The amount of money are auggie and his friend johnny gonna have by the end of the party is $110
How much money are auggie and his friend johnny gonna have by the end of the party?Cost of getting into the party = $10
Number of adults at the party = 4
Number of friends at the party= 9
Total number of people at the party = Number of adults at the party + Number of friends at the party
= 4 + 9
= 11
Total money are auggie and his friend johnny gonna have by the end of the party = Total number of people at the party × Cost of getting into the party
= 11 × $10
= $110
Hence, auggie and his friend johnny will have $110 at the end of the party.
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Find the distance between the points (6,5 √ 2) and (4,3 √ 2)
Answer:
2\(\sqrt{2}\)
Step-by-step explanation:
distance formula = square root of the difference of the y-values, squared, plus the difference of the x-values, squared
= \(\sqrt{4 + 4}\)
= \(\sqrt{4}\) \(\sqrt{2}\)
= 2 \(\sqrt{2}\)
Jamie and Amy are married and both work for Coastal Company. Jamie works in a department for which the mean hourly rate is $18.80 and the standard deviation is $3.20. Amy works in a department where the mean rate is $17.50 with a standard deviation of $2.80. Relative to their departments, who is better paid if Jamie earns $19.75 and Amy earns $19.15? Assume that both departments’ pay scales are normally distributed.
Answer:
Amy is better paid
Step-by-step explanation:
The mean hourly rate in the department for which Jamie works, μ₁ = $18.80
The standard deviation hourly rate for Jamie's department, σ₁ = $3.20
The mean hourly rate in the department for which Amy works, μ₂ = $17.50
The standard deviation hourly rate for Amy's department, σ₂ = $2.80
The amount Jamie earns, x₁ = $19.75
The amount Amy earns, x₂ = $19.15
The z-score which is the number of sample standard deviation a given value in a sample is above the mean of the sample is given as follows;
\(Z=\dfrac{x-\mu }{\sigma }\)
Jamie's standard score, z = (19.75 - 18.80)/3.20 = 0.296875 ≈ 0.3
From the z-table, we get p (z < 0.296875) = 0.61791
Therefore, the probability of earning higher than $19.75 in Jamie's department is p (z >0.296875) = 1 - 0.61791 = 0.38209 or 38.209% earn higher than Jamie
Amy's standard score, z = (19.15 - 17.50)/2.80 ≈ 0.5893
From the z-table, we get p (z > 0.5893) = 1 - 0.71904 = 0.28096
Therefore, the probability of earning higher than $19.15 per hour in Amy's department is 0.28096 or only 28.096% of the people working in Amy's department earn higher than her
Therefore, given that Amy's earns more than 71.904% of the people in her department while Jamie's earns more than 61.791% of the people in his department, Amy is better paid relative to her department's members pay statistics than Jamie.
Divide 12x3 − 16x2 − 4x by −4x.
−3x2 + 4x − 1
−3x2 + 4x + 1
−3x3 − 4x2 − x
−3x2 + 4x
Answer:
-3x2+4x+1
Step-by-step explanation:
assuming the numbers after x are squares, cubes etc. 12x3 -16x2 -4x all need to be divided by -4x. 12x3/-4x(12/4 and to divided x cubed by x, -1 to the exponent) =-3x2. -16x2/-4x(-16/-4 and to divide x squared by x, -1 to the exponent)=4x. -4x/-4x(anything divided by itself is 1) therefore you have -3x2+4x+1
Answer:
\(-3x^2+4x+1\)
Step-by-step explanation:
\(=\frac{4x\left(3x^2-4x-1\right)}{-4x}\)
\(=\frac{x\left(3x^2-4x-1\right)}{-x}\)
\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-1}=-a\)
\(=-\left(3x^2-4x-1\right)\)
\(Simplify\)
\(=-\left(3x^2-4x-1\right)\)
hope this helps :P
What is the value of the expression when b= 2 and c= -3
Answer:ax^2+2x-3
Step-by-step explanation:From ax^2+bx+c=ax^2+2x+(-3)=ax^2+2x-3
Answer:
is it envision or what?????
