The relative frequency of people who strongly agree with the statement "I feel respected by those I work for" is 0.312, or 31.2%.
This means that out of the 500 employees surveyed, 156 strongly agreed with the statement. To find the relative frequency, you simply divide the number of people who strongly agree by the total number of people surveyed (156/500).
This result suggests that the majority of employees feel respected by their employers, which is a positive sign for the workplace culture.
However, it's important to note that there are still a significant number of employees who either disagree or feel neutral about this statement, indicating that there may be room for improvement in terms of fostering a more respectful and supportive work environment.
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Mrs smith the soup kitchens chef estimates that they will serve 40 000 people soup. If they give each person 1 cup of soup over 2 weeks , if the month has 5 weeks. Is Mrs smith estimations correct
If Mrs. Smith's estimation only accounted for a 4-week month, it would be incorrect. However, if she factored in the additional 10 days, then her estimation of serving 40,000 people soup with 1 cup per person over 2 weeks is correct.
Soup kitchens are community-based organizations that provide meals, primarily soup, to people in need. These facilities are often run by volunteers and rely heavily on donations from local businesses and individuals to provide food for those who cannot afford it.
Mrs. Smith, the soup kitchen chef, estimates that they will serve 40,000 people soup, giving each person 1 cup of soup over 2 weeks, and with the month having 5 weeks.
To determine if Mrs. Smith's estimation is correct, we need to do some calculations. One cup of soup per person over two weeks means that each person will receive 2 cups of soup in total. Therefore, to serve 40,000 people with 2 cups of soup each, the soup kitchen would need to provide a total of 80,000 cups of soup.
With the month having 5 weeks, it means that there are 10 days extra in the month compared to a standard 4-week month. Therefore, the soup kitchen will need to serve an additional 1/5 of the total amount of soup to cover the additional 10 days.
So, to determine if Mrs. Smith's estimation is correct, we can multiply the total cups of soup needed (80,000) by 1/5, which equals 16,000 cups. We then add this to the original total, which gives us 96,000 cups of soup needed for the month.
In conclusion, if Mrs. Smith's estimation only accounted for a 4-week month, it would be incorrect. However, if she factored in the additional 10 days, then her estimation of serving 40,000 people soup with 1 cup per person over 2 weeks is correct.
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7 Plot (6,2) on the grid.
My teacher never thought us this and this was on my homework I give you 59 points if you give me a answer
Answer:Go to the 6 number on the bottom line.Then go up until you reach 2
Step-by-step explanation:
|
|
|
|
| .
|______
Should look like that-ish
Answer:
Step-by-step explanation:
Put the point to the right 6 times and up two times
URGENTEEEE!! REPONDER RAPIDO POR FAVOR!!!
Which of the following could be the graph of f(x)=(2/5)^x?
Answer:
The third graph from the top could be the graph of f(x) = (2/5)^x. As x approaches infinity, f(x) approaches 0.
For security purposes I regularly change my six-digit passcode for internet banking. I always
choose a code that is made up of three different two-digit square numbers (i. E. Square numbers
between 10 and 99), with the sixth digit the same as the first digit.
-Which two digits never appear in any of my passcodes?
-How many different passcodes can I use?
The sum of the six digits of my current passcode is also a square number.
-What is my current passcode?
The two digit Combinations that never appear in any of the passcodes are 5 and 6.
There are 49 different passcodes that can be used. The sum of the six digits of the current passcode is 81, which is a square number. Therefore, the current passcode is made up of three different two-digit square numbers with the sum of their digits equal to 9.
The possible combinations are
(16, 25, 40),
(16, 49, 16),
(25, 36, 20),
(36, 49, 4),
(49, 64, 9),
(64, 81, 16), and
(81, 16, 64).
The only combination that has the same first and sixth digits is (16, 25, 40), so the current passcode is 162540.
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A florist sells flower bouquets. the table shows the prices for various amounts and kinds of bouquets.
total price
bouquets
2
flower
daisies
tulips
roses
$23.90
$60.80
2
1
2
a
the expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is
$18.45 more than a bouquet of tulips.
b
the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is
$18.45 more than a bouquet of daisies.
с
the expression 23.90 - 60.80 represents that a bouquet of tulips is $36.90 more than a
bouquet of daisies.
d
the expression 60.80 - 23.90 represents that a bouquet of daises is $36.90 more than a
bouquet of tulips.
