We can expect 4 giant swallowtails to visit Ellie's garden.
In total, there were 96 butterfly visits (32 monarchs + 56 gulf fritillaries + 8 giant swallowtails).
Now, we can calculate the probability of a giant swallowtail visit:
Probability
= (number of giant swallowtails) / (total butterfly visits)
= 8/96
= 1/12
Given that 48 butterflies visit her garden, we can expect the number of giant swallowtails to be:
Expected giant swallowtails
= (total butterflies) × (probability of giant swallowtails)
= 48 × (1/12)
= 4
So, we can expect approximately 4 giant swallowtails to visit Ellie's garden out of the 48 butterflies.
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Can someone answer this for me?
Answer: as per question statement
we need to set up an equation first
p(t)=1200e(0.052*t)
they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present
we need to find population at t=6
we need to plug t=6 in p(t).
P(6)=1200e(0.052*6)=1639.38
1638.38 bacteria were present at that time t=6
Step-by-step explanation: I hope this helps.
which of the following is an improper fraction 1 DIVIDE 2 or 4 Divide 25 or 25 divide 7 of None of these
Answer:
25 divide 7
Step-by-step explanation:
hope this helps you
Jayce wants to buy a tancy bike today, the first of the month, which is priced at the non-regotint amount of \$30,000. Jabce is willing to finance the bike at monthly rate of 1% and to muke monthly payments of $500 at the end of each month for 5 years. Find the down payment/
The down payment for Jayce to purchase the tancy bike today would be $7,440.
To find the down payment, we need to calculate the total amount that Jayce will finance for the tancy bike.
The tancy bike is priced at $30,000. Jayce will make monthly payments of $500 for 5 years, which is equivalent to 60 months. The monthly interest rate is 1% or 0.01.
We can use the present value formula to determine the financed amount:
Financed amount = (Monthly payment * (1 - (1 + interest rate)^-number of months)) / interest rate
Substituting the values into the formula:
Financed amount = ($500 * (1 - (1 + 0.01)^-60)) / 0.01
Financed amount = ($500 * (1 - 0.5488)) / 0.01
Financed amount = ($500 * 0.4512) / 0.01
Financed amount = $22,560
The down payment is the difference between the price of the bike and the financed amount:
Down payment = Price of the bike - Financed amount
Down payment = $30,000 - $22,560
Down payment = $7,440
Therefore, the down payment for Jayce to purchase the tancy bike today would be $7,440.
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How will more grass grew as a result of more rain.
How will more grass affect the deer that live in the forest?
A. They will get sick.
B. They will get less food.
C. Their population will increase.
O
D. They will leave the forest forever.
Answer:
Just as forest habitat can affect deer, deer can affect forests. ... High deer populations can degrade vegetation communities and habitat for other wildlife species. Without that, no one has a place to call home.
Step-by-step explanation:
In April, the party and occasions department had an opening inventory at 57,000 at retail. The sell thru percentage rate for April was 28 %, and the closing stock was 49. 0. What were the net sales in the department during the month of April
The net sales in the department during the month of april is $15960.
Sell-thru perecentage rate = Units sold / Units recieved
In our case:
Net sales = (Sell-thru rate)*(opening inventory)
Net sales = (0.28)*($57000)
= $15960
Net sales refer to the total amount of revenue generated by a company from its primary business operations, minus any returns, allowances, and discounts. This figure reflects the actual revenue earned by a company after accounting for any deductions and is a critical metric for evaluating the financial performance of a business.
Net sales are reported on a company's income statement and are a key component of the top line, which also includes other sources of revenue, such as interest income or gains from the sale of assets. Understanding a company's net sales is essential for assessing its growth potential, profitability, and overall financial health. Investors, creditors, and other stakeholders use net sales as a metric to evaluate a company's ability to generate revenue from its core operations, as well as its ability to compete effectively in its industry.
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Which is a source of bias in a survey question?
a multiple-choice question that does not list commonly known options
a question that is so difficult most students will miss it
a question that asks a student to give an example of a concept in the lesson
a question that is so easy all students give the right answer
The source of bias in a survey question is D. a question that is so easy all students give the right answer.
