The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).
The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.
The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:
(i) Worked at least one hour as paid employees
(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise
(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.
⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.
⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.
⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.
Therefore, all the options are correct , which is Option(d).
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The given question is incomplete, the complete question is
Who of the following are included in the Bureau of Labor Statistics "employed" category?
(a) certain unpaid workers
(b) part-time workers
(c) workers on vacation
(d) All of the above are correct.
Lincoln spent $95 of his pocket money every month and saved the rest. This month he
decided to spend only $75, thereby increasing his savings by 40%.
a)What was his pocket money every month?
b) Find the ratio of his expenditure to his savings for this month?
A baseball team has home games on Thursday and Sunday. The two games together earn $4064.50 for the team. Thursday's game generates $400.50 less than Sunday's game. How much money
was taken in at each game?
The Sunday game brought in $2232.50, while the Thursday game brought in $1832.00.
What does this gain and loss mean?A company's income, costs, and profit are compiled in a profit and loss (P&L) statement, a financial report. It provides information to investors and other interested parties about a company's operations and financial viability.
The issue informs us that the combined revenue from the two games was $4064.50.
S + (S - 400.50) = 4064.50
Simplifying the left side, we get:
2S - 400.50 = 4064.50
Adding 400.50 to both sides, we get:
2S = 4465
Dividing both sides by 2, we get:
S = 2232.50
So the Sunday game generated $2232.50, and the Thursday game generated $2232.50 - $400.50 = $1832.00.
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3. You get three summer jobs to help you save for college expenses. In your job as a cashier,
you work 20 hours per week and earn $9.50 per hour. Your second and third jobs are at a local
hospital. There, you earn $9.00 per hour as a payroll clerk and $7.00 per hour as an aide. You
always work 10 hours less per week as an aide than you do as a payroll clerk. Your total weekly
salary depends on the number of hours you work at each job.
a. Determine the input and output variables for this situation.
b. Explain how you calculate the total amount earned each week.
c. If x represents the number of hours you work as a payroll clerk, represent the number of
hours you work as an aide in terms of x.
d. Write an equation that describes the total amount you earn each week. Use x to represent
the input variable and y to represent the output variable. Simplify the expression as much
as possible.
e. If you work 12 hours as a payroll clerk, how much will you make in one week?
f. What are the practical replacement values for x? Would 8 hours at your payroll job be a
realistic replacement value? What about 50 hours?
g. When you don't work as an aide, what is your total weekly salary?
Please help!
Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.
What is a Variable?A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. .
a. Input variables: hours worked as a cashier, payroll clerk, and assistant.
The total amount earned each week is the output variable.
b. To determine the weekly total, multiply the number of hours worked at each job by the hourly rate and put them together. As a result, the equation would be:
Total weekly wage = (hours worked as a cashier x cashier hourly rate) + (hours worked as a payroll clerk x payroll clerk hourly rate) + (hours worked as an aide x rate per hour as an aide)
c. The amount of hours worked as an assistant is always 10 hours fewer than that of a payroll clerk. Therefore, if x denotes the number of hours worked as a payroll clerk, then the number of hours worked as an assistant may be denoted as (x - 10).
d. The equation describing the total money earned each week is as follows:
(20 x 9.5) + (x x 9) + ((x - 10) x 7) = y
This expression is simplified as follows:
y = 190 + 9x - 70 + 7x
y = 16x + 120
Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.
f. The realistic replacement values for x would be determined by the maximum number of hours you may work at each job as well as the amount of time available to work. Working 8 hours as a payroll clerk may be a reasonable substitute value if you have restricted availability, but 50 hours is unlikely.
g. If you do not work as an aide, you may calculate your total weekly income by setting the number of hours worked as an aide to zero in the calculation for the total amount earned each week. This results in:
y = 16x + 120 + 0
y = 16x + 120
As a result, the total weekly wage would be determined only by the number of hours performed as a cashier and payroll clerk.
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Lucy is trying to find the radius of a circle. She is stuck on this step: 121=r
2
What is the radius?
