To solve a Pythagorean triangle of 7 squared + 2 squared, you need to use the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the unknown side, which we'll call x. So, we have:
7² + 2² = x²
Simplifying this equation, we get:
49 + 4 = x²
53 = x²
To find the value of x, we need to take the square root of both sides:
√53 = x
So the answer to the problem is √53. When you square root it, you get a decimal approximation of approximately 7.28.
In summary, to solve a Pythagorean triangle, you need to use the Pythagorean theorem and find the square root of the sum of the squares of the other two sides to find the length of the unknown side.
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NEED ANSWERS ASAP
Peter creates a square pyramid
model for History class. The
base of the pyramid has an
area of 20 square inches. Each
triangle has an area of 10
square inches. If Peter wants to
cover the entire pyramid with
gold paper, how much paper
will he need?
WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
Peter will need 60 square inches of gold paper to cover the entire square pyramid for his History class.
You need to find the total surface area of the square pyramid that Peter creates for his History class to determine how much gold paper he will need. This can be done as follows.
1: Identify the given information.
Base area: 20 square inches
Triangle area: 10 square inches
2: Determine the number of triangles in a square pyramid.
A square pyramid has 4 triangular faces.
3: Calculate the total area of the triangular faces.
Multiply the area of one triangle by the number of triangles: 10 square inches x 4 = 40 square inches.
4: Calculate the total surface area of the pyramid.
Add the base area and the total area of the triangular faces: 20 square inches (base) + 40 square inches (triangles) = 60 square inches.
Hence, the gold paper to cover the entire square pyramid is 60 square inches.
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Jonana has a board thats 6 ft long she wants to cut it into pieces that are each 1/4 foot long. Write an equation to represent the number of pieces she cut.
Jonana cut 24 pieces of 1/4 foot length from the 6-foot board
How to Write an equation to represent the number of pieces she cutLet "x" be the number of pieces that Jonana cut.
Each piece is 1/4 foot long.
So, the total length of all the pieces is x * 1/4 = x/4 feet.
But the total length is also 6 feet.
So we can set up the equation:
x/4 = 6
Solving for x:
x = 24
Therefore, Jonana cut 24 pieces of 1/4 foot length from the 6-foot board.
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In ΔMNO, the measure of ∠O=90°, OM = 1. 7 feet, and NO = 6. 7 feet. Find the measure of ∠N to the nearest degree
The measure of ∠N to the nearest degree is 82°.
Calculate the nearest degree?To find the measure of ∠N, we can use the Pythagorean theorem and trigonometric functions.
First, we can use the Pythagorean theorem to find the length of MN:
MN² = NO² - OM²
MN² = (6.7 feet)² - (1.7 feet)²
MN² = 44.56 feet²
MN = 6.67 feet
Now, we can use the sine function to find the measure of ∠N:
sin(N) = MN/NO
sin(N) = 6.67 feet / 6.7 feet
sin(N) ≈ 0.994
N ≈ sin⁻¹(0.994)
N ≈ 82.4°
The measure of ∠N to the nearest degree is 82°.
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Will give brainliest
find the area of this triangle.
round to the nearest tenth.
12 cm
330
5.5 cm
[ ? ] cm2
Answer:
30 cm²
Step-by-step explanation:
Formula : [tex]Area = \frac{hb}{2}[/tex]
A particular base ball field is a quarter circle with a radius of 290 feet. The baseball diamond is a square with a side length of 90 feet, and bases at its vertices. What is the area of the shaded section of the field?
The area of the shaded region of the circle is A = 57,918.5 feet²
Given data ,
First, we need to find the area of the quarter circle:
Area of quarter circle = (1/4) π ( r )²
= (1/4) π ( 290 )²
= 66,018.5 feet²
Next, we need to find the area of the square:
Area of square = side²
= 90²
= 8,100 feet²
Now, we can find the area of the shaded section by subtracting the area of the square from the area of the quarter circle:
Area of shaded section = Area of quarter circle - Area of square
= 66,018.5 feet² - 8,100 feet²
= 57,918.5 feet²
Hence , the area of the shaded section of the field is 57,918.5 feet²
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< ABC ≈ < DEF
False
True
Answer:
True (I think)
Step-by-step explanation:
Same pattern.