The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.
The given table shows the prices for various amounts and kinds of bouquets sold by a florist. The prices depend on the number and type of flowers in the bouquet. The table shows prices for bouquets of 2 flowers with daisies, tulips, and roses.
The expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is $18.45 more expensive than a bouquet of tulips. This is because the cost of a 2-flower bouquet of daisies is $23.90 and the cost of a 2-flower bouquet of tulips is $60.80, so the difference between them is $36.90.
However, we subtract 2 from each price to get the price of the actual flowers in the bouquet, which are the same for both daisies and tulips. Therefore, we get the difference of $18.45.
Similarly, the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is $18.45 more expensive than a bouquet of daisies. Here, we subtract the price of a 2-flower bouquet of daisies plus the cost of 2 flowers from the price of a 2-flower bouquet of tulips.
Again, the actual cost of flowers in both bouquets is the same, so we get the difference of $18.45.
The expressions 23.90 - 60.80 and 60.80 - 23.90 represent the price difference between bouquets of daisies and tulips, respectively. The former expression gives a negative result of $36.90, which means that a bouquet of tulips is $36.90 more expensive than a bouquet of daisies.
The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.
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The student council at Newberg High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs, meanwhile, are $7 per shirt, plus a setup fee of $65. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
Let's assume that the number of shirts that must be sold to cover the costs is x.
The revenue from selling x shirts is 12x dollars, and the total cost is the sum of the setup fee and the cost per shirt multiplied by the number of shirts, which is 65 + 7x dollars.
To break even, the revenue must be equal to the cost:
12x = 65 + 7x
Subtracting 7x from both sides:
5x = 65
Dividing both sides by 5:
x = 13
Therefore, the student council must sell 13 shirts to break even.
To find the total costs, we can substitute x = 13 into the expression for the total cost:
65 + 7x = 65 + 7(13) = 156
So the total costs will be $156.
Answer:
The student council's costs will be $146 and they need to sell 13 shirts to cover their costs.
Step-by-step explanation:
Let's call the number of shirts sold "x".
The revenue from selling x shirts at $12 each is:
Revenue = 12xThe total cost of making x shirts is:
Total Cost = 7x + 65In order to break even (i.e. cover their costs), the revenue must equal the total cost:
[tex]\sf:\implies 12x = 7x + 65[/tex]
Solving for x:
[tex]\sf:\implies 5x = 65[/tex]
[tex]\sf:\implies \boxed{\bold{\:\:x = 13\:\:}}\:\:\:\green{\checkmark} [/tex]
Therefore, the student council must sell 13 shirts to break even.
To find the total costs, we can substitute x = 13 into the total cost equation:
[tex]\sf:\implies Total\: Cost = 7(13) + 65 = \boxed{\bold{\:\:\$146\:\:}}\:\:\:\green{\checkmark} [/tex]
So the student council's costs will be $146 and they need to sell 13 shirts to cover their costs.
Savannah and Josiah read the following problem in their math class: Five rectangular pizzas were shared equally by 4 families. How much pizza did each family receive? Savannah and Josiah solve the problem differently. Savannah gives each family 1 whole pizza and then divides the remaining pizza among the 4 families. Josiah divides all of the pizzas into fourths and then shares the fourths equally among the 4 families. Use Scratchpad to illustrate both studentsâ solutions
This will show that each family gets 5/16 of a pizza.
Sure, I'd be happy to help you with your question!
So, Savannah and Josiah read the following problem in their math class: Five rectangular pizzas were shared equally by 4 families. How much pizza did each family receive?
Savannah and Josiah solve the problem differently. Savannah gives each family 1 whole pizza and then divides the remaining pizza among the 4 families. Josiah divides all of the pizzas into fourths and then shares the fourths equally among the 4 families.
To illustrate both students' solutions, we can use Scratchpad. For Savannah's solution, we can draw 5 rectangular pizzas and then divide them into 4 equal parts each. Then, we can shade in 1 whole pizza and divide the remaining pizza equally among the 4 families. This will show that each family gets 1 whole pizza and a quarter of a pizza.
For Josiah's solution, we can draw 5 rectangular pizzas and then divide each pizza into fourths. Then, we can divide the fourths equally among the 4 families.
This will show that each family gets 5/16 of a pizza.
