The difference between the volume and surface area of both balls is: 108101.69 cubic centimeters.
The formula for the volume of a sphere is V = (4/3)π[tex]r^3[/tex], where r is the radius of the sphere, and the formula for the surface area of a sphere is A = 4π[tex]r^2[/tex].
Let's start by finding the radius of each ball. The diameter of the first ball is 85 cm, so its radius is 85/2 = 42.5 cm. The diameter of the second ball is 65 cm, so its radius is 65/2 = 32.5 cm.
The volume of the first ball is:
V1 = (4/3)π[tex](42.5)^3[/tex] = 256905.53 cubic centimeters
The volume of the second ball is:
V2 = (4/3)π[tex](32.5)^3[/tex] = 139379.44 cubic centimeters
The difference in volume is:
V1 - V2 = 256905.53 - 139379.44 = 117526.09 cubic centimeters
To find the difference in surface area, we plug in the radius values:
A1 = 4π[tex](42.5)^2[/tex] = 22698.16 square centimeters
A2 = 4π[tex](32.5)^2[/tex] = 13273.76 square centimeters
The difference in surface area is:
A1 - A2 = 22698.16 - 13273.76 = 9424.40 square centimeters
Therefore, the difference between the volume and surface area of both balls is: 117526.09 cubic centimeters - 9424.40 square centimeters, rounded to the nearest hundredth, is 108101.69 cubic centimeters.
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why is 101 not in the sequence of 3n-2
101 is not in the sequence of 3n-2 because it cannot be obtained by multiplying a positive integer n by 3 and subtracting 2 from the product.
The sequence 3n-2 is a set of numbers obtained by taking a positive integer n, multiplying it by 3 and then subtracting 2 from the product. For example, if n = 1, then 3n-2 = 1. If n = 2, then 3n-2 = 4. If n = 3, then 3n-2 = 7, and so on.
Now, you may wonder why the number 101 is not in the sequence of 3n-2. To understand this, we need to determine whether there exists a positive integer n such that 3n-2 is equal to 101.
Let's start by assuming that such an n exists. Then we can write:
3n-2 = 101
Adding 2 to both sides, we get:
3n = 103
Dividing both sides by 3, we get:
n = 103/3
This means that n is not a whole number, which contradicts our assumption that n is a positive integer. Therefore, there cannot exist any positive integer n such that 3n-2 equals 101.
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个
Work out the volume of this prism.
Area =
20 cm²
9cm
The diagram is not drawn to scale.
cm³
The volume of the prism is 180 cm³.
How to work out the volume of a prism?A prism is a 3D (three-dimensional) solid which has faces that are identical at both ends. The other faces are flats. A prism is named after its base.
The volume of any prism can be calculated using the formula:
V = A[tex]_{B}[/tex] * h
where A[tex]_{B}[/tex] is area of base and h is height of prism
In this case, we have the following information about the prism:
A[tex]_{B}[/tex] = 20 cm²
h = 9cm
V = 20 * 9
V = 180 cm³
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Complete Question
Check attached image
Where should one start to learn maths if they're really bad at it
Consistent practice is key to improving your math skills over time.
How to learn math if you feel like you're really bad at it?If you feel like you're really bad at math, it's important to start with the basics. This might mean reviewing concepts like arithmetic, fractions, decimals, and percentages. You can find resources online or in books that can help you with this. Once you have a solid foundation, try to identify your strengths and weaknesses so you can focus your efforts on the areas where you need the most improvement. Find a learning style that works best for you, whether it's working independently, with a tutor, or in a study group. Finally, remember that consistent practice is key to improving your math skills over time. Don't give up, and don't be afraid to ask for help when you need it.