Step-by-step explanation:
An amusement park sold 42 discount tickets and 18 full-price tickets. What percentage of the tickets sold were discount tickets?
Answer:
43%
Step-by-step explanation:
18/42 ≈ 43%
HELLLLLLLLLLLLLPPPPPPPPPP
second one is correct
mark me brainlist
Write and equation given slope and a point.
M= -1 and (-2,3)
Step-by-step explanation:
y - 3 = -1(x- -2)
y-3 = -x -2
Y = -x +1
for continuous random variables, the probability of any specific value of the random variable is one. true or false
The given statement "for continuous random variables, the probability of any specific value of the random variable is one." is false because the random variable taking on any specific value is then given by the area under the PDF curve at that value, which is zero.
In fact, for continuous random variables, the probability of any specific value is zero. This may seem counterintuitive at first, but it is a fundamental property of continuous random variables.
The PDF is a function that describes the relative likelihood of the random variable taking on a particular value within its range. The probability of the random variable taking on a specific value is then given by the area under the PDF curve at that value.
Since the PDF is a continuous function, the probability of the random variable taking on any specific value is zero. This is because the area under a continuous curve at any single point is zero.
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lan has $6,000. He wants to buy a car within $1,500 of this
amount. What is the price range of the car he wants to
purchase?
f. x2 $4,500 or x 2 $7,500 g. $4,500 2 x 2 $7,500
h. x < $4,500 or x = $7,500 j. $4,500 < x < $7,500
Answer: $7,500
Step-by-step explanation:
Part II: True / False / Uncertain ( 20 points)
Instructions. Determine whether each of the following statements is true, false or uncertain, and briefly justify your answer (2-3 sentences). No credit will be given for unsupported answers.
1. (5 points) Spain has an absolute productivity advantage in producing shoes, so it will export shoes.
2. (5 points) The Ricardian Model is useful to examine how workers in the same sector can be differently affected due to international trade.
3. (5 points) Specific factors of production gain more from trade (or trade liberalization) than mobile factors.
4. (5 points) Suppose that Home and Foreign can produce two goods (M and X) using two factors of production ( K and L ) with a bowed-out production possibilities frontier (PPF), and suppose that production of M is K-intensive. If Home has a relative abundance of L compared with Foreign, then K owners in Home should be against free trade policies.
1. True: If Spain has an absolute productivity advantage in producing shoes, then it will have a lower opportunity cost for producing shoes than the rest of the world, allowing them to sell them at a lower price, which would encourage exporting.
2. True: The Ricardian Model explains how nations can gain by specializing in the production of goods that they are relatively more efficient in producing and then trading. It can be used to explain how workers in the same sector can be differently affected due to international trade. 3. Uncertain: The extent to which a specific or mobile factor of production benefits from trade (or trade liberalization) depends on several factors, and cannot be generalized.
4. False: Suppose that Home has a relative abundance of L compared with Foreign, then it means that K is scarce relative to L in Home. Thus, K owners in Home will benefit from free trade policies as it will lead to an increase in the demand for K.
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based on the 2010 census ,the population of gorgia was 9.6 x 10^6 people wihch state has a higher population
New York had the larger population with 1.9 x 10⁷ people. The correct option is B.
To compare the populations of the states, we need to convert all the populations to the same unit of measurement. In this case, all the populations are given in terms of millions (10⁶).
We can see that New York's population is 1.9 x 10⁷, which means 19 million people. Georgia's population is given as 9.6 x 10⁶, which is 9.6 million people. Comparing these two values, it is evident that New York has a larger population than Georgia.
Check the populations of the other states:
Alaska: 7.1 x 10⁵ = 0.71 million people
Wyoming: 5.6 x 10⁵ = 0.56 million people
Idaho: 1.5 x 10⁶ = 1.5 million people
New York's population of 19 million is much larger than any of the other states listed, making it the state with the largest population among the options provided. The correct option is B.
