The sampling method used in this scenario is random Systematic random sampling
Systematic random sampling
Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.
If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.
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sydney wants to make 15 beaded rings for a craft show. she needs 60 beads for each ring. she has 852 beads. does sydney have enough beads to make 15 complete rings?
No , Sydney does not have enough beads to make 15 rings .
beads required for one ring = 60
total rings she have to make is = 15
total beads she has to make rings = 852 beads
now,
60 beads make ring = 1
852 beads make rings = 1/60 x 852
= 14.2 rings
OR
14 total rings
So , Sydney does not have enough beads to make 15 rings . she can only make 14 beads from the given amount of beads.
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Can someone please help me?
The curriculum runs from Mon 27/7/2020 to Fri 27/11/2020, work out how many full weeks this is by using a calendar.
a) Number of weeks:
b) Convert the number of weeks to fortnights:
You work on your studies 3 days of the week
a) What is the total number of days that you study using the number of weeks you calculated earlier and 3 days a week
b) If you work 2 hours a day what would the total number of hours be over the course?
Using proportions, the amounts are given as follows:
a) Number of weeks: 17.
b) Number of fortnights: 8.5.
a) Number of days studied: 51.
b) Number of hours studied: 102.
What is a proportion?A proportion is a fraction of a total amount, and this fraction is used to build relations, using basic arithmetic operations such as multiplication or division, to obtain the desired measures in the context of a problem.
Using a calendar, the number of weeks between these two dates is of:
17.
A fortnight is composed by two weeks, hence the number of fortnights is:
17/2 = 8.5.
You studied 3 days a week, hence the number of days studying was of:
17 x 3 = 51 days.
You studied 2 hours a hence, hence the number of hours studying was of:
51 x 2 = 102 hours.
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the average flight time for the pilots is found to be 8.12 hours. the standard deviation reported by the faa is 0.72 hours, and there were 81 pilots in the sample. what is the t-statistic for this hypothesis test? report to two decimal places.
The t-statistic for this hypothesis test will be 1.50 as "the average flight time for the pilots is found to be 8.12 hours. the standard deviation reported by the faa is 0.72 hours, and there were 81 pilots in the sample."
What is test statistic?A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data match the distribution predicted by the statistical test's null hypothesis.
Here,
test statistic t is,
t = (x' - μ)/(σ/√n)
x'=8.12 hours
μ=8 hours
σ=0.72 hours
n=81 pilot
t=(8.12-8)/0.72/(√81)
=0.12/0.08
t=1.5
For this hypothesis test, the t-statistic will be 1.50 as "The pilots' average flight time was found to be 8.12 hours. There were 81 pilots in the sample, and the faa reported a standard deviation of 0.72 hours."
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adriel finds some dimes and quarters in his piggy bank. how much money (in dollars) does he have if he has 12 dimes and 10 quarters? how much money (in dollars) does he have if he has xx dimes and yy quarters?
Answer:
$3.70
Step-by-step explanation:
12 dimes, and dimes are ten cents each. So we will multiply 10*12=120. Which is $1.20.
10 quarters, and quarters are twenty-five cents each. So we will multiply 10*25=250. Which is $2.50
Now we take our two totals and add them together. 1.20+2.50=3.70.
So we have $3.70.
I hope this helps!!!
How do you solve this equation to find x?
Answer: x=10
Step-by-step explanation:
Images below
Help this helps
a manufacturer knows that their items have a lengths that are skewed right, with a mean of 18.8 inches, and standard deviation of 6.2 inches. if 48 items are chosen at random, what is the probability that their mean length is greater than 20.1 inches?
The probability that their mean length is greater than 20.1 inches is 0.32.
Standard deviation:
The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
The given value are:
Mean = 18.8 inches
Standard deviation = 6.2 inches
We have to find the probability that their mean length is greater than 20.1 inches.
Variance of sample mean = 6.2 / 48
= 0.13
S.D of sample mean= [tex]\sqrt{0.13}[/tex]
= 0.36
Z score for the length of 20.1 is ( 20.1 - 18.8) / 0.36 = 0.468
The p-value for 0.468 in the standard normal table is 0.32.
Therefore 0.32 chance of the sample means is greater than 20.1 inches.
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Given that ABCD is a rectangle, where EC = 7x -3 and AE=4x + 8. Find DE.
The length of segment DE on the rectangle, considering the midpoint, is given as follows:
DE = 22.67.