Answer:
I am not good at this but i gess itis 11 √121 equals 11
The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 360 grams and a standard deviation of 9 grams find the weight that corresponds to each event(use excel or appendix c to calculate the z value round your final answers to 2 decimal places
Answer:
Step-by-step explanation:
We'Re looking at a normal distribution here- let's start by drawing it out to the mean me- is 315 grams standard. Deviation is 16 point. We want to know the weight corresponding to each of these events and we can use either the appendix which i assume is a z, school table or excel so the first 1. We want the highest 20 percent up here somewhere. This is what we would call the 80 percent. It separates the bottom 80 percent from the highest 20 percent. So how do we work the well? We need to start by getting the z score for it. So how do we get that, while in excel you're going to use the norm inverse function which looks like this? So it's calls norm and then in here you just put in x, where x is your percentage and that will spit out the z score and i'm using this rather than a table, because it will give me a more exact value. So we're going to do that, and so here the percent is the 80, so it's not .8 and that spits out the z score of nort .8416 to 4 decimal places. But i'm always going to this exact score, because we now have to turn it from a z score to a piece of real data. Z score is a measure of how many standard deviations away from the mean a value is so we're. Looking for the value not .84 standard deviations, above the mean or if we write it like this x, is equal to z, sigma plus mu. So here we take our exact zedscore, because we can still just use excels, multiply it by 16 and add it on to the mean and we'll get our value of 328.447328 .47 grams to 2 decimal places for part b. We want to be middle 60 percent. Now we need to cut off points and within here where, in this interval we have 60 percent of values, which means we have 40 percent of values, not in here. So we can label our 3 sections. These 2 add up to 40 percent, so they have to be 20 percent. Each are called nor .2 and not .2, and then this middle bit here is nor .6 for the total of 100 percent point. So we need these cut off points when you, the z, scores first, and because these are equal distances away from a mine they're going to have the same z score. Just 1 is going to be positive or negative, so z is going to be equal to plus and minus. Let'S look at the lower 1. This is the 20 percent here so into this excel command. We put 20 percent nor .2 and out of it we get the z score of minus, not .8416. So it's actually very similar to the top question, because the top question asked you for the 80 percent be 80 percent. Is the upper cut off point here? 20? Is below cutoff point, so we already have the up 1, let's just calculate below 1, so we've got to be minus, nor .8416 multiplied by 16, but the standard deviation and on to the mean- and we get 301.53 and the upper cut off point is from part A so that's the middle 60 percent makes more space a part c. We want to be highest 80 percent. So now what we want is the cut off between the lowest 20 and the highest 80, which we've just got from part c part b. It'S this lower 1, here, 301.53 grams. That'S an easy! 1! Now we want the lowest 15 percent, so the lowest 15 percent is the 15 percent. So we go to our exylgamant put in the 15 for percent, so that would be no .15 and it's a z score of minus 1.036 keeping the exact value put into this formula. We multiply our z by 16, as on 315, to get 298.42 grams.
The weight that corresponds to this event are approximately 344.03 grams and 375.97 grams.
What is normal distribution?To find the weight that corresponds to each event, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given mean and standard deviation to z-scores using the formula:
z = (x - μ) / σ
where x is the weight we want to find, μ is the mean (360 grams), and σ is the standard deviation (9 grams).
Then, we can use a standard normal distribution table or calculator to find the probability of each event, and convert it back to a weight using the inverse of the z-score formula:
x = μ + z * σ
where z is the z-score that corresponds to the desired probability.
Event 1: The weight is less than 345 grams.
z = (345 - 360) / 9 = -1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.67 is approximately 0.0475.
x = 360 + (-1.67) * 9 = 344.03 grams
Therefore, the weight that corresponds to this event is approximately 344.03 grams.
Event 2: The weight is between 355 and 365 grams.