What is a bias?Source bias is the propensity to favor sources of information that corroborate or contradict a certain set of views or values.
When systematic inaccuracy is added to sampling or testing during research, bias emerges. This happens when one outcome or response is preferred over others. Bias can appear at any stage of the research process, including study design, data collection, data analysis, and publication.
It should be noted that when the question is so easy, it ilustrates bias since it was intentional.
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find the missing side of the triangle below. please round your final answer to the nearest tenth. Be sure to show all work! Use pythagorean theorem
on a certain sum of moneylent out at 20 %per annum for 1 and a half year the compound interest reconked yearly and and recokned yearly half is 178.75 . find the sum
The sum of moneylent out at interest 20 %per annum for 1 and a half year the compound interest reconked yearly and and recokned yearly half is 178.75 is 16250.
Let sum be p. Here r = 20%, n =3/2 yrs = 1 1/2 yrs.
When compounded yearly i.e. A.
A = p(1+r/100) * [1+{1/2 r}/100)]
= p(1+20/100) * [1+{1/2 *20}/100]
= p x 6/5 x 11/10 = 33p/25
Compound interest = A - p
= 33p/25 - p
= 8p/25
Now when compounded half yearly, then
A = p[1+(1/2 x r)/100]ⁿ*²
= p[1+(1/2 x 20)/100]⁽³/²⁾*²
= p[11/10]³
= 1331p/1000
Compound interest = 1331p/1000 - p = 331p/1000.
Now as per questions,
331p/1000 - 8p/25 = 178.75
p x 11/1000 = 178.75
p = 178.75 x 1000/11
p = 16250
Hence, the sum of moneylent out at interest 20 %per annum for 1 and a half year the compound interest reconked yearly and and recokned yearly half is 178.75 is 16250.
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Did I do this right?
Answer:
yes you did
Step-by-step explanation:
I hate math and my math teacher
Identify the sets of congruent angles. Explain your conclusions.
Answer:CB,CH,AE,AB
Step-by-step explanation:
A ball is released at the left end of three different tracks. The tracks are bent from equal-length pieces of channel iron.
a. From fastest to slowest, rank the speeds of the balls at the right ends of the tracks.
b. From longest to shortest, rank the tracks in terms of the times for the balls to reach the ends.
c. From greatest to least, rank the tracks in terms of the average speeds of the balls. Or do all the balls have the same average speed on all three tracks?
a. From fastest to slowest, the speeds of the balls at the right ends of the tracks will depend on the curvature of the tracks.
If the tracks are of equal length but have different curvatures, the ball on the track with the least curvature will have the highest speed, followed by the ball on the track with the next least curvature, followed by the ball on the track with the most curvature.
b. From longest to shortest, the tracks in terms of the times for the balls to reach the ends will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the most curvature will have the longest time for the ball to reach the end, followed by the track with the next most curvature, followed by the track with the least curvature.
c. From greatest to least, the tracks in terms of the average speeds of the balls will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the least curvature will have the highest average speed, followed by the track with the next least curvature, followed by the track with the most curvature.
All the balls will have the same average speed on all three tracks if the track lengths are equal, but will have different speeds at the end of each track due to the different curvatures.
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A scarf needs ¾ of a yard of fabric. How many scarves can be made from 9 yards of fabric?
Answer:
exactly 12 !
Step-by-step explanation:
3/4 is the length need, times 12, which is the end result of scarves, equals 9, the yards of fabric !!
3/4 x 12 = 9
i hope this helped!!!!
The point at which two lunes intersect.
The point at which two lines intersect is referred to as point of intersection.
What is a point of intersection?In Mathematics and Geometry, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
In order to graph the solution to a system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
x² + y² = 100 ......equation 1.
3x - y = 30 ......equation 2.
Based on the graph shown, the solution to this system of equations is the point of intersection of the lines given by the ordered pairs (10, 0) and (8, -6).
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Complete Question:
What is the point at which two lines intersect?