A -> B -> C.
D -> E -> F.
Would be false if either one didn't share the same pattern.
5. Vanessa and Nancy plan to make a birthday cake. Working together, Vanessa and Nancy can complete the
birthday cake in 2 hours. If Nancy works alone, it will take her 3 times as long as it would take Vanessa to
complete the birthday cake. The equation below represents this situation.
2 2
-+-=1
3x
How many hours would it take Nancy to complete the birthday cake if she worked alone?
X
Using an equation, if Nancy worked alone, the number of hours it would take her to complete the birthday cake is 1 hour 30 minutes.
What is an equation?An equation is a mathematical statement that proves the equality or equivalence of two or more mathematical expressions.
Equations use the equal symbol (=) unlike algebraic expressions, which combine variables with numbers, constants, and values using mathematical operands.
The number of hours for Vanessa and Nancy working together to make a birthday cake = 2 hours
The number of hours it takes Vanessa to complete the cake working alone = x
The number of hours it takes Nancy to complete the cake alone = 3x
Equation:3x + x = 2
4x = 2
x = 0.5 = 30 minutes
The total time for Nancy to complete the cake = 3x = 1.5 (3 x 0.5)
= 1 hour 30 minutes
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andy can run 20 miles in 6 hours. how much miles can he run in 1 hour.
I see that this is a rate of change time of problem
If andy can run 20 miles in 6 hours, than our goal is to find out how much he runs in a hour
So, we just have to divide 20 by 6.
It's sorta hard to explain
Questions?
Anyhow, the answer is around 3.3 miles per hour
Answer:
3.33 miles
Step-by-step explanation:
We Know
Andy can run 20 miles in 6 hours.
How many miles can he run in 1 hour?
We Take
20 / 6 ≈ 3.33 miles
So, Andy can run about 3.33 miles in 1 hour.
Find the area inside the square and outside the circle use 3.14 for pi. please help
The area inside the square and outside the circle is 0.86 square units.
To find the area inside the square and outside the circle, we need to first find the area of the square and the area of the circle.
Let's assume that the square has sides of length 2 units, which means its area is:
Area of square = side^2 = 2^2 = 4 square units
Now, let's assume that the circle has a radius of 1 unit, which means its area is:
Area of circle = pi * radius^2 = 3.14 * 1^2 = 3.14 square units
To find the area inside the square and outside the circle, we need to subtract the area of the circle from the area of the square:
Area inside square and outside circle = Area of square - Area of circle
= 4 - 3.14
= 0.86 square units
Therefore, the area inside the square and outside the circle is 0.86 square units.
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Solve systems of Equation by substitution method
3(x-2) + y = 7
4x - 3(y-1) = 16
The values of the variables are x = 4 and y = 1
How to solve the equationWe have the equations as;
3(x-2) + y = 7
4x - 3(y-1) = 16
Using the substitution method
Make 'y' the subject of formula from equation (1), we have;
y = 7 - 3(x-2)
Now, substitute the expression as y in equation (2), we get;
4x - 3(7 - 3(x-2) - 1) = 16
expand the bracket, we have;
4x - 3(7 - 3x + 6 - 1) = 16
collect the like terms
4x - 3(12 - 3x) = 16
4x - 36 + 9x = 16
collect the like terms
13x = 52
x = 4
Substitute the value
y = 7 - 3(4 -2 )
y = 7 -3(2)
y = 1
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ANSWER ASAP PLEASE
The band club has $2,100 to spend on music stands and songs. Each music stand costs $15 and each song costs $350. Let x represent the number of music stands and let y represent the number of songs.
Part A
Write an equation that describes the number of music stands and songs the band club can buy.
x +
y =
Part B
What is the greatest number of each item that the club can buy?
greatest number of music stands =
greatest number of songs =
Part A: The equation that describes the amount of music stands and songs that the band club can purchase is 15x + 350y = 2100.
Part B: The greatest number of music stands the club can buy is 6, and the greatest number of songs the club can buy is 3.