First, we need to find the z-scores that correspond to the two boundaries:
z1 = (355 - 360) / 9 = -0.56
z2 = (365 - 360) / 9 = 0.56
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -0.56 is approximately 0.2123, and the probability of a z-score less than 0.56 is approximately 0.7123. Therefore, the probability of a z-score between -0.56 and 0.56 is:
0.7123 - 0.2123 = 0.5
x1 = 360 + (-0.56) * 9 = 355.16 grams
x2 = 360 + (0.56) * 9 = 364.84 grams
Therefore, the weight that corresponds to this event is any weight between 355.16 and 364.84 grams.
Event 3: The weight is greater than 375 grams.
z = (375 - 360) / 9 = 1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1.67 is approximately 0.0475.
x = 360 + (1.67) * 9 = 375.97 grams
Therefore, the weight that corresponds to this event is approximately 375.97 grams.
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in the right triangle round to your nearest tenth. 18 15 X help please
The value οf the given angle x = 39.8 degree
What is Trigοnοmetric Functiοns?Trigοnοmetry uses six fundamental trigοnοmetric οperatiοns. Trigοnοmetric ratiοs describe these οperatiοns. The sine functiοn, cοsine functiοn, secant functiοn, cο-secant functiοn, tangent functiοn, and cο-tangent functiοn are the six fundamental trigοnοmetric functiοns.
The ratiο οf sides οf a right-angled triangle is the basis fοr trigοnοmetric functiοns and identities. Using trigοnοmetric fοrmulas, the sine, cοsine, tangent, secant, and cοtangent values are calculated fοr the perpendicular side, hypοtenuse, and base οf a right triangle.
In the figure tanx = p/h
[tex]x = tan^{-1(15/18)}[/tex]
x = 39.8
Hence the value οf the given angle x = 39.8 degree
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The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble?
A) 11
B) 33
C) 32
D) 22
Answer:
B) 33 times.
Step-by-step explanation:
The total amount of pebbles is 50. There is 22 yellow pebbles.
Note that 3/2 * 50 is 75. 3/2 * 22 = 33.
He should expect to choose a yellow pebble B) 33 times.
What percent of 2160 is 270?
The percent of the number 2160 which is 270 is 12.5%.
Given a number 2160.
It is required to find the percent of this number which is 270.
Let x be the percent of 2160 which is 270.
Then, this can be written as:
2160 × (x/100) = 270
2160 × x = 270 × 100
2160 × x = 27000
x = 27000 / 2160
= 12.5
Hence the required percentage is 12.5%.
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Please help...Experimental Probability and Theoretical Probability..I'm getting the wrong answer
Answer:
(a) 0.413
(b) 0.400
(c) 1 — ... the difference should be small
Step-by-step explanation:
Given a table of experimental results from 1000 spins and a diagram of a spinner, you want the experimental and theoretical probabilities of landing on Red. You also want a statement comparing them.
(a) ExperimentalThe table tells you 1000 experiments resulted in 413 reds. The experimental probability of landing on red is ...
413/1000 = 0.413
(b) TheoreticalThe diagram of the spinner shows 10 equal segments, of which 4 are red. The theoretical probability of landing on red is ...
4/10 = 0.400
(c) ComparisonThe presumption in statistics is that any experiment repeated a sufficient number of times should see experimental results approaching theoretical results. We expect a small difference between experimental and theoretical results for a large number of trials.
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Which of these shapes is a polygon?
Image :
A
B
C
Answer: The correct answer is C, the X.
which of the following assumptions must be true in order for this to be the correct sampling distribution
Since means cannot be smaller than 0, the sampling distribution of the mean is always right skewed.
No matter the sample size, the form of the sampling distribution of means is always the same as the population distribution.
We require two assumptions in order to apply the sampling distribution model to sample proportions: The selected values must be independent of one another, according to the independence assumption. The Sample Size Assumption demands that the sample size, n, be sufficiently large.
While doing a t-test, it is typical to make the following assumptions: the measuring scale, random sampling, normality of the data distribution, sufficiency of the sample size, and equality of variance in standard deviation.