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3−(−1)+(−1)−33, minus, left parenthesis, minus, 1, right parenthesis, plus, left parenthesis, minus, 1, right parenthesis, minus, 3
The calculated value of the expression 3 - (-1) + (-1) - 3 using a calculator is 0
Finding the value of the expression 3 - (-1) + (-1) - 3From the question, we have the following parameters that can be used in our computation:
The expression 3 - (-1) + (-1) - 3
We can add the numbers using a calculator
So, we have the following representation
Value = 3 - (-1) + (-1) - 3
Using the above as a guide, we have the following:
Value = 0
This means that the value of the expression 3 - (-1) + (-1) - 3 using a calculator is 0
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Use the following bond listing for Pacific Bell to answer the following: A 5-column table with 1 row. Column 1 is labeled Bonds with entry PacBell 6 and StartFraction 5 Over 8 EndFraction 34. Column 2 is labeled current yield with entry 6. 55. Column 3 is labeled Volume with entry 5. Column 4 is labeled Close with entry 99 and one-fourth. Column 5 is labeled net change with entry + StartFraction 1 Over 8 EndFraction. How many bonds were traded during this session?
5 bonds were traded during this session.
Based on the provided bond listing for Pacific Bell, the number of bonds traded during this session is 5. Here's the breakdown of the information in the 5-column table:
- Column 1 (Bonds): PacBell 6 5/8 34
- Column 2 (Current Yield): 6.55
- Column 3 (Volume): 5
- Column 4 (Close): 99 1/4
- Column 5 (Net Change): +1/8
The "Volume" column indicates the number of bonds traded during the session. In this case, the volume entry is 5. Therefore, 5 bonds were traded during this session.
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Let ⋆ be the binary operation on z (set of integers) defined by
a ⋆ b = 2ab + 5
show that ⋆ is commutative. hint: show that a ⋆ b = b ⋆ a
solution:
show that ⋆ is associative. hint: show that (a ⋆ b) ⋆ c = a ⋆ (b ⋆ c)
solution:
a. let ⋆ be the binary operation on z (set of integers) defined by
a ⋆ b = a + b + ab
1. show that ⋆ is commutative. hint: show that a ⋆ b = b ⋆ a
solution:
2.show that ⋆ is associative. hint: show that (a ⋆ b) ⋆ c = a ⋆ (b ⋆ c)
solution:
Since the expression is the same, we can conclude that the binary operation ⋆ is associative.
To show that the binary operation ⋆ is commutative, we need to demonstrate that a ⋆ b is equal to b ⋆ a for any integers a and b.
Let's start by evaluating a ⋆ b:
a ⋆ b = 2ab + 5.
Now let's evaluate b ⋆ a:
b ⋆ a = 2ba + 5.
By comparing the expressions for a ⋆ b and b ⋆ a, we can see that they are indeed equal:
2ab + 5 = 2ba + 5.
Since the expression is the same, we can conclude that the binary operation ⋆ is commutative.
To show that the binary operation ⋆ is associative, we need to demonstrate that (a ⋆ b) ⋆ c is equal to a ⋆ (b ⋆ c) for any integers a, b, and c.
Let's evaluate (a ⋆ b) ⋆ c:
(a ⋆ b) ⋆ c = (2ab + 5) ⋆ c = 2(2ab + 5)c + 5 = 4abc + 10c + 5.
Now let's evaluate a ⋆ (b ⋆ c):
a ⋆ (b ⋆ c) = a ⋆ (2bc + 5) = 2a(2bc + 5) + 5 = 4abc + 10a + 5.
By comparing the expressions for (a ⋆ b) ⋆ c and a ⋆ (b ⋆ c), we can see that they are indeed equal:
4abc + 10c + 5 = 4abc + 10a + 5.
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Admission Charge for Movies The average admission charge for a movie is $5. 81. If the distribution of movie admission charges is approximately normal with a standard deviation of $0. 81, what is the probability that a randomly selected admission charge is less than $3. 50
The probability that a randomly selected admission charge is less than $3. 50 is 0.23% or 0.0023.
To find the probability that a randomly selected admission charge is less than $3.50, we will use the z-score formula and a standard normal table. The z-score formula is:
Z = (X - μ) / σ
Where X is the value we are interested in ($3.50), μ is the average admission charge ($5.81), and σ is the standard deviation ($0.81).
Z = (3.50 - 5.81) / 0.81 ≈ -2.84
Now, look up the z-score (-2.84) in a standard normal table, which gives us the probability of 0.0023. Therefore, the probability that a randomly selected admission charge is less than $3.50 is approximately 0.23% or 0.0023.