3(4x - 12) + 8 = 12x - 6
Answer:
No solution
Step-by-step explanation:
3(4x-12)+8=12x-6
12x-36+8=12x-6
12x-28=12x-6
Consider the process x, = 3x -1 + 5*7-2 2 2 +3*,-2 +2, +52,-, where z, -WN(0,0?). , +z (2) i) Write the process {x} in backshift operator. (2) ii) Is x, stationary process? Justify your answer. (2) iii) Is x, invertible process? Justify your answer. (2) iv) Find Vx, process. (2) v) Is Vx, stationary process. Justify your answer. vi) Classify the process in part iv) as ARIMA(p,d,g) model. (3) vii) Evaluate the first three t-weights
i) Writing the process {x} in backshift operator notation:
{x_t} = 3{x_{t-1}} - 1 + 57 - 2^2 + 3{-2} + 2{x_{t-2}} + 52{-1} - {-2}^2
Using the backshift operator (B), we can rewrite the process as:
{x_t} = 3B{x_t} - 1 + 57 - 2^2 + 3(-2) + 2B^2{x_t} + 52B{x_t} - (-2)^2
ii) To determine if x_t is a stationary process, we need to examine whether its mean and variance are constant over time. Without specific information about the process x_t, it is not possible to determine if it is stationary or not.
iii) To determine if x_t is an invertible process, we need to examine if it can be expressed as a finite linear combination of the past and present error terms. Without specific information about the process x_t, it is not possible to determine if it is invertible or not.
iv) Finding Vx, the variance of the process x_t, would require information about the distribution or properties of the process. Without specific information, it is not possible to calculate Vx.
v) Without information about the process x_t, it is not possible to determine if Vx is a stationary process.
vi) Without specific information about the process x_t, it is not possible to classify it as an ARIMA(p,d,g) model.
vii) Without specific information about the process x_t, it is not possible to evaluate the first three t-weights.
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Graph the function. F(x) = 2x^2-5
Answer:
see attached
Step-by-step explanation:
You want a graph of the function F(x) = 2x² -5.
GraphA graphing calculator can help a lot when you want the graph of a function. This one is an x² function with a vertical translation of -5 and a vertical stretch by a factor of 2.
It is often useful to consider points ±1 or ±2 either side of the vertex, and the vertex itself.
The graph is attached.
the life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hours. caitlynn wants to find the probability that a light bulb she purchased from this manufacturer will last no more than 14,500 hours
Hence, the probability that a light bulb purchased from this manufacturer will last no more than 14,500 hours is approximately 0.8944.
To solve this problem, we need to standardize the normal distribution and use the standard normal distribution table.
Let X be the random variable representing the life of the manufacturer's compact fluorescent light bulbs. Then, X is normally distributed with mean μ = 12,000 hours and standard deviation σ = 2,000 hours.
We want to find the probability that a light bulb will last no more than 14,500 hours. In other words, we need to find P(X ≤ 14,500).
To standardize X, we use the formula:
Z = (X - μ) / σ
Substituting the values, we get:
Z = (14,500 - 12,000) / 2,000 = 1.25
Now, we look up the probability from the standard normal distribution table. We find that the probability of Z ≤ 1.25 is 0.8944.
Therefore, P(X ≤ 14,500) = P(Z ≤ 1.25) = 0.8944.
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how do you Multiply fractions? could you explain with a few examples?
The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. For example
\(\begin{gathered} \frac{2}{3}\cdot\frac{5}{6}=\frac{2\cdot5}{3\cdot6}=\frac{10}{18} \\ \text{ Now simplify} \\ \frac{10}{18}=\frac{2\cdot5}{2\cdot9}=\frac{5}{9} \\ \text{Then} \\ \frac{2}{3}\cdot\frac{5}{6}=\frac{5}{9} \end{gathered}\)In other words, multiply linearly and simplify
If you have to multiply mixed fractions, first you transform the fraction from mixed to improper and then multiply, for example
\(\begin{gathered} 3\frac{1}{4}\cdot-\frac{8}{5}=\frac{3\cdot4+1}{4}\cdot-\frac{8}{5}=\frac{12+1}{4}\cdot-\frac{8}{5}=\frac{13}{4}\cdot-\frac{8}{5} \\ \text{ Apply the law of signs of the multiplication} \\ 3\frac{1}{4}\cdot-\frac{8}{5}=\frac{13}{4}\cdot-\frac{8}{5}=\frac{13\cdot-8}{4\cdot5}=\frac{-104}{20} \\ \text{Simplify} \\ \frac{-104}{20}=\frac{2\cdot-26}{2\cdot10}=\frac{-26}{10} \\ \text{Then} \\ 3\frac{1}{4}\cdot-\frac{8}{5}=\frac{-26}{10} \end{gathered}\)The law of signs for multiplication is
\(\begin{gathered} +\cdot+=+ \\ +\cdot-=- \\ -\cdot+=- \\ -\cdot-=+ \end{gathered}\)Multiplying fractions starts with the multiplication of the given numerators, followed by the multiplication of the denominators. ...