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Complete question:
Based on the 2010 census, the population of Georgia was 9.6 x 10^6 people. Which state had a larger population? A. Alaska: 7.1 x 10^5 B. New York: 1.9 x 10^7 C. Wyoming: 5.6 x 10^5 D. Idaho: 1.5 x 10^6
Which of the following are possible equations of a parabola that has no real solutions and opens downward?
Oy=(x-4)2+2
Oy=-(x+4)²-2
Oy=(x-4) 2-2
Oy=-x²-2
Oy=-(x+4)² +2
Answer:
Oy= -(x+4)^2 -2
potentially Oy= -x^2 -2
Use the appropriate normal distribution to approximate the resulting binomial distributions. A fair coin is tossed 130 times. What is the probability of obtaining between 70 and 82 tails, inclusive
The probability of obtaining between 70 and 82 tails, inclusive is 0.2143.
What is Normal Approximation to Binomial?The likelihood of getting either head or tail while tossing a coin is constant. As a result, its probability can be computed using the binomial distribution, however as the sample size grows, it is preferable to approximation the distribution using the Normal distribution.
Now according to the question,
A fair coin is tossed 130 times; n = 130
The probability of getting a tail; p = 0.5.
The probability of getting a head; q = 0.5.
np = 130×0.5
np = 65 (as it is more than 10 so acceptable)
nq = 130×0.5
nq = 65 (as it is more than 10 so acceptable).
As np and nq > 10, as a result, we can use the normal distribution to approximate the distribution.
The mean population;
μ = np = 65
Standard variation population
σ = √npq
σ = 5.7 (approx)
Now, calculate the z-score;
\(Z=\frac{X-\mu}{\sigma}\)
where x is the number of times tails appears.
Using the continuity correction factor
\(\begin{aligned}&P(70 \leq X \leq 82)=P(70-0.5 < X < 82+0.5) \\&P(70 \leq X \leq 82)=P(69.5 < X < 82.5)\end{aligned}\)
Now, when X = 69.5, find z-score
\(Z=\frac{69.5-65}{5.7}\)
z = 0.79 (approx)
When X = 82.5, z-score is;
\(Z=\frac{82.5-65}{5.7}\)
z = 2.71 (approx)
\(P(69.5 < X < 82.5)=P(0.78 < Z < 2.71)\)
\(P(69.5 < X < 82.5)\) = 0.9966 - 0.7823 (check from positive z-score table)
\(P(69.5 < X < 82.5)\) = 0.2143
Therefore, the probability of obtaining between 70 and 82 tails, inclusive is 0.2143.
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What equation is being represented by this line?
Answer:
The equation that represented by the line is y = -x + 2
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
m is the slope of the lineb is the y-intercept (value y at x = 0)The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where
(x1, y1) and (x2, y2) are two points on the lineFrom the given figure
∵ The line passes through points (2, 0) and (0, 2)
∴ x1 = 2 and y1 = 0
∴ x2 = 0 and y2 = 2
→ Substitute them in the rule of the slope to find it
∵ m = \(\frac{2-0}{0-2}=\frac{2}{-2}=-1\)
∴ m = -1
→ Substitute it in the form of the equation above
∵ y = -1(x) + b
∴ y = -x + b
∵ b is value y at x = 0
∵ At x = 0, y = 2
∴ b = 2
→ Substitute it in the equation above
∴ y = -x + 2
∴ The equation that represented by the line is y = -x + 2
help meee plzzz
help me
Answer:
I only know the second one sooorrry
if you say its classification so that type of traingle is obtuse triangle
Step-by-step explanation:
3.4 Let X have a chi-square distribution with n degrees of freedom. Use the moment generating function technique to find the limiting distribution of the random variable ? X-n V2n [10] Explain how the result of the above question can be used for practical purposes. [2]
Using the moment generating function technique, we can determine the limiting distribution of X as n approaches infinity, but the exact form of the distribution will depend on the value of t and may require additional approximation methods to evaluate.