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A theater is selling tickets to a ''preview night'' of their new musical. The tickets cost $12 per adult and $7. 50 per child. Due to limit on seating, they can sell no more than 150 tickets. However, they would like to make at least $675 from ticket sales
A theater can make at least $675 from ticket sales by selling at least 100 adult tickets and up to 50 child tickets.
To solve this problem, we can use a system of equations. Let's define:
- x as the number of adult tickets sold
- y as the number of child tickets sold
We know that:
- x + y ≤ 150 (due to the limit on seating)
- 12x + 7.5y ≥ 675 (they want to make at least $675)
We can solve this system of equations using substitution or elimination. Let's use elimination:
- Multiply the second equation by 2 to get rid of the decimals: 24x + 15y ≥ 1350
- Multiply the first equation by 15: 15x + 15y ≤ 2250
- Subtract the second equation from the first: 9x ≥ 900
- Divide both sides by 9: x ≥ 100
So they need to sell at least 100 adult tickets to make at least $675. Let's see if that's possible:
- If they sell 100 adult tickets, that leaves 50 tickets for children
- 100 adult tickets * $12 = $1200
- 50 child tickets * $7.50 = $375
- Total ticket sales = $1575 (more than $675)
So they can make at least $675 from ticket sales by selling at least 100 adult tickets and up to 50 child tickets.
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Triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is drawn on the coordinate
grid below. what is the area. in square units, of triangle TUV
The area of the triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is 13.58
How did we arrive at the above?First using distance calculator we derived the length of TV and the length of VU.
Since TV = Height; and
VU = Base
and the triangle is a right triangle,
Then, area is given by 1/2 base x Height
Length of TV usign distance calculator is 6.40312
Lenght of VU using distance calculator is 4.24264
So area = 1/2 * 6.40312 * 4.24264
Area = 13.58
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Given that f(x) = (h(x))10 = h(-1) = 3 h'(-1) = 6 Calculate f'(-1).
The final value is f'(-1) = 16,777,2160.
We can use the chain rule and the power rule of differentiation to find f'(-1).
Recall that the chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) h'(x). Applying this rule to f(x) = (h(x))^10, we get:
f'(x) = 10(h(x))^9 h'(x)
Now, we can substitute x = -1 into the above equation, since we are asked to find f'(-1). Thus, we have:
f'(-1) = 10(h(-1))^9 h'(-1)
We are given that h(-1) = 3 and h'(-1) = 6, so we can substitute these values to get:
f'(-1) = 10(3)^9 (6)
Simplifying, we get:
f'(-1) = 16,777,2160
Therefore, f'(-1) = 16,777,2160
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As runners in a marathon go by, volunteers hand them small cone shaped cups of water. The cups have the dimensions shown. Abigail sloshes 2/3 of the water out of her cup before she gets a chance to drink any. What is the volume of water remaining in Abigail’s cup?
The volume of water remaining in Abigail’s cup can be found to be 25. 14 cm³ .
How to find the volume left ?First, find the volume of water in the cup when it is full. This would be the volume of the cup which is the formula of the volume of a cone :
Volume = ( 1 / 3 ) × π × r² × h
Volume = ( 1 / 3 ) × π × ( 3 cm )² × ( 8 cm )
Volume = 24π cm³
If Abigail too 2 / 3 to slosh on her face, the amount of water left would be :
= 24π cm³ - ( 1 - 2 / 3 )
= 24π cm³ - 1 / 3
= 8π cm³
= 25. 14 cm³
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According the April 12, 2017 Pew Research survey, 58% of Americans approve of U. S. Missile strikes in
Syria in response to reports of the use of chemical weapons by Bashar al-Assad's government (the
Syrian government). A sample of 50 Americans are surveyed. Let o be the sample proportion of
Americans who approve the U. S. Missile strikes.
1. What is the population proportion?
(decimal form)
2. What is the sample size?
3. Can the normal approximation be used with this distribution?
4. What is the mean of the sampling proportion?
Answer:
The population proportion is given as 58% or 0.58 in decimal form.