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For evrey 500g of reactants, 3. 1 g of catalyst were required. How much catalyst was required for 900g of reactants
5.58g of catalyst is required for 900g of reactants.
How much catalyst for 900g reactants?If 500g of reactants require 3.1g of catalyst, then for 900g of reactants, we can use the following proportion:
500g reactants / 3.1g catalyst = 900g reactants / x
Where x is the amount of catalyst required for 900g of reactants.
To solve for x, we can cross-multiply:
500g reactants * x = 3.1g catalyst * 900g reactants
Then, we can divide both sides by 500g reactants to isolate x:
x = (3.1g catalyst * 900g reactants) / 500g reactants
Simplifying this expression gives:
x = 5.58g catalyst
Therefore, 5.58g of catalyst is required for 900g of reactants.
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You spin a spinner that has 12 equal-sized sections numbered 1 to 12. Find the probability of p(even or less than 8)
The probability of getting an even number or a number less than 8 is:
P = 0.83
How to find the probability for the given event?The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.
The numbers that are even or less than 8 are:
{1, 2, 3, 4, 5, 6, 7, 8, 10, 12}
So 10 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:
P = 10/12 = 0.83
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Write 7.725666118 as a percentage
please show the method too.
The number written as a percentage is:
772.5666118%
How to write any number as a percentage?To do this, just multiply the number by 100%.
For example, for any number A, the percentage form of A is:
p = A*100%
Here the number is 7.725666118, then the percentage form of this number will be:
N = 7.725666118*100% = 772.5666118%
That is the number as a percentage.
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i need to factor 1/2y-5 1/2 and i can't seem to get it
The factored form of the equation is 1/2(y - √5)
To factor this expression, we need to look for any common factors that can be pulled out of both terms. We can see that both terms contain a factor of 1/2, so we can factor that out:
1/2(y - 5 1/2)
Now we need to see if there are any further factors that we can find. The term inside the parentheses, y - 5 1/2, cannot be factored any further using real numbers. However, we can write the expression as y - √5, which shows that it involves the square root of 5.
So the final factored form of the expression is:
1/2(y - √5)
This means that if we multiply 1/2 by (y - √5), we get back the original expression 1/2y - 5 1/2.
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2 A model of (CH₂O)4 was created using colored beads. Carbon atoms were
represented by black beads, hydrogen atoms by red beads, and oxygen atoms
by blue beads. Which of the following combinations of beads shows an accurate
model of (CH₂O)4?
A 4 black, 8 red, and 4 blue
B 1 black, 2 red, and 1 blue
C 4 black, 6 red, and 4 blue
D
1 black, 8 red, and blue
The correct number of beads is; 4 black, 8 red, and 4 blue. Option A
What is a molecular model?A molecular model is a depiction of molecules or chemical compounds made physically, visually, or mathematically in order to comprehend their behavior and characteristics. These models can range from real models made of plastic or metal to computer-generated graphics or mathematical formulae, and they can be straightforward or sophisticated.
There are four carbon atoms, eight hydrogen atoms and four oxygen atoms.
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I’ve been having a hard time at edulastic and my parents are confused about this so please help!
The area of the composite figure is equal to 104 square feet.
How to determine the area of a composite figure
In this question we have a composite figure formed by a part of a rectangle and an entire triangle. The area formulas for a rectangle and a triangle are introduced below:
Rectangle
A = b · h
Triangle
A = 0.5 · b · h
Where:
b - Base, in feet.h - Height, in feet.Now we proceed to determine the area of the mural:
A = (10 ft) · (8 ft) - 0.5 · (10 ft) · (5 ft) + 0.5 · (14 ft) · (7 ft)
A = 104 ft²
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A rectangular mural measures 1 meter by 3 meters. Rebekah creates a new mural that is 0. 5 meters longer. What is the perimeter of Rebekah's new mural?
The perimeter of Rebakh's new mural is 9 meters.
Rebakh has created a new mural which is a rectangle. It is a two-dimensional shape with length and breadth. The original rectangular mural was having dimensions of 1 meter by 3 meters, but the mural Rebekah created was 0.5 meters longer than the original one.
So, now the new mural created by Rebakh has a width of (3 + 0.5 ) = 3.5 meters and a length of 1 meter. The perimeter is defined as the total length of the four sides of the rectangle. To find the perimeter, we will add up the length and width of the rectangle and multiply it by 2. The perimeter of the new mural, in this case, is 1 + 1 + 3.5 + 3.5 = 9 meters.