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the actual question is :
Which of the following is true about the sampling distribution of the mean?
a. It is an observed distribution of scores
b. It is a hypothetical distribution
c. It will tend to be normally distributed with a
standard deviation equal to the population
standard deviation
d. The mean will be estimated by the standard
error
e. Both (a) and (b)
10 points! HELP ASAP PLEASE HELP ME FIND THE AREA and the perimeter
Answer:
307ft^2
Step-by-step explanation:
To explain this, you are looking for the area of half a circle + the area of a triangle.
To first find the area of half a circle, we need the equation Area = pir^2/2
Plug-in radius, which is 10ft
pi(10)^2/2
= 157ft^2
Next, we find the area of the triangle. The equation to find the area of a triangle is A=1/2(b)(h)
B=base
h=height
To find the base, we simple make the base equal to the diameter of the circle, which is the radius multiplied by 2
So base = 10*2 = 20
The height is given so
height=15
Plug in base and height = 20*15/2
= 150ft^2
Then you want to add both areas found together
157ft^2+150ft^2
= 307ft^2
check all statements, that correctly describe traits and restrictions of superclasses and subclasses.
The statement "car:toyota" correctly describes a subclass (Toyota) of the superclass (car). Similarly, "ducks:pond" correctly describes a subclass (ducks) of the superclass (pond). So, option A) and B) are correct.
Superclasses and subclasses are used in object-oriented programming to create a hierarchical relationship between classes. In this hierarchy, a subclass is a specialized version of a superclass.
The statement "car:toyota" and "ducks:pond" correctly describes a subclass (Toyota, ducks) of the superclass (car, pond). However, "toes:feet" and "rock:stone" do not correctly describe a subclass-superclass relationship. Rather, they describe a part-whole relationship. Toes are part of feet and rock is a type of stone.
It is important to note that a subclass can inherit traits from its superclass, but it may also have its own unique traits and restrictions. For example, a Toyota car may have some traits inherited from the car superclass, but it may also have unique features that set it apart from other car subclasses. So, correct answer are option A) and B).
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____The given question is incomplete, the complete question is given below:
check all statements, that correctly describe traits and restrictions of superclasses and subclasses.
car:toyota
ducks:pond
toes:feet
rock:stone
Which graph represents the function f(x)=∣x+1∣−3?
By looking at the vertex of the graph, we can see that the fourth graph is the correct option.
Which graph represents the function f(x)=∣x+1∣−3?Here we want to see which one of the given graphs represents the given absolute value function.
Remember that for the absolute value function:
f(x) = |x - a| + b
Has a vertex at the point (a, b) and opens up.
Then in this particular case, with the function f(x)=∣x+1∣−3, the vertex will be at the point (-1, -3), so we just need to identify which one of the given graphs has that vertex, we can see that the correct option is the fourth option.
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For each dozen cookies Rachel used 1 1/2 cups of milk. How many cups of milk did she use for 16 dozen cookies?
Show your work.
Answer: For 16 dozen cookies, Rachel used 24 cups of milk.
Step-by-step explanation:
We know that for each dozen cookies, Rachel uses 1 1/2 cups of milk. To find out how much milk she used for 16 dozen cookies, we need to multiply the amount of milk used for one dozen by 16. Here are the steps:
Calculate the amount of milk used for one dozen cookies:
1 1/2 cups of milk = 3/2 cups of milk
For one dozen cookies, Rachel used 3/2 cups of milk.
Multiply the amount of milk used for one dozen by 16:
3/2 cups of milk x 16 = 24 cups of milk
Therefore, Rachel used 24 cups of milk for 16 dozen cookies.
If each dozen cookies Rachel used [tex]1\frac{1}{2}[/tex] cups of milk then 24 cups of milk she uses for 16 dozen cookies
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that each dozen cookies Rachel used [tex]1\frac{1}{2}[/tex] cups of milk.
We have to find the number of cups of milk required to make 16 dozen cookies
As Rachel used [tex]1\frac{1}{2}[/tex] cups of milk for 1 dozen cookies.
She would use [tex]1\frac{1}{2}[/tex] x 16 = 24 cups of milk for 16 dozen cookies.