The sample size is given as 50 Americans.
Yes, the normal approximation can be used with this distribution because the sample size is sufficiently large (n=50) and the underlying population is assumed to be large enough to satisfy the independence requirement.
The mean of the sampling proportion (o) can be calculated using the formula:
mean = population proportion = 0.58
Therefore, the mean of the sampling proportion is 0.58 or 58%.
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Assume that a cell is a sphere with radius 10-3 or 0.001 centimeter, and that a cell’s density is 1.1 grams per cubic centimeter. koalas weigh 6 kilograms on average. how many cells are in the average koala? hippos weigh 1,400 kilograms on average. how many cells are in the average hippo? solution
There would be 1.302 x 10¹² cells in koala, and there are 3.04 x 10^17 cells in the average hippo.
To find the number of cells in the average koala, we first need to find the volume of the koala in cubic centimeters, since we know the density of the cell and can use that to find the mass of the koala in grams.
The average weight of a koala is 6 kilograms, which is equivalent to 6,000 grams. We can use the density of the cell to find the volume of the koala:
Density = Mass / Volume
1.1 g/cm³ = 6,000 g / Volume
Volume = 6,000 g / 1.1 g/cm³
Volume = 5,454.54 cm³
Next, we need to find the volume of one cell:
Volume of cell = 4/3 * π * (0.001 cm)³
Volume of cell = 4.188 x 10⁻⁹ cm³
Finally, we can divide the volume of the koala by the volume of one cell to find the number of cells in the average koala:
Number of cells = 5,454.54 cm³ / (4.188 x 10⁻⁹ cm³)
Number of cells = 1.302 x 10¹²
Therefore, there are approximately 1.302 x 10¹² cells in the average koala.
To find the number of cells in the average hippo, we can follow the same process. The average weight of a hippo is 1,400 kilograms, which is equivalent to 1,400,000 grams. Using the density of the cell, we can find the volume of the hippo:
Density = Mass / Volume
1.1 g/cm^3 = 1,400,000 g / Volume
Volume = 1,400,000 g / 1.1 g/cm³
Volume = 1,272,727.27 cm³
Dividing the volume of the hippo by the volume of one cell, we get:
Number of cells = 1,272,727.27 cm³ / (4.188 x 10⁻⁹ cm³)
Number of cells = 3.04 x 10¹⁷
Therefore, there are approximately 3.04 x 10¹⁷ cells in the average hippo.
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“The mode of a data set is one of the values in the data set.” This statement is ____________.
Karissa wants to use the data to determine which brand is most absorbent. Based on the data collected at the beginning of the contest, enter the approximate number of paper towels needed to clean each square foot of the spill. Enter the number of Brand A paper towels needed per square foot in the first box. Enter the number of Brand B paper towels needed per square foot in the second box. Enter the number of Brand C paper towels needed per square foot in the third box
Answer:
Step-by-step explanation:
Una presa se construye en un rio. El nivel del agua del estanque esta dado por n = 4,5t + 28, dónde t es el tiempo en años. Traza la gráfica y determina el nivel del agua que tenía la presa al ser construida. (ayuda por favor)
The initial water level is given as follows:
28 units.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The function for this problem is defined as follows:
n = 4.5t + 28.
The intercept is of b = 28, representing the initial amount of water.
The graph is given by the image presented at the end of the answer.
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How do i solve for surface area on a rectangular prism
To solve for the surface area of a rectangular prism, you'll need to find the area of each of its six faces and add them together.
A rectangular prism has three pairs of faces: two each for length (L), width (W), and height (H).
First, find the area of the two faces with dimensions L x W. The area is calculated by multiplying length by width: A₁ = L * W. Since there are two such faces, the total area for these is 2A₁ = 2(L * W).
Next, find the area of the two faces with dimensions L x H. The area is calculated by multiplying length by height: A₂ = L * H. The total area for these faces is 2A₂ = 2(L * H).
Finally, find the area of the two faces with dimensions W x H. The area is calculated by multiplying width by height: A₃ = W * H. The total area for these faces is 2A₃ = 2(W * H).