Therefore, the perimeter of Rebakh's new mural is 9 meters.
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Suppose you have a bag of m&ms 4 green 6 yellow 7 purple 3 red. what is the probability you select a brown m&m
The probability of selecting a brown M&M from this bag is 0.
Since there are no brown M&Ms mentioned in your bag, the probability of selecting a brown M&M is 0. In probability terms, we can express this as:
Probability of selecting a brown M&M = Number of brown M&Ms / Total number of M&Ms
There are 0 brown M&Ms, and there are a total of 4 green + 6 yellow + 7 purple + 3 red = 20 M&Ms in the bag. So the probability is:
Probability = 0 / 20 = 0
Thus, the probability of selecting a brown M&M from this bag is 0, meaning it's impossible with the given information.
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The height of each cone and the cylinder is 5 (cm) centimeters. The radius of the base of each cone and the cylinder is 4 (cm). What is the volume of the composite figure?
Therefore, the volume of the composite figure is approximately 419.05 cubic cm.
What is volume?Volume is the amount of space occupied by a three-dimensional object or shape. It is measured in cubic units such as cubic centimeters, cubic inches, or cubic meters. The volume of an object can be calculated by multiplying the area of its base by its height, or by using specific formulas depending on the shape of the object. The volume of an object is an important parameter in many areas of science and engineering, such as physics, chemistry, fluid mechanics, and material science, as it allows us to determine how much space an object will occupy or how much material is needed to fill a container or build a structure.
Here,
The composite figure consists of a cylinder and two cones, so we need to find the volume of each of these shapes and add them together.
Volume of cylinder = πr²h
= π(4²)(5)
= 80π cubic cm
Volume of one cone = (1/3)πr²h
= (1/3)π(4²)(5)
= (1/3)(80π)
= 26.67π cubic cm
Volume of both cones = 2(26.67π)
= 53.34π cubic cm
Total volume of composite figure = Volume of cylinder + Volume of both cones
= 80π + 53.34π
= 133.34π
= 419.05 cubic cm (rounded to two decimal places)
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when rounding to the nearest hundred what is the greatest whole number that rounds to 500
The greatest whole number that rounds to 500 when rounding to the nearest hundred is 550.
When rounding a number to the nearest hundred, you need to look at the digit in the tens place. If that digit is 5 or greater, you round up the hundreds digit; if it is less than 5, you round down the hundreds digit.
For example, let's say we have the number 2,548. The digit in the tens place is 4, which is less than 5, so we round down the hundreds digit (2) to get 2,500.
Now, if we are looking for the greatest whole number that rounds to 500 when rounded to the nearest hundred, we need to find the largest number that has 5 in the tens place and 0 in the ones place. That number is 550. When we round 550 to the nearest hundred, we get 500.
Therefore, the greatest whole number that rounds to 500 when rounded to the nearest hundred is 550.
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A laundry detergent box measures 12 inches by 8 inches by 3 inches. What is the volume of two boxes of detergent?
Formula:
Plug in values
Solution:
Hi! I'd be happy to help you with your question. To find the volume of two laundry detergent boxes, each measuring 12 inches by 8 inches by 3 inches,
you can follow these steps:
Formula: Volume = Length × Width × Height
Step 1: Plug in the values for one box:
Volume = 12 inches × 8 inches × 3 inches
Step 2: Calculate the volume of one box:
Volume = 288 cubic inches
Step 3: Multiply the volume of one box by 2 to find the volume of two boxes:
Total volume = 288 cubic inches × 2
Solution: The total volume of two laundry detergent boxes is 576 cubic inches.
Your answer: The volume of two boxes of detergent is 576 cubic inches.
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Given m||n, find the value of x
The value of x is 32.
A set of angles that are between the two line parallels but on each side of the transverse are referred to as alternate external or exterior angles. The measure of the alternate external or exterior angles is equal.
According to the alternate outside angle theorem, alternate exterior angles are regarded as congruent angles or degrees of equal magnitude when two parallel lines intersected by a transversal.
Given that the lines m and n are parallel, and the angles are [tex](3x-2)^{0}[/tex] and [tex](2x+30)^{0}[/tex].
The given angles are alternate external or exterior angles. So, they must be equal.