Example: Multiply the following fractions: 1/3 × 3/5.
Solution: We start by multiplying the numerators: 1 × 3 = 3, then, multiply the denominators: 3 × 5 = 15.
A company that makes hard candy have a standard bag of hard candy with 150 pieces. The hard candy has three distinct colors red, white and orange and equal proportion of each candy is present in the standard bag. The manager wants to know whether the bags produced last Monday were similar to the standard bag. To test this, they plan to choose a random bag from the batch and compare it with the standard bag. You will have to answer questions below to assist the manager in comparing the two bags. Based on the data provided above how many degrees of freedom will you have while performing the necessary test of comparison
Answer:
The degrees of freedom, Df = The number of bags produced on Monday - 1
Step-by-step explanation:
The number of degrees of freedom is the limiting number of values that are logically not influenced by other values such that they are capable of having variation
The degrees of freedom = The sample size - 1 = N - 1
Therefore, the degrees of freedom, Df = The number of bags produced on Monday - 1
The probability of a call center receiving over 400 calls on any given day is 0.2. If it does receive this number of calls, the probability of the center missing the day’s target on average caller waiting times is 0.7. If 400 calls or less are received, the probability of missing this target is 0.1. The probability that the target will be missed on a given day is:
0.70
0.20
0.22
0.14
Therefore, the probability that the target will be missed on a given day is 0.22, or 22%.
To calculate the probability that the target will be missed on a given day, we need to consider the two scenarios: receiving over 400 calls and receiving 400 calls or less.
Scenario 1: Receiving over 400 calls
The probability of receiving over 400 calls is given as 0.2, and the probability of missing the target in this case is 0.7.
P(Missed Target | Over 400 calls) = 0.7
Scenario 2: Receiving 400 calls or less
The probability of receiving 400 calls or less is the complement of receiving over 400 calls, which is 1 - 0.2 = 0.8. The probability of missing the target in this case is 0.1.
P(Missed Target | 400 calls or less) = 0.1
Now, we can calculate the overall probability of missing the target on a given day by considering both scenarios:
P(Missed Target) = P(Over 400 calls) * P(Missed Target | Over 400 calls) + P(400 calls or less) * P(Missed Target | 400 calls or less)
P(Missed Target) = 0.2 * 0.7 + 0.8 * 0.1
P(Missed Target) = 0.14 + 0.08
P(Missed Target) = 0.22
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PLSS HELP Traci plans to conduct a coin-flipping experiment to see if the probability of landing on "heads" or "tails" is close to the theoretical probability of 1 2 . Which experiment is likely to yield a result FARTHEST from the theoretical probability? A) 25 coin tosses B) 35 coin tosses C) 55 coin tosses D) 75 coin tosses
Answer:
Its A- 25 coin tosses
Step-by-step explanation:
I took the test
The relationship between the amount of time a basketball player spent practicing the day before a game and the number of points he scored in the game is graphed on the scatter plot shown.
Describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
A.As the time a basketball player practices increases, the number of points scored in a game increases with a strong linear association.
B.As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
C.As the time a basketball player practices increases, the number of points scored in a game decreases with a weak linear association.
D. As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
PLS FAST 100 POINTS TO WHO ANSWERS FIRST
The type and the degree of association that we have here is As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
What is a non linear relationship?
We can see the trend that the plot is taking, it is going upwards. This shows that the increase in practice time was making him better at scoring points.
When he practiced at 20 minutes, he scored 10 points
Also the relationship is non linear given that all of the points do not fall on the same line if it is to be ruled. There are points outside.