What is the midpoint?The midpoint of a segment divides a segment into two segments of equal length, having half the length of the entire segment.
In this problem, the diagonal of the rectangle represented by segment AC has midpoint E, hence the measure of x is calculated as follows:
EC = AE.
The measures are as follows:
EC = 7x - 3.AE = 4x + 8.Hence:
7x - 3 = 4x + 8
7x - 4x = 8 + 3
3x = 11
x = 11/3.
Segment DE is also half of a diagonal, hence it's length is obtained with the numeric value of any segment EC or AE, as follows:
DE = EC = 7x - 3 = 7 x 11/3 - 3 = 77/3 - 9/3 = 68/3 = 22.67.
Missing InformationThe rectangle is given by the image at the end of the answer.
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Dakota earned $15.75 in interest in Account A and $28 in interest in Account B after 21 months. If the simple rate is for 3% for Account A and 4% for Account B, which account had the greater principal?
The greater principal is there for Account A as $400.
What is simple interest?Simple interest can be defined as a type of interest where the rate is applied on the same principal.
Given that,
The interest for Account A is $15.75 and Account B is $28.
The total time for interest is 21 months.
Rate of interest for Account A is 3% and Account B is 4%.
Now, the time period can be written in years as,
21 months = 21 / 12 years
= 7 / 4
Suppose the principal for Account A and Account B is P₁ and P₂ respectively.
The formula for simple interest is given as,
(P × r × t) / 100
Substitute the respective values for both the accounts to get,
For Account A,
15.75 = (P × 3 × 7 / 4) / 100
⇒ P = (1575 × 4) / (3 × 7)
⇒ P = 300
For Account B,
28 = (P × 4 × 7 / 4) / 100
⇒ P = 2800 / 7
⇒ P = 400
Hence, Account B had greater principal.
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-16 > -4y solve for the inequality of y and simplify your answer as much as possible
The given inequality solved for y is y > 4
Solving linear inequalitiesFrom the question, we are to solve the given linear inequality.
To solve an inequality, we will solve for the variable in the inequality.
The given inequality is
-16 > -4y
The variable in the inequality is y.
Now, we will solve for y
-16 > -4y
Divide both sides by -4
-16/-4 > -4y/-4
4 < y
Thus,
y > 4
Hence, the solution is y > 4
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line JK passes through points J(-4,-5) and k(-6,3). if the equation of the line is written in slope-intercept form, y=mx+b, what is the value of b?
The value of b of the equation is -9/5
How to find the value of b with the equation in slope-intercept form?Given that: line JK passes through points J(-4,-5) and K(-6,3) and if the equation of the line is written in slope-intercept form, y=mx+b
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system
Using the y-y₁/y₂-y₁ = x-x₁/x₂-x₁
where (x₁, y₁) = (-4,-5) and (x₂, y₂) = (-6,3), the equation is:
y-(-5) / 3-(-5) = x-(-4)/-6-(-4)
y+5 / 3+5 = x+4 /6+4
(y+5)/8 = (x+4)/10 cross multiply:
10(y+5) = 8(x+4)
10y + 50 = 8x + 32
10y = 8x +32 - 50
10y = 8x - 18
y = 8x/10 - 18/10
y = 4x/5 - 9/5
Comparing y = 4x/5 - 9/5 with y=mx+b
b = -9/5
Therefore, the value of b is -9/5
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In AJKL, JL is extended through point L to point M, m/LJK = (x+9)°,
m/JKL = (x - 2)°, and m/KLM = (5x - 11)°. Find m/LJK.
For the given triangle JKL, the value of x is 10. An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint.
What is meant by angle?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. Angle is derived from the Latin word angelus, which means "corner." An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angelus," which means "corner." The two rays are known as the sides of an angle, and the common endpoint is known as the vertex.When two lines intersect at a common point, an angle is formed. They are expressed in degrees, which are denoted by the symbol °.Given information:
In ∠J K L,JL is extended through point L to point M.
[tex]$&m \angle J K L=(2 x+14)^{\circ} \\[/tex]
[tex]$&m \angle L J K=(3 x+15)^{\circ} \\[/tex]
[tex]$&m \angle K L M=(7 x+9)^{\circ}[/tex]
See the attached figure.