[tex](3x-2)^{0} = (2x+30)^{0}[/tex]
Rearrange the above equation to find the value of x as follows,
[tex]3x-2x=30+2[/tex]
[tex]x=32[/tex]
Hence, the value of x is 32.
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Is 2352 a perfect square? If not, find the smallest number by
which 2352 must be multiplied so that the product is a perfect
square. Find the square root of new number.
No, 2352 is not a perfect square.
To find the smallest number by which 2352 must be multiplied so that the product is a perfect square, we need to factorize 2352 into its prime factors.
2352 = 2^4 x 3 x 7^2
To make it a perfect square, we need to multiply it by 2^2 and 7, which gives us:
2352 x 2^2 x 7 = 9408
Now, we can take the square root of 9408:
√9408 = √(2^8 x 3 x 7) = 2^4 x √(3 x 7) = 16√21
Therefore, the smallest number by which 2352 must be multiplied so that the product is a perfect square is 2^2 x 7, which gives us the square root of 9408 as 16√21.
Answer:
The smallest number by which 2352 must be multiplied so that the product is a perfect square = 3
The square root of the new number = 84
Step-by-step explanation:
√2352 ≈ 48.5 so not a perfect square
Prime factorization of 2352 yields
2352 = 2 x 2 x 2 x 2 x 7 x 7 x 3
In exponential form this is
2⁴ x 7² x 3¹
So
[tex]\sqrt{2352} = \sqrt{2^4 \cdot 7^2 \cdot 3}\\\\= \sqrt{2^4} \cdot \sqrt{7^2} \cdot \sqrt{3}\\\\= 2^2 \cdot 7 \cdot \sqrt{3}\\\\= 28 \sqrt{3}[/tex]
To get rid of the radical in the square root and get a whole number, all you have to do is multiply [tex]\sqrt{2352}[/tex] by √3
[tex]28 \sqrt{3} \cdot \sqrt{3} = 28\cdot 3 = 84\\\\84^2 = 7056 = 2352 \cdot 3\\[/tex]
This means that if you multiply 2352 by 3 it will become a perfect square
Check:
[tex]2352 \cdot 3 = 7056\\\\\sqrt{7056} = 84[/tex]
A. The mean selling price (in $ thousands) of the homes was computed earlier to be $357. 0, with a standard deviation of $160. 7. Use the normal distribution to estimate the percentage of homes selling for more than $500. 0. Compare this to the actual results. Is price normally distributed? Try another test. If price is normally distributed, how many homes should have a price greater than the mean? Compare this to the actual number of homes. Construct a frequency distribution of price. What do you observe?
b. The mean days on the market is 30 with a standard deviation of 10 days. Use the normal distribution to estimate the number of homes on the market more than 24 days. Compare this to the actual results. Try another test. If days on the market is normally distributed, how many homes should be on the market more than the mean number of days? Compare this to the actual number of homes. Does the normal distribution yield a good approximation of the actual results? Create a frequency distribution of days on the market. What do you observe?
a) The mean is the midpoint of the distribution, the percentage of homes with a price greater than the mean is 19.7%.
b) The percentage of homes on the market for more than the mean number of days is 72.1%.
a) Firstly, the mean selling price of homes is $357.0 thousand, with a standard deviation of $160.7 thousand. To estimate the percentage of homes selling for more than $500.0 thousand, we can use the normal distribution. This assumes that the distribution of home prices is approximately normal. Using the standard normal distribution table, we can find the z-score for a price of $500.0 thousand.
z = (500.0 - 357.0) / 160.7 = 0.88
Using the z-score, we find that the percentage of homes selling for more than $500.0 thousand is approximately 19.7%.
b) Moving on to the days a home spends on the market, the mean is 30 days and the standard deviation is 10 days. To estimate the number of homes on the market for more than 24 days, we can again use the normal distribution. Assuming that the distribution of days on the market is approximately normal, we can find the z-score for 24 days as:
z = (24 - 30) / 10 = -0.6
Using the z-score, we find that the percentage of homes on the market for more than 24 days is approximately 72.1%.
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An artist buys 2 liters of paint for a project. When he is done with the project, he has 350 milliliters of the paint left over. The paint costs 2¢ per milliliter. How many dollars’ worth of paint does the artist use for the project?
The artist used a total of $0.33 worth of paint for the project.
The artist purchased 2 liters of paint, which is equivalent to 2,000 milliliters of paint. This amount of paint was used to complete a project, and after the project was finished, there were 350 milliliters of paint left over.