Hence, if each dozen cookies Rachel used [tex]1\frac{1}{2}[/tex] cups of milk then 24 cups of milk she uses for 16 dozen cookies
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Angle 4 and angle ____ are vertical angles.
A: 1
B: 2
C: 3
Answer:
angle 4 and angle 1 are vertical angles
Step-by-step explanation:
vertical angles are opposite each other
please help me 25 points
Answer:
7. 300 miles
8. 60 miles
9. 5 miles
10. 1000 meters
Step-by-step explanation:
7.
We Take
60 x 5 = 300 miles
So, Ruth drives 300 miles in 5 hours.
8.
5 miles = 10 minutes
1 mile = 2 minutes
2 hours = 120 minutes
We Take
120 / 2 = 60 miles
So, Carl drive 60 miles in 2 hours
9.
1 hour and 25 minutes = 85 minutes
We Take
85 / 17 = 5 miles
So, Nick travels 5 miles in an hour and 25 minutes.
10.
100 meters = 2 minutes
50 meters = 1 minute
We Take
50 x 20 = 1000 meters
So, Stan swims 1000 meters in 20 minutes.
Answer:
7. 300 miles/hours
8. 60 miles in 2 hours
9. 5 miles in 2 hours and 25 mins.
10. 1000 meters in 20 minutes.
Step-by-step explanation:
7. 60 x 5= 300 miles/hours
8. 5 miles in 10 minutes so in 2 hours it will be 5 x 12 = 60 miles in 2 hours
9. 5 miles in 2 hours and 25 mins.
10. 1000 meters in 20 minutes.
he brain volumes (cm3) of 20 brains have a mean of 1190.7 cm3 and a standard deviation of 120.4 cm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1411.5 cm3 be significantly high?
Answer:
Step-by-step explanation:
The range rule of thumb states that the range of a dataset is approximately four times the standard deviation. Using this rule, we can estimate the range of brain volumes in this dataset:
Range ≈ 4 × standard deviation = 4 × 120.4 cm3 = 481.6 cm3
To identify the limits separating values that are significantly low or significantly high, we can add and subtract half the range to and from the mean:
Lower limit = mean - (range/2) = 1190.7 cm3 - (481.6 cm3 / 2) = 949.9 cm3
Upper limit = mean + (range/2) = 1190.7 cm3 + (481.6 cm3 / 2) = 1431.5 cm3
Therefore, any brain volume below 949.9 cm3 or above 1431.5 cm3 would be considered significantly low or significantly high, respectively.
A brain volume of 1411.5 cm3 is within the range of values that are not considered significantly high or low. Its z-score can be calculated as follows:
z-score = (1411.5 - 1190.7) / 120.4 = 1.84
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 1.84 or higher is approximately 0.0336. This means that a brain volume of 1411.5 cm3 would be considered uncommon, but not extremely rare.
Is this figure a polygon dont answer if you don’t know the answer
Polygon - a plane figure with at least three straight sides and angles, and typically five or more.
Answer:
No
Step-by-step explanation:
Since a polygon has straight sides, with 3 or more, it cannot be a polygon since one side is curved.
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Perpendicular lines form acute angles.
A) True
B) False
Answer:
B) False
Step-by-step explanation:
Perpendicular lines form right angles. It does not form acute angles.
Given the equation x² + 4x + y²-2y = 20: (HINT: Type in the equation is the desmos calculator and get the answers from the graph.)
What is the radius of the circle?
What is the center of the circle?
Answer:
The radius of the circle is 3.
The center of the circle is (-2, 1).
Step-by-step explanation:
Rewrite the equation in standard form:
We need to rewrite the given equation in standard form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. To do this, we complete the square for both the x and y terms.
x² + 4x + y²-2y = 20
(x² + 4x + 4) + (y² - 2y + 1) = 20 + 4 + 1
(x + 2)² + (y - 1)² = 25
Identify the center and radius:
Now that we have the equation in standard form, we can identify the center and radius of the circle.
The center is the point (-2, 1), which we can read directly from the equation.
The radius is the square root of the number on the right side of the equation, which is 5. Therefore, the radius is sqrt(5) or approximately 2.236.