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1/4 OF MY POINTS For this assignment, you will use sinusoids to model mathematical and real-world problems.
Background Information
Data sets that are cyclical, harmonic, oscillating, or periodic can be modeled with sinusoidal functions.
Finding key features such as minimum, maximum, amplitude, period, and frequency are helpful in
determining a sinusoidal model. Recall that the general forms of equations of sinusoids can be in these
forms: y = a sin(b(x – h)) + k or y = a cos(b(x – h)) + k.
Assignment Instructions
For this project, you are expected to submit the assignment (Parts 1 and 2) at the end of this document.
Step 1: Prepare for the performance task.
a) Read through the guide before you begin so you know the expectations for this assignment.
b) If there is anything that is not clear to you, be sure to ask your teacher.
a) If your word processing program has an equation editor, you can insert your equations here.
Otherwise, print this activity sheet and write your answers by hand.
Step 2: Complete Parts 1 and 2 in the Assignment section of this document.
a) Read all directions carefully.
b) Complete each task.
c) Insert images or screenshots of graphs when needed. Be sure that all graphs or screenshots
include appropriate information such as titles, labeled axes, etc.
d) Be sure to show all your work, You will be given partial credit based on the work you show and
the completeness and accuracy of your explanations
e) Consider underlining and circling important components in the problems.
Step 3: Evaluate your project using this checklist.
If you can check each box below, you are ready to submit your project.
Have you answered all questions in Part 1 and Part 2?
Have you shown your work?
Did you include an image or screenshot of a graph when requested?
Are all your equations correct? Be sure to check your formatting carefully.
Step 4: Revise and submit your project.
a) If you were unable to check off all of the requirements on the checklist, go back and make
sure that your project is complete. Save your project before submitting it.
b) Your teacher will give you further directions about how to submit your work. You may be
asked to submit your responses through the virtual classroom, email it to your teacher, or print
it and hand in a hard copy.
c) Congratulations! You have completed your project.
Answer:
A) (x + 3)2
+ (y -1)2
= 2
B) (x - 3)2
+ (y + 1)2
= 2
C) (x + 3)2
+ (y - 1)2
= 4
D) (x - 3)2
+ (y + 1)2
= 4A) (x + 3)2
+ (y -1)2
= 2
B) (x - 3)2
+ (y + 1)2
= 2
C) (x + 3)2
+ (y - 1)2
= 4
D) (x - 3)2
+ (y + 1)2
= 4
Step-by-step explanation:
It is estimated that 26% of the population of Gingerland have red hair. If 10 residents are chosen at random, what is the probability that... (assume each person is independent)
a) exactly 4 of them have red hair?
b) less than 5 of them have red hair?
c) at least one of them has red hair?
d) What is the expected (mean) number of people you will find with red hair in this group of 10?
Answer:
The answer for me would be a) exactly 4 of them have red hair
Step-by-step explanation:
being that there is 26 percent of people in Gingerland that gave red hair I cam assume that that is a lot of people being that Gingelrand is like a city/town so exactly 4 of them is what I assume is the amswer
Let x be an integer. Prove that if x is not divisible by 3, then
(x + 1)(x + 2) is divisible by 3
Answer:
(x + 1)(x + 2) is divisible by 3.
Step-by-step explanation:
Assume that x is not divisible by 3. This means that x can be expressed as x = 3k + r, where k is an integer and r is the remainder when x is divided by 3. Since x is not divisible by 3, the remainder r must be either 1 or 2.
Case 1: r = 1
If r = 1, then x = 3k + 1. Now let's consider (x + 1)(x + 2):
(x + 1)(x + 2) = (3k + 1 + 1)(3k + 1 + 2)
= (3k + 2)(3k + 3)
= 3(3k^2 + 5k + 2)
We can see that (x + 1)(x + 2) is divisible by 3.
Case 2: r = 2
If r = 2, then x = 3k + 2. Now let's consider (x + 1)(x + 2):
(x + 1)(x + 2) = (3k + 2 + 1)(3k + 2 + 2)
= (3k + 3)(3k + 4)
= 3(3k^2 + 7k + 4)
We can see that (x + 1)(x + 2) is divisible by 3.
Hence, the statement is proven.