To determine how much paint was used for the project, we subtract the amount of leftover paint from the total amount of paint purchased, which gives us 2,000 - 350 = 1,650 milliliters of paint used for the project.
The cost of the paint is 2 cents per milliliter, which is equivalent to $0.02/100 milliliters or $0.0002 per milliliter. To determine the cost of the paint used for the project, we multiply the amount of paint used by the cost per milliliter.
Therefore, the cost of 1,650 milliliters of paint used for the project can be calculated by multiplying 1,650 milliliters by $0.0002 per milliliter, which gives us $0.33.
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If an inflatable ball with a volume of 96pi loses air until its radius is half of its original size, what is the new volume?
The new volume of the inflatable ball after the radius becomes half of the original one is 16π.
The original volume of the ball is given as 96π
The radius then becomes half of its original size which means if the radius of the ball is 'r' then the new radius becomes 'r/2'.
The formula for the volume of the ball is equal to, where 'r' is the radius of the ball. (4/3)π X r³
With this the original volume of the ball is
(4/3)π X r³
and the new volume of the ball after it's halved is
V₂ = (4/3)π X (r/2)³
After simplification
V₂ = (4/3)π X (r³/8)
The new volume of the ball is:
V₂ = (1/6) X πr³
So the new volume is (1/6) of the original volume. We can calculate this as
V₂ = (1/6) X 96π
= 16π
Therefore, the new volume of the inflatable ball is 16π.
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Can you help me do 1+1
Answer:
The answer to 1+1 is 2.
Answer:
2
Step-by-step explanation:
Jayce has a cylindrical dowel that she cuts in parallel to the base , What is the circumference of the horizontal cross section of the dowel rounded to the nearest whole number
If the dowel has a radius of 3.5 cm, we can round it to 4 cm and use the formula to find an estimated circumference of C ≈ 2π(4) ≈ 25.1 cm.
When Jayce cuts the cylindrical dowel in parallel to the base, she creates a circular cross section. The circumference of a circle is the distance around its perimeter, and it can be calculated using the formula C = 2πr, where C is the circumference, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.
Since the dowel is cylindrical, its cross section will also be a circle. Therefore, to find the circumference of the horizontal cross section of the dowel, we need to know the radius of the circle.
However, we can estimate the circumference by rounding the radius to the nearest whole number. For example, if the dowel has a radius of 3.5 cm, we can round it to 4 cm and use the formula to find an estimated circumference of C ≈ 2π(4) ≈ 25.1 cm. Rounded to the nearest whole number, the circumference would be 25 cm.
In summary, to find the circumference of the horizontal cross section of a cylindrical dowel that has been cut in parallel to the base, we need to know the radius of the resulting circle. We can estimate the circumference by rounding the radius to the nearest whole number and using the formula C = 2πr.
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3. Use the definition of the Riemann Sum to evaluate S12(x3 – 2x)dx. + - 4. Evaluate: S2x2+x=2 5. Given the velocity in meters/second for v(t) = 8 – 2t, 1 st 56 a.) find the displacement of the particle over the given time interval; b.) find the distance traveled by the particle over the given time interval.
Evaluation of S12(x3 – 2x)dx is- 92.875
We can use the definition of the Riemann Sum to evaluate S12(x3 – 2x)dx as follows:
First, we need to choose the width of our intervals.
Let's choose Δx = 1/2, which means we will have 24 subintervals.
Now, we can use the formula for the Riemann Sum to calculate the sum of the areas of the rectangles.
S12(x3 – 2x)dx ≈ ∑[f(xi)Δx] from i=1 to i=24
where xi is the right endpoint of the ith subinterval,
f(xi) = x[tex]i^3[/tex] – 2xi is the height of the rectangle, and Δx = 1/2 is the width of the rectangle.