At point L, the measure of angle JLK will be as,
[tex]$&m \angle J L K=180-m \angle K L M=180-7 x-9 \\[/tex]
[tex]$&=(171-7 x)^{\circ}[/tex]
Now, in triangle JKL, use the angle sum property to find the value of x as,
[tex]$$m \angle J K L+m \angle L J K+m \angle J L K=180[/tex]
[tex]$$$(2 x+14)^{\circ}+(3 x+15)^{\circ}+(171-7 x)^{\circ}=180$[/tex]
-2 x+200=180
2 x=20
x=10
Therefore, the value of x for the given triangle JKL is 10.
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does this equal to 10 or 5 abit confused I’ll brainlist .
The ratio of money in Brian's wallet to
Colin's wallet one day was 7:2.
Brian spent £39 that day.
Brian now had £4 less than Colin.
How much did Brian initially have?
Brian has £63 Initially, by using the ratio and proportion method.
What are Ratio and Proportion?
In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Numerous examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.
An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometers per hour is equal to the time it needs to travel 500 kilometers in five hours. Example: 100 km/hr = 500 km/5 hour. The division technique of comparing two amounts can be quite effective in some circumstances. We can argue that a ratio is a comparison or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio may be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".
In the question, It is given that:
The ratio of money in Brian's wallet to Colin's wallet one day was 7:2.
Let 7x denotes the amount in Brian's wallet and 2x denote the amount in Colin's wallet on that day.
we know that:
Brian spent £39 that day.
Amount left in Brian's wallet = 7x- 39
Brian now had £4 less than Colin.
⇒ 2x -4= 7x- 39
⇒ 7x-2x=4+39
⇒ 5x=35
⇒ x=7 [Divide both sides by 5 ]
So , The initial amount in Brian's wallet = 7(7)= £49
The initial amount in Colin's wallet = 2(7)= £14
The amount they had together = £49+£14 = £63
So, They had £63 altogether initially.
Therefore, Brian has £63 Initially.
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Answer: £14
Step-by-step explanation: Because Hegarty Maths says it is when I got this same Question Wrong :(Patricia has $3425.82 in her checking account. How much does she have in her account after
she makes a deposit (puts in )of $9120.75 and a withdrawal (takes out) of $185.90
We're given :
Patricia originally has $3425.82 in her account.
After that, she deposits $9120.75, meaning her amount in her account goes up by $9120.75
Lastly, she withdraws $185.90, meaning her amount in her account goes down by $185.90.
Therefore, after the transactions, she has a total of : 3425.82 + 9120.75 - 185.90 = $12360.67
work out the minimum number of hikers who could have walked between 6 miles and 17 miles work out the maximum number of hikers who could have walked between 6 miles and 17 miles
The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
We need to find the maximum number of hikers who could have walked between 6 miles and 17 miles.
What is meant by minimum and maximum value?When the derivative equals 0, rearrange the function using elementary algebraic principles to find the value for x. The x-coordinate of the function's vertex, which is where the maximum or lowest will occur, is provided in this answer. the solution back into the original function to determine the minimum or maximum.
From the table, we can see
Between intervals 5≤x<10 there are 2 hikers
Between intervals 10≤x<15 there are 9 hikers
Between intervals 15≤x<20 there are 8 hikers
So, total number of hikers = 2+9+8
= 19
Hence, the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
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(10x-20)°
(6x + 8)º. help
Answer:
x=12°
Step-by-step explanation:
10x-20+6x+8=180°
16x=180+20-8
16x=192
x=12°
The system of conics has two solutions.
(x−4)^2 + (y+1)^2 = 9
(x−4)^2/9 + (y+1)^2/81 = 1
What are the solutions to this system of conics?
The system of equations has its solutions to be (1, -1) and (7, -1)
How to solve the system of equations?The system of equations is given as
(x−4)² + (y+1)² = 9
(x−4)²/9 + (y+1)²/81 = 1
Make (y + 1)² the subject in the equation (x−4)² + (y+1)² = 9
So, we have
(y+1)² = 9 - (x−4)²
Substitute (y+1)² = 9 - (x−4)² in (x−4)²/9 + (y+1)²/81 = 1
This gives
(x−4)²/9 + [9 - (x−4)²]/81 = 1
Split
(x−4)²/9 + 9/81 - (x−4)²/81 = 1
Collect the like terms
(x−4)²/9 - (x−4)²/81 = 1 - 9/81
Evaluate the like terms
[9(x−4)² - (x−4)²]/81 = 72/81
So, we have
9(x−4)² - (x−4)² = 72
Evaluate the difference
8(x−4)² = 72
Divide by 8
(x−4)² = 9
Take the square roots
x - 4 = ±3
So, we have
x = 4 ± 3
Evaluate
x = 1 or 7
Substitute x = 1 or 7 in (y+1)² = 9 - (x−4)²
(y + 1)² = 9 - (1−4)² or (y + 1)² = 9 - (7−4)²
This gives
(y + 1)² = 0 or (y + 1)² = 0
This gives
y + 1 = 0
Evaluate
y = -1
Hence, the solution is (1, -1) and (7, -1)
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An animal shelter has 2 cats for every 3 dogs. If there are 45 animals in the shelter, how many dogs are there?