Alternatively, we can also use the Desmos graphing calculator to plot the equation and visually determine the center and radius. When we plot the equation, we see that it forms a circle with center (-2, 1) and radius 3.
change these fractions to decimals 1/35
Answer:
Step-by-step explanation:
In the equation , c denotes consumption and i denotes income. What is the residual for the 5th observation if =$500 and =$475?
Residual for the 5th observation if =$500 and =$475 is -$166.25 The consumption function C = 300 + 0.75i represents the relationship between consumption and income in a simple economy with no taxes. In this function, C is the dependent variable, while i is the independent variable.
To find the residual for the 5th observation, we need to first calculate the predicted value of consumption (C1 ) for the given value of income (i). We can do this by plugging the value of i into the consumption function and solving for C1 :
C1 = 300 + 0.75i
For the first scenario where i = $500, the predicted value of consumption is:
C 1= 300 + 0.75($500) = $675
To calculate the residual, we need to subtract the predicted value of consumption from the actual value of consumption (C):
Residual = C - C1+
For the 5th observation where C = $500, the residual would be:
Residual = $500 - $675 = -$175
This means that the actual value of consumption is $175 less than the predicted value based on the consumption function.
Similarly, for the second scenario where i = $475, the predicted value of consumption would be:
C1 = 300 + 0.75($475) = $641.25
And the residual would be:
Residual = $475 - $641.25 = -$166.25
In both cases, the residuals are negative, indicating that actual consumption is less than predicted consumption. This could be due to factors such as unexpected changes in consumer behavior, fluctuations in the economy, or measurement errors in the data.
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The equation for a consumption function in a simple economy, where there are no taxes, is given by C = 300 + 0.75i, What is the residual for the 5th observation if =$500 and =$475?c denotes consumption and i denotes income.
can anyone help me with this question triangles?
The missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.
What is a triangle?Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x
So, x = 30.
Therefore, the missing side x is 30
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Debra, Alan, and Shen have a total of 122 in their wallets. Alan has less than $7 Debra. She has 3 times what Alan has. How much do they have in their wallets?
Answer:
Debra has $10.50, Alan has $3.50, and Shen has $108.
Step-by-step explanation:
Set up a system of equations to represent the situation.
Let a represent Alan's money, d represent Debra's money, and s represent Shen's money.
1. a + d + s = 122
2. a = d - 7
3. d = 3a
Use equation's 1 and 2 alone to calculate a and d. Substitute Eq 3 into Eq 2 such that
a = 3a - 7
-2a = -7
a = $3.50
Use Alan's money to calculate Debra's money.
d = 3(3.5)
d = $10.50
Now use values of a and d to calulate Shen's money, given the total.
s + 3.5 + 10.5 = 122
s + 14 = 122
s = $108
So, Debra has $10.50, Alan has $3.50, and Shen has $108.
find the linear approximation of f (x )equals fifth root of x when x equals 32.
This is the linear approximation of f(x) = 5th root of x when x = 32. To find the linear approximation of f(x) = 5th root of x when x = 32, we need to first find the equation of the tangent line at x = 32.
The derivative of f(x) = 5th root of x is: f'(x) = 1/(5x⁴/⁵)
So, at x = 32, we have f(32) = 2 and f'(32) = 1/80.
Using the point-slope form of a line, we can write the equation of the tangent line as:
y - 2 = (1/80)(x - 32)
Simplifying this equation, we get:
y = (1/80)x + (79/40)
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in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a)
The bases for the row space and null space of A, we put A into reduced row echelon form and solve for the null space. The dot product of basis vectors shows they are orthogonal.