Evaluating this sum using the given formula, we get:
S12(x3 – 2x)dx ≈ [f(1/2) + f(1) + f(3/2) + ... + f(11)](1/2)
≈ [[tex](1/2)^3[/tex] – 2(1/2) + (1)^3 – 2(1) + (3/2[tex])^3[/tex] – 2(3/2) + ... + (11[tex])^3[/tex] – 2(11)](1/2)
≈ [- 2361/16](1/2)
≈ - 92.875
4) we can simply evaluate the given integral:
S2x2+x=2 = ∫(2[tex]x^2[/tex] + x)dx from 0 to 2
= [[tex]2/3 x^3 + 1/2 x^2[/tex]] from 0 to 2
= [[tex]2/3 (2)^3 + 1/2 (2)^2[/tex]] - [[tex]2/3 (0)^3 + 1/2 (0)^2[/tex]]
= 16/3
5), we can use the following formulas
to find the displacement and distance traveled by the particle over the given time interval:
Displacement = ∫v(t)dt from 1 to 5
Distance traveled = ∫|v(t)|dt from 1 to 5
where v(t) is the velocity function.
a) To find the displacement, we evaluate the integral:
∫v(t)dt = ∫(8 – 2t)dt from 1 to 5
= [8t – t^2] from 1 to 5
= [[tex]8(5) – (5)^2[/tex]] - [8(1) – [tex](1)^2[/tex]]
= 18 meters
b) To find the distance traveled, we evaluate the integral:
∫|v(t)|dt = ∫|8 – 2t|dt from 1 to 5
= ∫(8 – 2t)dt from 1 to 4 + ∫(2t – 8)dt from 4 to 5
= [8t – [tex]t^2[/tex]] from 1 to 4 + [-t^2 + 8t -16] from 4 to 5
= [8(4) – [tex](4)^2[/tex]] - [8(1) – [tex](1)^2[/tex]] + [[tex]-(5)^2[/tex] + 8(5) -16 -(-[tex](4)^2[/tex] + 8(4) -16)]
= 26 meters
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Write the equation for the circle graphed below. Center = (-5, -5) Radius= 4
Answer:
(x + 5)^2 + (y + 5)^2 = 16.
Step-by-step explanation:
(x - a)^2 + (y - b)^2 = r^2 where (a, b) is the centre and r =- the radius.
Here (a, b) = (-5, -5) and r = 4, so:
(x - (-5))^2 + (y - (-5))^2 = 4^2
(x + 5)^2 + (y + 5)^2 = 16
Which function is graphed to the right?
A. f(x) = ¹₂ +3 x-2
B. f(x)=¹+2
C. f(x) =3x+2
The rational function graphed in this problem is given as follows:
B. f(x) = 1/(x - 3) + 2.
How to obtain the rational function?From the graph, the asymptotes of the rational function are given as follows:
Vertical asymptote at x = 3 -> the function is not defined at x = 3.Horizontal asymptote at y = 2 -> as x goes to infinity, f(x) approaches y = 2.Considering that the function has a vertical asymptote at x = 3, we have that:
f(x) = 1/(x - 3).
Considering the horizontal asymptote at y = 2, we have that:
f(x) = 1/(x - 3) + 2.
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Use the following information to create a two way table that shows the type of music a person likes compared to their gender. 94 males were surveyed. 13 males liked jazz. 27 females liked rock. 90 people total liked rock. 66 females liked country. 200 people total were surveyed
Here is a two way table that shows the type of music a person likes compared to their gender:
| | Males | Females | Total |
|---------------|-------|---------|-------|
| Jazz | 13 | 0 | 13 |
| Rock | 54 | 27 | 81 |
| Country | 0 | 66 | 66 |
| Total | 67 | 93 | 200 |
In this table, we can see that out of the 94 males surveyed, 13 of them liked jazz. Out of the 106 females surveyed, 27 of them liked rock and 66 of them liked country. Overall, out of the 200 people surveyed, 81 of them liked rock, 13 of them liked jazz, and 66 of them liked country.
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Kristen is excited for her first overnight camping trip with her scout troop. the troop needs to take some parent chaperones with the on the trip. for a trip with s scouts, they need at least s/5 chaperones. there are 15 scouts going on the camping trip.
They may choose to bring 4 chaperones or even more depending on their preferences and logistical constraints.
How many chaperones are needed for the camping trip with 15 scouts?For the camping trip with 15 scouts, they will need at least 15/5 = 3 chaperones.
However, it's possible that they may want to have more than the minimum number of chaperones for additional supervision and safety. The number of chaperones they choose to bring may also depend on the ratio of chaperones to scouts that they want to maintain.
So, they may choose to bring 4 chaperones (1 chaperone for every 3.75 scouts), 5 chaperones (1 chaperone for every 3 scouts), or even more depending on their preferences and logistical constraints.
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