Answer: 27 dogs
Step-by-step explanation: 2 cats + 3 dogs= 5 in total for animals. 2/5x45=18 cats
3/5x45= 27 dogs
27+18=45 animals
There is 27 dogs in the shelter
there have been 2 earthquakes in the magnitude range 6.0-7.0 in the san francisco area over the past 30 years. what is the mean recurrence interval of earthquakes in this magnitude range?
The mean recurrence interval between earthquakes of this magnitude range over the previous 30 years essentially has been 4.769230 in a basically sort of big way in a subtle way.
Given, the earthquake's magnitude literally basically is between 6.0 and 7.0 in a very definitely big way, or so they for all intents and purposes thought. occurrences = 2 earthquakes
Duration: 30 years
particularly Mean Earthquake Recurrence Interval,
T=(n+1) / m
Where m = 6+7 / 2 = 6.5 , n = 30
T = ( 30+1)/6.5
= 31/6.5
= 4.769230
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Solve the equation for y
Answer:
y = [tex]\frac{2}{3}[/tex] x - 6
Step-by-step explanation:
y - [tex]\frac{2}{3}[/tex] x = - 6 ( isolate y by adding [tex]\frac{2}{3}[/tex] x to both sides )
y = [tex]\frac{2}{3}[/tex] x - 6
solve this :)
-7m+10m-8=25
Answer:
[tex]\huge\boxed{\sf m = 11}[/tex]
Step-by-step explanation:
Given equation:-7m + 10m - 8 = 25
3m - 8 = 25
Add 8 to both sides
3m = 25 + 8
3m = 33
Divide 3 to both sides
m = 33/3
m = 11
[tex]\rule[225]{225}{2}[/tex]
he management of an indoor shopping mall wants to survey its shoppers about the layout of the stores in the mall. at a specified time one day, they send a team of interviewers to survey 2 randomly selected customers in each of the 48 stores in the mall. this scenario describes
The scenario describes the stratified random sampling method .
There are many sampling techniques to collect sample from a given population such as Simple random sampling , Systematic Sampling , Cluster Sampling and so on . All of them vary in reliability , accuracy and efficiency .
Stratified Random Sampling : It is a method of sampling in which division of population is done into smaller subgroups known as strata .The strata are formed based on member's shared attributes or characteristics . It has numerous applications . It is also called proportional random sampling or quota random sampling .
Therefore , the scenario describes the stratified random sampling method .
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Sophia earned $36 at her job when she worked for 4 hours. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The ratio when Sophia earned $36 at her job when she worked for 4 hours is 1:9.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
From the information, Sophia earned $36 at her job when she worked for 4 hours.
The equivalent ratio to illustrate the information will be:
= 4 / 36
= 1/9
= 1:9
Note that the coordinates point weren't given in the question.
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a manufacturer wants to increase the absorption capacity of a sponge. based on past data, the average sponge could absorb 3.5 ounces. after the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9. what is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
Reject a null hypothesis because computed t is higher than 2.821 is the decision rule.
Define the term hypothesis?The hypothesis is a succinct statement of the researcher's estimate of the findings of the study, that may or may not be confirmed by the results, in such a scientific experiment or survey. The scientific method's fundamental step is hypothesis testing.A statistical hypothesis known as a null hypothesis asserts because no statistical significance can be found in a collection of provided observations.For the given question;
Test hypothesis:
H₀; μ = 3.5
Upper tailed test:
Hₐ; μ > 3.5
Significance value; α = 10.
Then, degree of freedom.
Df = α - 1
Df = 10 - 1
Df = 9
The critical value;
t(₀.₀₁, ₉) = 2.821
Rejection region;
Rejected H₀ for t > 2.821
Thus, reject a null hypothesis because computed t is higher than 2.821 is the decision rule for the absorption amount of the sponge.