To find the bases for the row space and null space of A, we perform row operations on A until it is in reduced row echelon form:
[ 1 -1 3 | 5 ] [ 1 -1 3 | 5 ]
[ 2 1 -5 | -9 ] -> [ 0 3 -11 | -19]
[-1 -1 2 | 2 ] [ 0 0 0 | 0 ]
[ 1 1 -1 | -1 ] [ 0 0 0 | 0 ]
The reduced row echelon form of A tells us that there are two pivot columns, corresponding to the first and second columns of A. The third and fourth columns are free variables. Therefore, a basis for the row space of A is given by the first two rows of the reduced row echelon form of A:
[ 1 -1 3 | 5 ]
[ 0 3 -11 | -19]
To find a basis for the null space of A, we solve the system Ax = 0. Since the third and fourth columns of A are free variables, we can express the solution in terms of those variables. Setting s = column 3 and t = column 4, we have:
x1 - x2 + 3x3 + 5x4 = 0
2x1 + x2 - 5x3 - 9x4 = 0
-x1 - x2 + 2x3 + 2x4 = 0
x1 + x2 - x3 - x4 = 0
Solving for x1, x2, x3, and x4 in terms of s and t, we get:
x1 = -3s - 5t
x2 = s + 2t
x3 = s
x4 = t
Therefore, a basis for the null space of A is given by the vectors:
[-3 1 1 0]
[ 5 2 0 1]
To verify that every vector in the row space of A is orthogonal to every vector in the null space of A, we compute the dot product of each basis vector for the row space with each basis vector for the null space:
[ 1 -1 3 | 5 ] dot [-3 1 1 0] = 0
[ 1 -1 3 | 5 ] dot [ 5 2 0 1] = 0
[ 0 3 -11 | -19] dot [-3 1 1 0] = 0
[ 0 3 -11 | -19] dot [ 5 2 0 1] = 0
Since all dot products are equal to zero, we have verified that every vector in the row space of A is orthogonal to every vector in the null space of A.
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_____The given question is incomplete, the complete question is given below:
in excercises 7 and 8 find bases for the row space and null space of a. verify that every vector in the row(a) is orthogonal to every vector in null(a). a = [ 1 -1 3 5 2 1 0 1 -2 -1 -1 1]
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 9 feet. Container B has a diameter of 8 feet and a height of 20 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
Step-by-step explanation:
the volume of container B is Travers from A to B.
so, the volume of the empty space in A is exactly the volume of container B.
the volume of a cylinder is
base area × height = pi×r² × height.
the reside is as always half of the diameter.
r = 8/2 = 4 ft
the volume of the empty space in A = the volume of container B =
= pi×4² × 20 = pi×16 × 20 = 320pi = 1,005.309649... ≈
≈ 1,005.3 ft³
Figure ABCD has been reflected across the y-axis to form figure
WXYZ. Which of the following statements is true?
A. MLA =MLY
B. MLD = MLX
C. AB = WX
D. AB = YZ
Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an answer does not exist, enter DNE.) f (x) = x^4 ? 8x^3 + 4relative minimum (x, y) =( )relative maximum(x, y) =( )
The relative maximum of the function is (0, 4), and the relative minimum is (6, -152).
To find the relative extrema of the function f(x) = x^4 - 8x^3 + 4, we first take the derivative of the function:
f'(x) = 4x^3 - 24x^2
Then we set f'(x) = 0 to find the critical points:
4x^3 - 24x^2 = 0
4x^2(x - 6) = 0
This gives us two critical points: x = 0 and x = 6.
Next, we find the second derivative of f(x):
f''(x) = 12x^2 - 48x
We can use the Second-Derivative Test to determine the nature of the critical points.
For x = 0, we have:
f''(0) = 0 - 0 = 0
This tells us that the Second-Derivative Test is inconclusive at x = 0.
For x = 6, we have:
f''(6) = 12(6)^2 - 48(6) = 0
Since the second derivative is zero at x = 6, we cannot use the Second-Derivative Test to determine the nature of the critical point at x = 6.
To determine whether the critical points are relative maxima or minima, we can use the first derivative test or examine the behavior of the function around the critical points.
For x < 0, f'(x) < 0, so the function is decreasing.
For 0 < x < 6, f'(x) > 0, so the function is increasing.
For x > 6, f'(x) < 0, so the function is decreasing.
Therefore, we can conclude that the critical point at x = 0 is a relative maximum and the critical point at x = 6 is a relative minimum.
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