To find the total surface area of the rectangular prism, add the areas of all six faces together: Surface Area = 2A₁ + 2A₂ + 2A₃ = 2(L * W) + 2(L * H) + 2(W * H).
So, the formula for the surface area of a rectangular prism is Surface Area = 2(L * W + L * H + W * H).
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Last week Deion ran a total of 32 miles. This week, he increased his running distance by 6. 4 miles. By what percentage did he increase the distance he ran? Please help waaaaaa
Deion increased the distance he ran by 20%.
To discover the percentage increase within the distance Deion ran, we need to first calculate the amount of increase.
The increase in distance that Deion ran this week compared to final week is:
6.4 miles
To find the proportion increase, we need to divide the increase by means of the original value (the distance he ran last week),
Then multiply by using a hundred to express the result as a percent.
The original price (last week's distance) is:
32 miles
Therefore, the percentage increase within the distance he ran is:
(6.4 miles / 32 miles) x 100% = 20%
So, Deion increased the distance he ran by 20%.
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Jacinta compares the volume of two boxes. Both boxes have a width of 2. 5 inches, and a height of 10 inches. The larger box has a length of 8 inches. The smaller box has a length that is 75 % of the length of the larger box.
Volume of large box =
Volume of small box =
What is the difference in the volumes of the two boxes?
Which units should be used for each of these answers?
The volume of the larger box is 200 cubic inches, and the volume of the smaller box is 150 cubic inches.
To find the volume of each box, we use the formula for the volume of a rectangular prism, which is V = lwh, where l is the length, w is the width, and h is the height.
For the larger box, we have l = 8 inches, w = 2.5 inches, and h = 10 inches, so
Volume of large box = = 8 x 2.5 x 10 = 200 cubic inches.
For the smaller box, we have l = 0.75 x 8 = 6 inches, w = 2.5 inches, and h = 10 inches, so
Volume of small box= 6 x 2.5 x 10 = 150 cubic inches.
The difference in the volumes of the two boxes is
Volume of large box - Volume of small box = 200 - 150 = 50 cubic inches.
The units for the volumes are cubic inches, since we are dealing with three-dimensional space.
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Josie is trying to justify the area formula for a circle with circumference C and radius r. To start, she cut a circle into 8 congruent sectors. Then, she put the sectors together to make this figure. She noticed that the figure is approximately the shape of a parallelogram. Select all of the statements that could help Josie to justify the area formula for a circle.
The base of the parallelogram is approximately equal to the circumference of the circle.
How can Josie justify the area formula for a circle using the figure made from congruent sectors?The following statements could help Josie justify the area formula for a circle:
The figure formed by putting the congruent sectors together approximates the shape of a parallelogram The opposite sides of a parallelogram are parallel.The base of the parallelogram corresponds to the circumference of the circle, denoted as C.The height of the parallelogram corresponds to the radius of the circle, denoted as r.The area of a parallelogram can be calculated by multiplying the base by the height.By considering that the base of the parallelogram is the circumference (C) and the height is the radius (r), the area of the parallelogram represents the area of the circle.Therefore, the area of the circle can be calculated using the formula A = C × r, or in terms of the radius, A = πr².
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La suma de dos números es 15 y la suma de sus cuadrados es 113. ¿Cuáles son los números?
La suma de dos números es 15 y la suma de sus cuadrados es 113. Por lo tanto, los dos números son 7 y 8.
Para resolver este problema, podemos utilizar el método de sustitución. Si llamamos a los dos números "x" e "y", podemos plantear dos ecuaciones con la información que nos dan:
x + y = 15 (ecuación 1)
x² + y² = 113 (ecuación 2)
De la primera ecuación, podemos despejar a "y" para obtener:
y = 15 - x
Ahora, podemos sustituir este valor de "y" en la segunda ecuación:
x² + (15 - x)² = 113
Expandiendo y simplificando:
x² + 225 - 30x + x² = 113
2x^2 - 30x + 112 = 0
Esta es una ecuación cuadrática que podemos resolver utilizando la fórmula general:
x = (-b ± sqrt(b² - 4ac)) / 2a
Donde:
a = 2
b = -30
c = 112
Sustituyendo:
x = (-(-30) ± sqrt((-30)² - 4(2)(112))) / 2(2)
x = (30 ± sqrt(900 - 896)) / 4
x = (30 ± 2) / 4
Esto nos da dos posibles valores para "x":
x₁ = 8
x₂ = 7
Para encontrar los valores correspondientes de "y", podemos utilizar la ecuación que obtuvimos antes:
y = 15 - x
Así que:
y₁ = 15 - 8 = 7
y₂ = 15 - 7 = 8
Por lo tanto, los dos números son 7 y 8.