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Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term.
–4, –3, –2, –1, ...
Answer:
[tex]a_{n}[/tex] = n - 5
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
- 3 - (- 4) = - 2 - (- 3) = - 1 - (- 2) = 1
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 4 and d = 1 , then
[tex]a_{n}[/tex] = - 4 + 1 (n - 1) = - 4 + n - 1 = n - 5
a researcher measures the amount of sugar in several cans of the same soda. the mean is 39.01 with a standard deviation of 0.5. the researcher randomly selects a sample of 100. find the probability that the sum of the 100 values is greater than 3,908. (round your answer to four decimal places.)
Using the concepts of probability, we got that 0.0764 is the probability that the sum of the 100 values is greater than 3,908 when a researcher measure the amount of sugar in several cans of the same soda.
The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:
Z=(X-μ)/σ
The z-score measures how many standard deviations the measure is above or below the mean.Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation .For this problem, these parameters are given as follows:
μ=39.01,σ=0.5,n=100,s=0.5/√100=0.05
A sum of 3908 is equivalent to a sample mean of 3908/100 = 39.08, which means that the probability is the p-value of Z when X = 39.08, hence:
Z=(X-μ)/σ
By the Central Limit Theorem:
Z=(X-μ)/s
=>Z=(39.08-39.01)/0.05
=>Z=(0.07)/0.05
=>Z=7/5
=>Z=1.4
Z = 1.4 has a p-value of 0.0764.
Hence, the probability that the sum of the 100 values is greater than 3,908 is 0.0764.
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A C B D E Which statement cannot be assumed from the figure? OA A ZABD and ZDBE are supplementary OB BD bisects ZADE. Oc LCDA and ZADE are complementary. OD ZEDB and ZBDA are adjacent and are not complementary.
The statement that cannot be assumed from the figure is
B) BD bisects ∠ADE
What are Supplementary and Complementary Angles?
Supplementary angles are two angles that have a sum of 180°.
Complementary angles are two angles that have a sum of 90°.
Given data ,
From the figure we can arrive at each conclusions
A)
∠ABD and ∠DBE are supplementary
Now , from the figure we can see that point B lies on the line AE
And , ∠ABD + ∠DBE = 180°
Hence , ∠ABD and ∠DBE are supplementary and the statement is TRUE
B)
Bisecting a line means dividing the line into two equal parts
And from the figure BD does not bisect ∠ADE
Hence , BD does not bisect ∠ADE so the statement is FALSE
C)
∠CDA and ∠ADE are complementary
From the figure we can see that ∠EDC is 90°
And , ∠CDA + ∠ADE = ∠EDC
So , ∠CDA + ∠ADE = 90°
Hence , ∠CDA and ∠ADE are complementary and the statement is TRUE
D)
∠EDB and ∠BDA are adjacent and are not complementary
From the figure we can see that ∠EDB and ∠BDA are adjacent
∠EDB + ∠BDA ≠ 90°
Hence , they are not complementary and the statement is TRUE
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find the equation of a line that is equidistant from the points (2,4) and (-4,6)
The equation of a line is y = 5x - 6
What is Equation of line ?
A straight line's general equation is y = mx + b, where m denotes the gradient or slope and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.
The given points are (2, 4) and (-4, 6)
The equation of line is given ,
y = mx + b
where, m = slope
b = y - intercept
To find slope , we have formula
slope (m) = (y2 - y1) / (x2 - x1)
let, (x1, x2) = (2, 4) and
(y2, y1) = (-4, 6)
Now, put the values in slope formula,
m = ( 6 - (-4) ) / ( 4 - 2)
m = (6 + 4) / 2
m = 10 / 2
m = 5
We get slope, now find y-intercept i,e, 'b'
y = 5x + b
so take any point to find 'b'
Let's take the point (2, 4) which is (x, y) so now put the (x, y) and find 'b'.
4 = 5 * 2 + b
4 = 10 + b
b = 4 - 10
b = -6
so, now put the values of slope and y-intercept in equation of line i.e, y = mx + b
y = 5x - 6
Hence, the equation of a line is y = 5x - 6
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Can anyone write the equation of the graph?
The equation of given graph is y = |x - 3| + 5.
The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.
Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.
As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.
So, by putting the value of vertex in general equation we get the equation of the graph,
y = |x - 3| + 5
Therefore, the equation of given graph is y = |x - 3| + 5.
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