To find the limiting distribution of the random variable X with a chi-square distribution, we can use the moment generating function (MGF) technique. The moment generating function of X is defined as M_X(t) = E(e^(tX)).
For a chi-square distribution with n degrees of freedom, the probability density function (pdf) is given by:
f(x) = (1/(2^(n/2) * Γ(n/2))) * x^((n/2)-1) * e^(-x/2)
To find the moment generating function, we evaluate the integral:
M_X(t) = ∫[0 to ∞] e^(tx) * f(x) dx
Substituting the pdf into the MGF expression, we have:
M_X(t) = ∫[0 to ∞] e^(tx) * (1/(2^(n/2) * Γ(n/2))) * x^((n/2)-1) * e^(-x/2) dx
Simplifying, we get:
M_X(t) = (1/(2^(n/2) * Γ(n/2))) * ∫[0 to ∞] x^((n/2)-1) * e^((t-1/2)x) dx
To find the limiting distribution, we take the limit of the MGF as n approaches infinity. Using the property of the gamma function, we have:
lim(n->∞) (1/(2^(n/2) * Γ(n/2))) = 1
So, the limiting moment generating function becomes:
lim(n->∞) M_X(t) = ∫[0 to ∞] x^((n/2)-1) * e^((t-1/2)x) dx
To evaluate this integral, we need to use techniques such as Laplace's method or the saddlepoint approximation. The exact form of the limiting distribution depends on the specific value of t and may not have a closed-form expression.
Therefore, using the moment generating function technique, we can determine the limiting distribution of X as n approaches infinity, but the exact form of the distribution will depend on the value of t and may require additional approximation methods to evaluate.
The result obtained for the limiting distribution of the random variable X with a chi-square distribution as n approaches infinity has practical implications in various areas. Here are a few examples:
Approximation of chi-square distributions: The limiting distribution can be used as an approximation for chi-square distributions with large degrees of freedom. When the degrees of freedom are sufficiently large, the limiting distribution can provide a good approximation to the chi-square distribution. This can be useful in statistical analysis and hypothesis testing, where chi-square distributions are commonly used.
Central Limit Theorem: The result is related to the Central Limit Theorem, which states that the sum or average of a large number of independent and identically distributed random variables tends to follow a normal distribution. Since the chi-square distribution arises in various statistical contexts, the limiting distribution can help in approximating the distribution of sums or averages involving chi-square random variables.
Statistical inference: The limiting distribution can have implications for statistical inference procedures. For example, in hypothesis testing or confidence interval estimation involving chi-square statistics, knowledge of the limiting distribution can aid in determining critical values or constructing confidence intervals. It can also be used to assess the asymptotic properties of estimators based on chi-square distributions.
Simulation studies: The limiting distribution can be used in simulation studies to generate random samples that mimic chi-square distributions with large degrees of freedom. This can be helpful in situations where directly simulating from the chi-square distribution is computationally expensive or difficult.
Overall, understanding the limiting distribution of the chi-square distribution as n approaches infinity provides insights into the behavior of chi-square random variables and can be used as a practical tool in various statistical applications, such as approximation, inference, and simulation studies.
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5x + 12 = 2x + 21
Step by step
(Right answer plz )
Answer:
\(5x + 12 = 2x + 21 \\ 5x - 2x = 21 - 12 \\ 3x = 9 \\ x = \frac{9}{3} \\ x = 3\)
Step-by-step explanation:
please mark me brainliest
Answer:
\(5x + 12 = 2x + 21 \\ 5x - 2x = 21 - 12 \\ 3x = 9 \\ x = \frac{9}{3}\\ \boxed{x = 3}\)
x = 3 is the right answer.Jackson is at colletibles fair. He has exactly $8 and will purchase a collectibles card from a vendor for $5. What percentage will jackson spend on the purchase?