Part A:
The cost of x music stands is 15x dollars, and the cost of y songs is 350y dollars. The total cost cannot exceed $2,100, so we can write the following equation:
15x + 350y = 2100
Therefore, the equation that describes the amount of music stands and songs that the band club can purchase is 15x + 350y = 2100.
Part B:
To find the greatest number of each item the club can buy, we can use the given equation and look for integer solutions for x and y that satisfy the equation.
We can rearrange the equation to solve for y:
y = (2100 - 15x) / 350
To get integer solutions for y, we need 2100 - 15x to be divisible by 350. The largest multiple of 350 that is less than or equal to 2100 is 6*350 = 2100. So, we can try x = 0, 1, 2, 3, ..., 6 and see which values give integer solutions for y.
When x = 0, y = 6, which is an integer solution.
When x = 1, y = 5, which is not an integer solution.
When x = 2, y = 4, which is not an integer solution.
When x = 3, y = 3, which is an integer solution.
When x = 4, y = 2, which is not an integer solution.
When x = 5, y = 1, which is not an integer solution.
When x = 6, y = 0, which is an integer solution.
So, the greatest number of music stands the club can buy is 6, and the greatest number of songs the club can buy is 3.
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2-3 Consider the indefinite integral da. The substitution (3x - 2)2 u = 3x – 2 transforms the integral into: / None of these options are correct. 1-2 3 3 du 22 u 7 s". du 9u2 du u2 s " 0 7 u du u2
The substitution (3x - 2)2 u = 3x - 2 transforms the indefinite integral da into none of the given options. It should result in the integral of the function being expressed in terms of u rather than x.
This substitution is an example of using a change of variables to simplify an integral by transforming it into a more manageable form. This can be particularly useful when dealing with complicated integrals that are difficult to solve by other methods. Additionally, using such transforms can often provide insight into the underlying structure of the problem being studied.
Based on your question, it appears that you want to perform a substitution to transform the indefinite integral of "da" using the substitution (3x - 2)² u = 3x - 2. However, the given integral "da" doesn't seem to be correct or complete. Please provide the complete integral, and I will be happy to help you with the transformation using the given substitution.
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one serving of almonds is 1/3 cup. booker bought 2 and 2/3 cups of almonds how many servings of almonds did booker buy
Booker bought 8 servings of almonds.
How many servings of almonds did Booker buy if he purchased 2 and 2/3 cups of almonds, and one serving of almonds is 1/3 cup?
One serving of almonds is equal to 1/3 cup.
To find how many servings of almonds Booker bought, we can divide the total amount of almonds he purchased by the amount in one serving:
2 and 2/3 cups of almonds = 8/3 cups of almonds
Number of servings = (total amount of almonds purchased) / (amount in one serving)
Number of servings = (8/3) / (1/3)
Number of servings = 8/3 x 3/1
Number of servings = 8
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Simplify the expression five to the third power +3(5-3)
Answer:
Step-by-step explanation:
The expression +3(5-3) can be simplified using the order of operations (PEMDAS) as follows: first, we need to perform the exponentiation operation, which gives us 125.
Then, we need to perform the operation inside the parentheses, which gives us 6. Finally, we multiply 3 by 6, giving us 18. Therefore, the simplified expression is 125 + 18 = 143.
To further explain this solution, we use the order of operations, which is a set of rules that dictate the order in which operations must be performed when evaluating an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, which represents the order of operations from left to right.
In this expression, we first need to evaluate the exponentiation operation, which is 5 to the third power. This gives us 125. Next, we need to perform the operation inside the parentheses, which is 5-3. This gives us 2. We then multiply 3 by 2, which gives us 6. Finally, we add 125 and 6, giving us 131.
It is important to follow the order of operations when simplifying an expression to ensure that we obtain the correct result. By using PEMDAS, we can systematically simplify an expression step-by-step, avoiding any potential errors and obtaining a clear and concise solution.