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Gray made a $3,500 tax-deductible contribution to his individual retirement account (IRA). Assuming he is in a 28 percent tax bracket, how much will this contribution save him on his taxes?
Gray's $3,500 tax-deductible contribution to his IRA will save him $980 on his taxes.
When Gray contributes $3,500 to his individual retirement account (IRA), it is considered a tax-deductible contribution. This means that the amount contributed is deducted from his taxable income, reducing the amount of taxes he owes.
Since Gray is in the 28 percent tax bracket, this means that for every dollar of taxable income, he pays 28 cents in taxes. To calculate the tax savings from his $3,500 IRA contribution, we need to multiply the contribution amount by his tax rate:
$3,500 (contribution) x 0.28 (tax rate) = $980 (tax savings)
In this case, Gray's $3,500 tax-deductible contribution to his IRA will save him $980 on his taxes. By contributing to his IRA, Gray not only invests in his future retirement but also takes advantage of the tax benefits associated with these accounts. In the end, he reduces his taxable income and, consequently, the amount of taxes he needs to pay.
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During their team meeting, both managers shared their findings. Complete the statement describing their combined results.
Select the correct answer from each drop-down menu.
The initial number of video views was (more than, fewer than, the same as,)the initial number of site visits, and the number of video views grew by (a smaller factor, the same factor, a larger factor) the number of site visits.
The difference between the total number of site visits and the video views after 5 weeks is(15,625, 20,825, 36,450, 52,075)
The initial number of video views was (fewer than) the initial number of site visits, and the number of video views grew by (a larger factor) the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is (20,825).
Video views refer to the number of times a video has been watched or viewed by viewers.
A site visit refers to a visit or session by a user to a website. It occurs when a user accesses and interacts with webpages or content on a particular website.
The initial number of video views was (fewer than) the initial number of site visits, and the number of video views grew by (a larger factor) the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is (20,825).
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(PLEASE HELP + POINTS)
Select the correct graph.
Smith's Produce sells packages of pre-cut vegetables. The company has a tolerance level of less than or equal to y grams for a 250-gram
package. Which graph could be used to determine the variance levels that would result in a package of vegetables being rejected because of
its weight, X?
(Picture of graphs)
The answer of the given question based on the graph could be used to determine the variance levels that would result in a package of vegetables is histogram.
To determine the variance levels that would result in a package of vegetables being rejected because of its weight, X, consider the following:
1. The company has a tolerance level of less than or equal to y grams for a 250-gram package. This means that the graph must represent a relationship between the weight of the package (X) and the tolerance level (y).
2. Since the package is rejected if it weighs more than the allowed tolerance, the graph should show that as the weight (X) increases, the acceptance range decreases (y decreases).
3. The graph should ideally have a boundary line that represents the maximum tolerance level (y). Any points above this line would represent rejected packages.
Based on these criteria, you should select the graph that best represents this relationship between the weight of the package (X) and the tolerance level (y), where packages with a weight exceeding the tolerance level are rejected.
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Find the permineter of the square. leave answers in simplified radical form and label with correct units.
To find the perimeter of a square, you simply add up the lengths of all four sides. If we let "s" be the length of one side of the square, then the perimeter P can be found using the formula:
P = 4s
Since all four sides of a square are equal, we can simplify this expression to:
P = s + s + s + s = 4s
Therefore, the perimeter of the square is equal to 4 times the length of one side. If the length of one side is given in simplified radical form (such as √2 or √3), then the perimeter should also be expressed in simplified radical form.