A. 0.625%
B. 3%
C. 40%
D. 62.5%
Please help me out or explain how do i do it, but if you give me the answer ill give you brainliest!
forest rangers at a national park want to take a sample of trees to estimate what proportion of trees in the park are infected with a certain disease. the population of trees in question is divided by a creek. east of the creek, most of the trees are oak. west of the creek, most trees are cedar, which are more likely to be infected. the rangers are considering taking a stratified random sample using each side of the creek as strata. they'll sample trees from each side proportionately based on the total number of trees on each side. why might the rangers choose stratification instead of a simple random sample to estimate the proportion of infected trees? choose all answers that apply: choose all answers that apply: (choice a, checked) a stratified random sample reduces the likelihood of getting disproportionate numbers of cedar or oak trees in the sample. a a stratified random sample reduces the likelihood of getting disproportionate numbers of cedar or oak trees in the sample. (choice b) in repeated sampling, estimates from this sort of stratified sample would likely vary less than estimates from simple random samples. b in repeated sampling, estimates from this sort of stratified sample would likely vary less than estimates from simple random samples. (choice c) a stratified sample eliminates the bias that arises from using a simple random sample. c a stratified sample eliminates the bias that arises from using a simple random sample.
Choices a and b are both valid reasons for why the rangers might choose stratification over a simple random sample.
Choice a is correct because stratification ensures that the sample includes a proportional representation of both oak and cedar trees, which is important because cedar trees are more likely to be infected with the disease the rangers are interested in. Without stratification, a simple random sample might accidentally oversample one type of tree over the other, leading to biased estimates of the overall proportion of infected trees in the park.
Choice b is correct because stratification generally reduces the variability of estimates compared to simple random samples. This is because stratification ensures that each stratum is represented in the sample, which can improve the precision of estimates compared to a simple random sample that might miss important subgroups in the population.
Choice c, on the other hand, is not necessarily true. While stratification can reduce bias compared to a simple random sample, it does not completely eliminate bias. Stratification can still be biased if the stratification variable is poorly chosen or if there are important variables that are not used for stratification. So while stratification can help reduce bias and improve precision, it is not a guarantee of unbiased estimates.
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Find the geometric mean between 28 and 32. Round to the nearest tenth if necessary.
A.29.9
B.7.7
C.30
D.10.9
The geometric mean between 28 and 32 is equal to 29.9 to the nearest tenth, which makes option A correct.
How to evaluate for the geometric meanIf x, y, z are consecutive terms of a geometric progression, then the expression for the geometric mean is given as: y = √xz
Thus; for the geometric mean between 28 and 32, we evaluate as follows:
geometric mean between 28 and 32 = √(28 × 32)
geometric mean between 28 and 32 = √896
geometric mean between 28 and 32 = 29.9333.
Therefore, the geometric mean between 28 and 32 is equal to 29.9 to the nearest tenth.
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clair is at the candy store buying treats for halloween.she buys 7 kilogramsof candy for $14.00
Answer:
Can I get more reference? I'll help though.
Step-by-step explanation:
f(x)=9 find the following values
2f(x) +3
Answer
this question is impossible no expert can solve this!11!1!!!
Step-by-step explanation:
none
Implement a linear time algorithm for the following problem:
Given a list A of n distinct numbers and an integer i, with 1 ≤ i ≤ n, find the element x ∈ A that is larger than exactly i − 1 other elements of A.
Hint: Note that we can solve this problem in O(n log n) time, since we can sort the numbers using QuickSort and then simply index the i th element in the output array. However, we want to do it faster. Implement the algorithm described below :
1. Divide the n elements of the input array into ⌊n/5⌋ groups of 5 elements each and at most one group made up of the remaining n mod 5 elements.
2. Find the median of each of the ⌊n/5⌋ groups by first insertion-sorting the elements of each group (of which there are at most 5) and then picking the median from the sorted list of group elements.
3. Use SELECT recursively to find the median x of the ⌊n/5⌋ medians found in step 2. (If there are an even number of medians, then by our convention, x is the lower median.)
4. Partition the input array around the median-of-medians x using the modified version of PARTITION. Let k be one more than the number of elements on the low side of the partition, so that x is the kth smallest element and there are n-k elements on the high side of the partition.