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answer questions 2-20 please 1 and 5-7 are already answered no need to correct them does not need to be correct but please have relistic answers : )
The Pythagorean Theorem with regards to the relationships between the lengths of the sides of a right triangle indicates that we get;
2. x = 51
3. x = 50
4. x = 82
8. x = 2·√(77)
9. x = √(39)
10. x = 2·√(19)
11. x = 2·√(154)
12. x = 3·√3
13. x = 6·√(13)
16. A right triangle
17. A right triangle
18. The triangle is not a right triangle
19. An obtuse triangle
20. An obtuse triangle
What is the Pythagorean Theorem?The Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the lengths of the other two sides.
2. x² = 45² + 24² = 2601
x = √(2601) = 51
3. x² = 30² + 40² = 2500
x = √(2500) = 50
x = 50
4. x² = 80² + 18² = 6724
x = √(6724) = 82
x = 82
8. According to the Pythagorean Theorem, in the right triangle we get;
x² = 18² - 4² = 308
x = 2·√(77)
9. x² = 8² - 5² = 39
x = √(39)
10. x² = 20² - 18²
x² = 76
x = √(76) = 2·√(19)
x = 2·√(19)
11. x² = 25² - 3² = 616
x = √(616) = 2·√(154)
x = 2·√(154)
12. x² = 6² - 3² = 27
x = √(27)
x = 3·√3
13. x² = 22² - 4² = 468
x = √(468) = 6·√(13)
x = 6·√(13)
16. A triangle is a right triangle if the square of the side that is the longest is equivalent to the square of the other two sides, therefore;
17² = 289
15² + 8² = 289
Therefore, the triangle is a right triangle
17. 45² = 2025
27² + 36² = 2025
Therefore, the triangle is a right triangle
18. 11² = 121
9² + 4² = 97
Therefore, the triangle is not a right triangle
19. 6² = 36
4² + 3² = 25
The square of the side that is longest is larger than the sum of the squares of the other two sides, which indicates that the angle facing the longest side is lar1ger than 90°, and the triangle is an obtuse triangle.
20. 16² = 256
9² + 11² = 202
16² > 9² + 11²; Therefore, the triangle is an obtuse triangle
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Ver en español
Of the last 20 contestants on a game show, 8 won a prize. What is the experimental probability that the next contestant will win a prize?
The probability that the next contestant will win a prize is 2/5.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
probability that the next contestant will win a prize = number of contestants that won in the last games / total number of contestants in the last games
=> 8/20
To transform to the simplest form. divide both the numerator and the denominator by 4
=> 2/5
Hence the probability that the next contestant will win a prize is 2/5.
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Troy went to a Westwood Wasps basketball game on Saturday night. He paid $86.25 for a ticket to the game. He also had to pay for the 3 hours his car was parked in the parking garage. Troy spent a total of $99.
Which equation can you use to find the cost, x, for each hour Troy's car was parked in the garage?
The equation is 86.25 + 3x = 99.
How to determine the equation that can be used to find the cost per hour for Troy's car parking in the garage?Let's assume the cost for each hour Troy's car was parked in the garage is x dollars.
Since Troy spent a total of $99, we can set up an equation based on the given information.
The cost of the ticket to the basketball game is $86.25, and Troy also had to pay for 3 hours of parking. Therefore, the equation can be written as:
86.25 + 3x = 99
In this equation, 86.25 represents the cost of the ticket, 3x represents the cost of parking for 3 hours at a rate of x dollars per hour, and 99 represents the total amount Troy spent.
Therefore, the equation is 86.25 + 3x = 99.
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Write a division expression for each fraction 1/2
Answer: 1 ÷ 2
Step-by-step explanation: I think this is what you mean?
Ishaan tiene 2 veces la edad de Christopher.
Hace 35 años Ishaan tenía 7 veces la edad de
Christopher.
¿Cuántos años tiene Ishaan actualmente?
Ishaan's current age is 84.
How to solve for the current ageLet Ishaan's current age be I and Christopher's current age be C.
Given, I = 2C ...........(1) (Ishaan is twice the age of Christopher)
35 years ago, I - 35 = 7(C - 35) (Ishaan was 7 times the age of Christopher 35 years ago)
Simplifying the above equation, we get:
I - 35 = 7C - 245
I = 7C - 210 ...........(2)
Substituting equation (1) in equation (2), we get:
2C = 7C - 210
5C = 210
C = 42
Therefore, Christopher's current age is 42.
