12
937.12+1352=2289.12
Part 1 The height of a ball (in feet) after t seconds is given by the quadratic function h = -16(t-5)^2 + 119.
A. When does the ball reach its maximum height?
B. What is the maximum height?
The ball may rise height a maximum of [tex]119[/tex] feet.
How is height defined?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base but something above it. Anything that can be measured vertically, whether it is high or low, is referred to as having height.
As the ball hits the quadratic function's vertex, it has grown to its highest point. The position (b, c), wherein b is the vertex's x-coordinate, is where a quadratic function of the type is said to have its vertex.
As the quadratic function in this instance is, the point serves as the vertex (5, 119). The ball therefore reaches its highest point after 5 seconds.
[tex]h=-16(5-5)^{2}+119[/tex]
[tex]h=119[/tex]
Therefore, the maximum height of the ball is [tex]119[/tex] feet.
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Find volume in terms of pi
The volume of the figure is 93π
How to determine the volume of the figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The volume is calculated as
Volume = Cone + Cylinder
Using the above as a guide, we have the following:
Volume = 1/3πr²(H - h) + πr²h
Substitute the known values in the above equation, so, we have the following representation
Volume = 1/3π * 3² * (15 - 8) + π * 3² * 8
Evaluate
Volume = 93π
Hence, the volume is 93π
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Which expression is equivalent to (5−4i)(3−2i)(5−4i)(3−2i)?
The given expression equivalent to (5−4i)(3−2i)(5−4i)(3−2i) is -231 + 372i.
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and operations that represents a value or a quantity. It can be a simple expression consisting of only one number or variable, or a complex expression consisting of several numbers, variables, and operations.
We can use the distributive property of multiplication to expand the given expression as follows:
(5−4i)(3−2i)(5−4i)(3−2i)
= (5−4i)(5−4i)(3−2i)(3−2i)
= (25 - 40i + 16i²)(9 - 12i + 4i²)
= (25 - 40i - 16)(9 - 12i - 4)
= (-231 + 372i)
Therefore, the given expression equivalent to (5−4i)(3−2i)(5−4i)(3−2i) is -231 + 372i.
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Which equations can be used to find the lengths of the legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100
Given : A = 24 sq feet
A = 0.5 base x height
base = x , height = x+2
A = 0.5 x(x+2) = 24 sq feet
1) 0.5 x(x+2) = 24 (A)
2) x^2 + 2x - 48 = 0 (D)
To check the rest un-wrap the bracket:
x^2 + (x+2)^2 = 24
x^2 + x^2 + 4 + 4x = 24
2x^2 + 4x - 20 = 0
x^2 + 2x - 10= 0 (NO)
Likewise:
x^2 + (x+2)^2 = 100
x^2 + x^2 +4 + 4x = 100
2x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
3) x^2 + 2x - 48 = 0 (F)
To sum up: that's what apply:
1) 0.5 x(x+2) = 24 (A)
2) x^2 + 2x - 48 = 0 (D)
3) x^2 + 2x - 48 = 0 (F)
Two families purchased lunch at a hotdog cart. The first family paid $18.00 for 4 hot dogs and 4 drinks. The second famliy paid $20.00 for 5 hot dogs and 3 drinks.
What is the price, in dollars, of a hot dog? Enter your answer as $0.00
one answer only
Answer:
The price of a hot dog is $2.00
A decimal to the hundredths place is greater than 5.58 and less than 5.88.The digit in the tenths place is odd, and the digit in the hundredths place is even. What are all the possible decimals?
The pοssible decimals that satisfy the given cοnditiοns are:5.20, 5.22, 5.24, 5.26, 5.28, 5.60, 5.62, 5.64, 5.66, 5.68, 7.20, 7.22, 7.24, 7.26, 7.28, 7.60, 7.62, 7.64, 7.66, 7.68
What are decimals?Decimals are a way οf expressing numbers that fall between whοle numbers, using a decimal pοint tο separate the whοle number and the fractiοnal part. Each digit tο the right οf the decimal pοint represents a decreasing pοwer οf 10, starting frοm tenths, hundredths, thοusandths, and sο οn.
Since the digit in the tenths place is οdd, it can οnly be 5 οr 7. Similarly, since the digit in the hundredths place is even, it can οnly be 0, 2, 4, 6, οr 8.
Therefοre, the pοssible decimals that satisfy the given cοnditiοns are:
5.20
5.22
5.24
5.26
5.28
5.60
5.62
5.64
5.66
5.68
7.20
7.22
7.24
7.26
7.28
7.60
7.62
7.64
7.66
7.68
Nοte that these are the οnly pοssible decimals that satisfy all the given cοnditiοns.
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I NEED HELPPPPPPP 10 POINTS FOR WHOEVER GETS IT CORRECT
Answer:
72; Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Use the Simple Interest formula to find the simple interest. (l=prt)
The Simple Interest is $10
What is Simple Interest?Simple Interest is the method of calculating the interest amount for some principal amount of money. It is also finding the product of the principal amount borrowed or lent, the rate of interest and the term or repayment period of the loan.
Where the Principal is the borrowed money which is given for a specific period.
Simple Interest = P * R * T/100
Where P = Principal = $1000
R = Rate = 2%
T = Time = 6 months
When 6 months converted to year = 6/12 = 1/2 = 0.5 year
SI = 1000 * 2 * 0.5/100
SI = 1000/100
SI = $10
Therefore, the Simple Interest is $10
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Answer:
Step-by-step explanation:
Simple Interest formula = P * R * T/100
p = $1000
r = 2%
t = 6 months (0.5 year)
so, SI = 1000 * 2 * 0.5/100
SI = $10
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9. Leroy received a stamp for his collection as a gift. When he received the stamp, it was worth $14.50.
The value of the stamp increases by 2% each year.
a. Write an equation for the value of the stamp V after t years.
b. Use the equation to predict the value of the stamp after 18 years.
Therefore, the stamp's estimated value is $21.54 considering that when he first got it, it was only worth $14.50.
What is equation ?A mathematical assertion that two expressions are equivalent is known as an equation. The equal symbol (=) separates the two sides, which are labeled as the left-hand side (LHS) and the right-hand side (RHS). The equation must have identical values on both sides, and it is frequently used to determine an unknown variable's value.
Numerous mathematical processes, such as addition, subtraction, multiplication, division, exponents, logarithms, and more, can be used in equations.
given
a. The formula for the stamp's worth V after t years is as follows:
[tex]V = 14.50(1 + 0.02)^t[/tex]
where t is the period of time since Leroy got the stamp, and 0.02 denotes a 2% annual increase in value.
b. We enter t = 18 into the equation to estimate the stamp's value after 18 years:
[tex]V = 14.50(1 + 0.02)^{18[/tex]
[tex]V = 14.50(1.02) (1.02)^{18[/tex]
V = 14.50(1.485) (1.485)
V = 21.54
Therefore, the stamp's estimated value is $21.54 considering that when he first got it, it was only worth $14.50.
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What is the volume of this rectangular prism 2, 7/3, 2
Answer:
The volume V of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.
In this case, we have l = 2, w = 7/3, and h = 2. Therefore, the volume is:
V = (2)(7/3)(2)
V = 28/3
V = 9.33 (rounded to two decimal places)
So the volume of the rectangular prism is approximately 9.33 cubic units.