For example, if the length of one side is 2√2 units, then the perimeter would be:
P = 4s = 4(2√2) = 8√2 units
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A standard number cube is rolled to play a certain board game. What is the Sample Space? Use proper notation as necessary and no extra spaces.
Answer: 1.3
Step-by-step explanation:
i need to know the full quadratic equation answer
Required Answer :
x(2x + 4)= x²+ 4 (9 - 3x)
2x² + 4x = x² + 36 - 12x
2x² - x² + 4x + 12x - 36=0
x² + 16x - 36=0
Quadratic equation in Standard form,
a = 1, b = 16c = -36Using Quadratic formula,
[tex] \implies \sf x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ \implies \sf x = \dfrac{ - 16 \pm \sqrt{ {16}^{2} - 4(1)( - 36)} }{2 \times 1} \\ \\ \implies \sf x = \dfrac{ - 16\pm \sqrt{256 - ( - 144)} }{2} \\ \\ \implies \sf x = \frac{ - 16 \pm \sqrt{256 + 144} }{2} \\ \\ \implies \sf x = \frac{ - 16 \pm \sqrt{400} }{2} \\ \\ \implies \sf x = \dfrac{ - 16 \pm20}{2} \\ \\ \implies \sf x = \dfrac{ - 16 \pm 20}{2} \\ \\ \implies \sf x = \dfrac{4}{2} \: or \: \dfrac{ - 36}{2} \\ \\ \implies \sf x = 2 \: or \: - 18[/tex]
Read and imagine what is happening in this problem. Hannah mixed 6. 83 lb of pretzels with 3. 57 lb of popcorn. After filling up 6 bags that were the same size with the mixture, she had 0. 35 lb left.
Hannah mixed 6.83 lb of pretzels with 3.57 lb of popcorn to make 10.4 lb of mixture. She then filled up 6 bags with an average of 1.68 lb of mixture per bag, leaving her with 0.35 lb of mixture left over.
In this problem, Hannah mixed 6.83 lb of pretzels with 3.57 lb of popcorn. This means that she had a total of 10.4 lb of mixture. She then filled up 6 bags that were the same size with the mixture, which means that each bag had approximately 1.73 lb of mixture (10.4 lb / 6 bags).
After filling up all 6 bags, Hannah had 0.35 lb of the mixture left over. This means that she used a total of 10.05 lb of mixture for the bags (10.4 lb - 0.35 lb).
To find out how much mixture was used per bag, we can divide the total amount of mixture used (10.05 lb) by the number of bags (6). This gives us an average of approximately 1.68 lb per bag.
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A cylinder has a volume of cubic centimeters and a height of 12 centimeters. What is the radius of the base of the cylinder, in centimeters?"
Answer:
Step-by-step explanation:
Jason wants to earn at least $250 each week working during the
summer.
Jason earns $6. 00 an hour babysitting.
Jason earns $7. 75 an hour working at a store.
He can work no more than 40 hours each week.
Let b equal hours of babysitting, and s equal hours working at the
store.
Which system of inequalities models the constraints?
O 6. 00b + 7. 755 2 250
b +5 s 40
O 6. 00b + 7. 75s 250
b +5 s 40
O 6. 000 + 7. 75s 40
b + s 250
O 6. 00b + 7. 75s 2 40
b + s 250
Answer:
The correct system of inequalities that models the constraints is:
6.00b + 7.75s ≥ 250
b + s ≤ 40
Explanation:
The first inequality represents the requirement that Jason needs to earn at least $250 each week. The earnings from babysitting are $6.00 per hour, and the earnings from working at the store are $7.75 per hour.
Therefore, the total earnings from both jobs can be represented by the expression 6.00b + 7.75s. This expression must be greater than or equal to $250, hence the first inequality.
The second inequality represents the constraint that Jason can work no more than 40 hours each week. The variables b and s represent the number of hours worked babysitting and working at the store, respectively.
The sum of these hours must be less than or equal to 40, hence the second inequality.
Therefore, the correct system of inequalities is:
6.00b + 7.75s ≥ 250
b + s ≤ 40
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