Substituting C = 42 in equation (1), we get:
I = 2C = 2(42) = 84
Therefore, Ishaan's current age is 84.
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The question is translated to English as
Ishaan is twice the age of Christopher. 35 years ago Ishaan was 7 times the age of Christopher. How old is Ishaan now?
Find the total surface area of the following
cone. Leave your answer in terms of a.
4 cm
3 cm
SA = [ ? ]7 cm
Hint: Surface Area of a Cone = tre + B
Where e = slant height, and B = area of the base
The total surface area of the cone is 44π cm², where π represents the mathematical constant pi.
We have,
To find the total surface area of a cone, we need to calculate the lateral surface area (denoted by L) and the base area (denoted by B), and then sum them.
The lateral surface area of a cone is given by L = πrℓ, where r is the radius of the base and ℓ is the slant height.
The base area is given by B = πr², where r is the radius of the base.
Given the dimensions:
Radius of the base (r) = 4 cm
Slant height (ℓ) = 7 cm
We can calculate the lateral surface area as L = π(4)(7) = 28π cm².
The base area can be calculated as B = π(4^2) = 16π cm².
Now, to find the total surface area (SA), we sum the lateral surface area and the base area:
SA = L + B = 28π + 16π = 44π cm².
Therefore,
The total surface area of the cone is 44π cm², where π represents the mathematical constant pi.
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Find the radius of the circle with equation x² + y² = 19²
r=0
Submit Answer
The radius of the circle of equation x² + y² = 19² is given as follows:
r = 19 units.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.
The equation of the circle in this problem is given as follows:
x² + y² = 19².
Hence the radius is obtained as follows, comparing to the general equation:
r² = 19²
r = 19 units.
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Some lemon, lime, and cherry lollipops are placed in a bowl. Some have a
chocolate center, and some do not. Suppose one of the lollipops is chosen
randomly from all the lollipops in the bowl. According to the table below, if it
is known to be lime, what is the probability that it does not have a chocolate
center?
OA. 35%
OB. 25%
O C. 45%
O D. 55%
See picture of diagram, I need this correct please help asap
Answer:
A (35%)
Step-by-step explanation:
Just divide what you want to find with the total. Does not have chocolate = 7. Total Lime = 20 (13 + 7) 7/20 = 0.35/35%
Question 10 > Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "DNE" 4 ( 1 -dz 22 +1 00
To determine the convergence of the integral 4(1-z)/(2^2 +1)² dz from 0 to infinity, we can use the comparison test.
First, note that (1-z) is bounded between 0 and 1, so we can compare it to the integral of 4/(2² +1)² dz from 0 to infinity, which is convergent since it is a constant times the convergent p-series with p=2.
Therefore, by the comparison test, the original integral is also convergent. To evaluate it, we can use partial fractions:
4(1-z)/(2² +1)^2 = A/(2+i)² + B/(2-i)²
Solving for A and B, we get A = (1+i)/5 and B = (1-i)/5.
Then, the integral becomes:
∫ 4(1-z)/(2² +1)² dz = A ∫ 1/(2+i)² dz + B ∫ 1/(2-i)² dz
= (1+i)/5 [-1/(2+i)] + (1-i)/5 [-1/(2-i)] from 0 to infinity
= [(1+i)(2-i) - (1-i)(2+i)]/25(2² +1)
= 0
Therefore, the integral is convergent and evaluates to 0.
To determine if an integral is convergent or divergent, you need to look at its limits and the function you are integrating. Convergent means that the integral has a finite value, while divergent means the integral does not have a finite value.
For example, if you have an integral like this:
∫(f(x) dx) from a to b,
you need to evaluate the limits 'a' and 'b' and the function 'f(x)'. If 'a' or 'b' is infinity (∞) or the function 'f(x)' behaves such that it leads to an infinite value for the integral, it is divergent. Otherwise, it is convergent.