5. If i z = k, then return x. Otherwise, use SELECT recursively to find the ith smallest element on the low side if i > k
The algorithm finds the element x in a list A that is larger than exactly i - 1 other element of A using a linear time approach based on the median of medians.
1. Divide the n elements of the input array into ⌊n/5⌋ groups of 5 elements each and at most one group made up of the remaining n mod 5 elements.
2. Find the median of each of the ⌊n/5⌋ groups by first insertion-sorting the elements of each group (of which there are at most 5) and then picking the median from the sorted list of group elements.
3. Use SELECT recursively to find the median x of the ⌊n/5⌋ medians found in step 2. If there are an even number of medians, x is the lower median.
4. Partition the input array around the median-of-medians x using a modified version of the PARTITION algorithm. Let k be one more than the number of elements on the low side of the partition so that x is the kth smallest element and there are n-k elements on the high side of the partition.
5. If i = k, then return x. Otherwise, use SELECT recursively to find the ith smallest element on the low side if i > k, or on the high side if i < k.
The algorithm utilizes the concept of finding the median of medians to efficiently find the desired element. By dividing the array into groups and recursively finding the median, it effectively reduces the problem size. The partitioning step helps to narrow down the search range based on the relationship between i and k.
This algorithm guarantees the linear time complexity of O(n), making it faster than the O(n log n) time complexity achieved by sorting and indexing the array.
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A regular octagon is inscribed in a circle of radius 1. Find a side of the octagon.
If regular octagon is inscribed in a circle of radius 1 a side of the octagon is \(\sqrt{ 2-\sqrt{2} }\)
What is the side of the octagon ?A polygon with 8 sides and 8 angles is called an octagon. That indicates that an octagon has 8 edges and vertices, respectively. The octagon is a two-dimensional, 8-sided polygon, often known as an 8-gon, in plain English. All of the sides of a regular octagon will be the same length.
Given that the radius= 1
The angle between adjacent sides of regular octagon can be expressed as
\(\frac{(8 -2)180}{8}\)
=135
We can represent the side length of regular octagon as (a) the sing the sine rule ,
\(\frac{a}{sin45} =\frac{1}{sin(62.5)}\)
\(a= \frac{sin45}{sin(62.5)}\)
= \(\sqrt{ 2-\sqrt{2} }\)
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A plastic extrusion process is in statistical control and the output is normally distributed. The extrudate is subsequently cut into individual parts, and the extruded parts have a critical cross-sectional dimension = 12.50 mm with standard deviation = 0.25 mm. Determine the process capability.
The process capability, Cp is calculated by dividing the upper specification limit minus lower specification limit by 6 times the process standard deviation.
This is the formula for the process capability.
Cp = (USL - LSL) / (6 * Standard deviation)
Where, Cp is process capability USL is the Upper Specification Limit LSL is the Lower Specification Limit Standard deviation is the process standard deviation.
The extrudate is subsequently cut into individual parts, and the extruded parts have a critical cross-sectional dimension = 12.50 mm with standard deviation = 0.25 mm. The mean of this distribution is the center line of the control chart and the critical cross-sectional dimension 12.50 mm is the target or specification value.
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Find the first six terms of the sequence.
a1 = -7, an = 4 • an-1
Answer:
- 7, - 28, - 112, - 448, - 1792, - 7168
Step-by-step explanation:
Using the recursive formula and a₁ = - 7 , then
a₂ = 4a₁ = 4 (- 7) = - 28
a₃ = 4a₂ = 4(- 28) = - 112
a₄ = 4a₃ = 4(- 112) = - 448
a₅ = 4a₄ = 4(- 448) = - 1792
a₆ = 4a₅ = 4(- 1792) = - 7168
A clothing store is having a sale buy one shirt at regular price and a second shirt of eqaul or lesser value of 35% off Jason buys 2 shirts a the sale the regular price of the first shirt is 32.00 and the regular price of the second shirt is 20.00 including sales tax jason pays 48.60 jason says he pays 8% sales tax is hecorrect
Jason's statement about the sales tax is correct.