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how to calculate marginal pmf
To calculate marginal PMF (Probability Mass Function), you need to follow these steps:determine the joint PMF of the two random variables X and Y, find the marginal PMF of X,and Y and finally calculate the marginal probabilities
1. First, determine the joint PMF of the two random variables X and Y. This can be done by multiplying the probabilities of the two variables for each possible outcome.
2. Next, to find the marginal PMF of X, you need to sum the joint PMF over all possible values of Y. This can be done using the formula: P(X=x) = ∑ P(X=x, Y=y).
3. Similarly, to find the marginal PMF of Y, you need to sum the joint PMF over all possible values of X. This can be done using the formula: P(Y=y) = ∑ P(X=x, Y=y).
4. Finally, you can use the marginal PMFs to calculate the marginal probabilities of each outcome for X and Y.
So, the marginal PMF can be calculated by summing the joint PMF over all possible values of the other variable.
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express the following limit as a definite integral: lim n→[infinity] n∑i=1 i6/n7=∫b1 f(x)dx
The given limit can be expressed as the definite integral: lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx
To express the given limit as a definite integral, we need to determine the appropriate function f(x) and the integration limits b and 1.
Let's start by rewriting the given limit:
lim (n→∞) (1/n) ∑(i=1 to n) \(i^6/n^7\)
Notice that the term i⁶/n⁷ can be written as (i/n)⁶/n.
Therefore, we can rewrite the above limit as:
lim (n→∞) (1/n) ∑(i=1 to n) (i/n)⁶/n
This can be further rearranged as:
lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶
Now, let's define the function f(x) = x⁶, and rewrite the limit using the integral notation:
lim (n→∞) (1/n^7) ∑(i=1 to n) (i/n)⁶ = ∫[a,b] f(x) dx
To determine the integration limits a and b, we need to consider the range of values that x can take. In this case, x = i/n, and as i varies from 1 to n, x varies from 1/n to 1. Therefore, we have a = 1/n and b = 1.
Hence, the given limit can be expressed as the definite integral:
lim (n→∞) n ∑(i=1 to n) i⁶/n⁷ = ∫[1/n, 1] x⁶ dx
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What is 2 1/4 divided by 4????
1. 5/8
2. 1/10
3. 10
4. 1 3/5
Step-by-step explanation:
2 1/4 = 9/4
9/4 ÷ 4
9/4 x 1/4
9/16
so neither of these answers?
For a population with µ = 80 and σ = 10, what is the X value corresponding to z = –2.00?
The X value corresponding to z = -2.00 is 60. The X value corresponding to z = -2.00 is 60. This means that the observation with a z-score of -2.00 is 60 units below the population mean of 80.
To find the X value corresponding to z = -2.00, we can use the formula:
z = (X - µ) / σ
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60
The z-score measures the number of standard deviations an observation is from the mean. In this case, the given z-score of -2.00 indicates that the observation is 2 standard deviations below the mean.
To find the corresponding X value, we use the formula:
z = (X - µ) / σ
Where z is the standard normal distribution value, X is the corresponding raw score, µ is the mean of the population, and σ is the standard deviation of the population.
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60
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2x^2 + 8x factor out the gcf
Answer:
2x(x + 4)
Step-by-step explanation:
The greatest common factor of 2x^2 and 8x is 2x. So, we can factor out 2x to get:
2x(x + 4)
The definition of a greatest common factor (GCF) is the largest number that is a factor of two or more numbers. In this case, 2x is the GCF of 2x^2 and 8x because it is the largest number that divides both numbers evenly.
Here are the steps on how to factor out the GCF:
Find the GCF of the two numbers. In this case, the GCF is 2x. Write the GCF as a factor of each number. Combine the factors to get the factored expression.In this case, the factored expression is 2x(x + 4).
The answer is:
⇨ 2x(x + 4)Work/explanation:
Let's find something that \(\sf{2x^2}\) and \(\sf{8x}\) have in common.
In other words, we find their GCF (greatest common factor).
The GCF of \(\sf{2x^2}\) and \(\sf{8x}\) is 2x.
So I factor it out :
\(\sf{2x(x+4)}\)
Hence, the answer is 2x(x + 4).