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A researcher is studying life expectancy in different parts of the world using birth and death records she randomly selects a sample of 20 people from town a and a samle of 20 people form town b and records their lifespans in years.
mean lifespan in years standard deviation
town a 78.5 11.2
town b 74.4 12.3
the researhers wants to test the claim that there is a significant differnce in lifepan for people in the two towns. what are the null and alternative hypotheses that should be used to test this claim?
a. null: mu1 - mu2 is not equal to 0; alternative: mu1 - mu2 > 0 <---- a
b. null: mu1 - mu2 = 0; alternative: p1 - p2 is not equal to 0 <---- b
c. null: mu1 - mu2 = 0; alternative: mu1 - mu2 is not equal to 0 <---- c
d. null: p1 - p2 = 0; alternative: p1 - p2 < 0 <---- d
The correct answer is: c. null: mu1 - mu2 = 0; alternative: mu1 - mu2 is not equal to 0
The null hypothesis states that there is no significant difference in the mean lifespan of people in the two towns, while the alternative hypothesis states that there is a significant difference in the mean lifespan of people in the two towns.
Since we are comparing the means of two populations, we use the difference between the means as the test statistic. Therefore, the null hypothesis is mu1 - mu2 = 0 (there is no difference between the means) and the alternative hypothesis is mu1 - mu2 is not equal to 0 (there is a difference between the means).
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Find the volume of the cone in cubic feet. Use 3. 14 for π and round your answer to the nearest tenth.
(1 m ≈ 3. 2808 ft)
135,648 ft3
3,843. 8 ft3
4,790,189. 2 ft3
444,925. 4 ft3
The volume of the cone in cubic feet is approximately 0.0 cubic feet
We need to convert the given dimensions from inches to feet before calculating the volume in cubic feet.
The height of the cone is 6 inches, which is equivalent to 6/12 = 0.5 feet (since there are 12 inches in 1 foot).
The radius of the cone is 4.5 inches, which is equivalent to 4.5/12 = 0.375 feet.
Using the formula for the volume of a cone, which is:
V = (1/3) * π * r^2 * h
Substituting the given values, we get:
V = (1/3) * 3.14 * (0.375 feet)^2 * 0.5 feet
V ≈ 0.0221 cubic feet
Rounding this to the nearest tenth gives:
V ≈ 0.0 cubic feet
Therefore, the volume of the cone in cubic feet is approximately 0.0 cubic feet. None of the given options match this result.
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Your rate of pay is $36. Per hour and you bill by the quarter hour you spent four hour and 30 minutes on a client project how much would I bill for 162. Or 144
If your rate of pay is $36 per hour and you bill by the quarter hour, you would bill $162 for 4 hours and 30 minutes project.
Based on the given information, your rate of pay is $36 per hour, and you bill by the quarter hour. You spent 4 hours and 30 minutes on a client project.
To calculate the bill, first convert the 30 minutes into quarter hours: 30 minutes = 2 quarter hours. In total, you worked for 4 hours and 2 quarter hours (18 quarter hours).
Now, multiply your rate of pay ($36) by the number of quarter hours (18) and divide by 4 to account for the quarter hour billing: ($36 * 18) / 4 = $162. Therefore, you would bill the client $162 for the project.
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A textbook company will ship a box of textbooks to college students. The weight of the box in pounds can be determined by the function w(x) = 7. 5x + 2, where x is the number of textbooks in the box. The company requires a student to order at least 2 books but not more than 6 books. What is the range of the function for this situation? *
A. 2 ≤ x ≤ 6
B. 17 ≤ y ≤ 47
C. {17, 24. 5, 32, 39. 5, 47}
D. {2, 3, 4, 5, 6}
The range of the function for this situation is {17, 24.5, 32, 39.5, 47}, The correct option is C.
To find the range of the function for this situation, we need to evaluate the function for x = 2, 3, 4, 5, and 6, since these are the only valid inputs based on the problem statement.
w(2) = 7.5(2) + 2 = 17
w(3) = 7.5(3) + 2 = 24.5
w(4) = 7.5(4) + 2 = 32
w(5) = 7.5(5) + 2 = 39.5
w(6) = 7.5(6) + 2 = 47
Therefore, the range of the function for this situation is {17, 24.5, 32, 39.5, 47}, which is option C.
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Air is being pumped into a spherical balloon so that its volume increases at a rate of 100cm³/s. How fast is the radius of the balloon increasing when the diameter is 50cm?