To determine whether Jason's statement about the sales tax is correct, we need to calculate the total cost of the two shirts before any tax or discounts are applied, and then calculate the final cost including the discount and any applicable sales tax.
The regular price of the first shirt is $32.00, and the regular price of the second shirt is $20.00. So the total cost of both shirts before any discounts or tax is applied is:
$32.00 + $20.00 = $52.00
According to the sale, the second shirt is eligible for a discount of 35% off its regular price. Since the regular price of the second shirt is $20.00, the discount amount is:
0.35 x $20.00 = $7.00
So the sale price of the second shirt is:
$20.00 - $7.00 = $13.00
The total cost of both shirts after the discount is applied is:
$32.00 + $13.00 = $45.00
Now we need to determine whether Jason's statement about the sales tax is correct. If he is correct, then the total cost of the two shirts including sales tax would be:
$45.00 + 0.08 x $45.00 = $48.60
So let's check if this is the amount Jason paid. It is, so he is correct!
Therefore, the amount of sales tax paid is:
$45.00 x 0.08 = $3.60
And the final cost of the two shirts including sales tax is:
$45.00 + $3.60 = $48.60
So Jason did pay 8% sales tax as he claimed.
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The volume of a sphere is 26667 cm³.
Calculate the diameter of the sphere.
Volume of sphere = πr³
cm
Given the volume of the sphere as 26667 cm³, we calculated the radius to be approximately 17.7 cm using the formula for the volume of a sphere. By multiplying the radius by 2, we found that the diameter of the sphere is approximately 35.4 cm.
To calculate the diameter of a sphere when given its volume, we can use the formula for the volume of a sphere:
V = (4/3) * π * r³
Where V is the volume and r is the radius of the sphere. Since we are given the volume, we can rearrange the formula to solve for the radius:
r = (\(\sqrt[3]{(3V / (4\pi )}\)))
Substituting the given volume V = 26667 cm³ into the formula, we have:
r = (\(\sqrt[3]{(3 * 26667 / (4\pi )))}\)
Calculating this expression, we find:
r ≈ (\(\sqrt[3]{80001 / \pi ))}\) ≈ 17.7 cm
Now that we have the radius, we can calculate the diameter by multiplying the radius by 2:
d = 2 * r ≈ 2 * 17.7 ≈ 35.4 cm
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. Fiona has 18 red carnations, 27 white carnations, and 36 blue carnations. She wants to make arrangements of red, white, and blue carnations.She plans to use all of the flowers and to have the same number of each color in each arrangement. If she makes the greatest number of arrangements possible, then how many blue carnations will be in each arrangement?
Answer:
9 blue carnations.
Step-by-step explanation:
Given that,
Fiona has 18 red carnations, 27 white carnations, and 36 blue carnations. She wants to make arrangements of red, white, and blue carnations.
If she makes the greatest number of arrangements possible, then we need to find how many blue carnations will be in each arrangement.
Greatest possible arrangements = HCF of 18,27 and 36
The factors of 18 are: 1, 2, 3, 4, 6, 9, 12, 18,
The factors of 27 are: 1, 3,9,27
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The greatest common factor = 9
For blue carnation,
B = (36/9) = 4
Hence, in each arrangements there are 9 blue carnations.
Which of these strategies would eliminate a variable in the system of equations?
The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 3 ,multiply the bottom equation by -2 then add the equation and is denoted as option B.
What is Equation?This is a mathematical term which is made up of two expressions and is connected by an equal sign.
In the example given below:
2x + 8y = -3
3x + 6y = -4
We can multiply the top by 3 and the bottom by -2 which will result in:
6x + 24y = -9
-6x - 12y = 8
They are then added to each other to give:
6x - 6x + 24y - 12y = -9+8
12y = -1
y = -1/12
From this we can notice that the variable x was eliminated which is why option B is the correct choice.
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