V = 4/3 πr³
When the diameter of the balloon is 50 cm, the radius of the balloon is increasing at a rate of approximately 0.0254 cm/s
How to find the radius of the balloon increasing when the diameter is 50cm?We are given that the volume of a spherical balloon is increasing at a rate of 100 cm³/s. We need to find how fast the radius of the balloon is increasing when the diameter is 50 cm.
Let's first find the expression for the volume of the balloon in terms of its radius.
V = 4/3 πr³
Differentiating with respect to time (t), we get:
dV/dt = 4πr² (dr/dt)
We are given that dV/dt = 100 cm³/s. When the diameter of the balloon is 50 cm, the radius is 25 cm.
Substituting these values, we get:
100 = 4π(25)² (dr/dt)
Simplifying, we get:
dr/dt = 100 / (4π(25)²)
dr/dt ≈ 0.0254 cm/s
Therefore, when the diameter of the balloon is 50 cm, the radius of the balloon is increasing at a rate of approximately 0.0254 cm/s
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A person is working in the purchasing department of an appliance retailer. This month he is stocking up on washers and dryers. His
supervisor informs him that his budget this month is $12,000. He knows that the average wholesale cost of a washer over the past
year has been $250, while the average wholesale cost of a dryer has been $200. Complete parts a through h
a) What is the maximum number of washers the person can purchase within the budget?
To calculate the maximum number of washers the person can purchase within the budget, we divide the budget by the cost per washer:
$12,000 ÷ $250 = 48 washers
b) What is the maximum number of dryers the person can purchase within the budget?
To calculate the maximum number of dryers the person can purchase within the budget, we divide the budget by the cost per dryer:
$12,000 ÷ $200 = 60 dryers
c) If the person wants to purchase an equal number of washers and dryers, how many of each can he purchase?
To purchase an equal number of washers and dryers, we need to find the common factor of both 48 and 60:
48 = 2 x 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
The common factor is 2 x 2 x 3 = 12. So, the person can purchase 12 washers and 12 dryers within the budget.
d) If the person purchases the maximum number of washers and dryers, what is the total cost of the purchase?
To calculate the total cost of the purchase, we multiply the maximum number of washers and dryers by their respective cost:
48 washers x $250 = $12,000
60 dryers x $200 = $12,000
The total cost of the purchase is $24,000.
e) If the person purchases an equal number of washers and dryers, what is the total cost of the purchase?
To calculate the total cost of the purchase, we multiply the number of washers and dryers by their respective cost:
12 washers x $250 = $3,000
12 dryers x $200 = $2,400
The total cost of the purchase is $5,400.
f) If the person wants to spend the entire budget on washers, how many washers can he purchase?
To spend the entire budget on washers, we divide the budget by the cost per washer:
$12,000 ÷ $250 = 48 washers
g) If the person wants to spend the entire budget on dryers, how many dryers can he purchase?
To spend the entire budget on dryers, we divide the budget by the cost per dryer:
$12,000 ÷ $200 = 60 dryers
h) If the person wants to spend the entire budget and purchase an equal number of washers and dryers, how many can he purchase?
To spend the entire budget and purchase an equal number of washers and dryers, we need to divide the budget by the sum of the cost per washer and cost per dryer, then find the common factor:
($12,000 ÷ ($250 + $200)) ÷ 2 = 18
The common factor of 18 is 2 x 3 = 6. So, the person can purchase 6 washers and 6 dryers within the budget.
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the diagonals of a rhombus are 8 and 10cm respectively. find the area of the rhombus
[tex]\sf Let \ d_1 \ and \ d_2 \ be \ the \ lengths \ of \ the \ sides \ of \ diagonals.[/tex]
[tex]\sf Given \ that \ d_1=8 \ cm[/tex]
[tex]\sf And \ d_2=10 \ cm[/tex]
[tex]\therefore\sf Area \ of \ rhombus=\dfrac{1}{2} (d_1)(d_2)=\dfrac{1}{2}(8)(10)=40 \ cm^2[/tex]
[tex]\rightarrow\boxed{\sf Area \ of \ rhombus=40 \ cm^2}[/tex]