The Natural Unemployment Rate based on the information is 5%.
What is natural rate of unemployment?The natural rate of unemployment is the lowest unemployment rate when inflation is stable, or the unemployment rate when inflation is not accelerating. The natural rate of unemployment (NAIRU) is the rate of unemployment caused by all factors other than changes in aggregate demand. Potential GDP estimates are based on the long-term natural rate.
The unemployment rate is the proportion of the total labor force that is unemployed but actively looking for work and willing to work. Cyclical unemployment is associated with an industry's business cycle. It is a direct result of a drop in consumer demand, which has resulted in a drop in labor demand. If cyclical unemployment rises, it indicates that the economy is slowing, which is not good.
Cyclical unemployment occurs when labor forces are reduced as a result of business cycles or economic fluctuations. If you are cyclically unemployed, it means that your employer has laid you off to save money during a period of slow business.
In this case, the unemployment will be:
= Actual unemployment rate - Cyclical unemployment rate
= 12% - 7%
= 5%
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Which graph represents the function f(x)=(13)−x?
Answer:
Bottom left
Step-by-step explanation:
Let's look at it as (1/3)^x first. This function would have a y-intercept of (0,1) (because (1/3)^0 is 1), and would then become (1/3) times smaller for every 1 unit increment of x. This would look like the top left graph in these options. However, we are given (1/3)^-x, which means, in terms of transformations, that the graph is flipped across the y-axis. Algebraically, this looks like (1/3)^(-x) which equals to [tex]\frac{1}{(1/3)^x}[/tex], which simplifies down to 3^x, which would look like the bottom left graph.
a square has a perimeter of 12 ft what is the length of each side
Answer:
3 feet
Step-by-step explanation:
All 4 sides are equal so 12/4=3
PLEASE HELP!!! QUESTION ON PICTURE
Answer:
27
Step-by-step explanation:
I broke the figure up into 3 rectangles.
5x2 = 10
2x3 = 6
4x5 = 20
This adds to 36. Then subtract out the green square of 9
36 - 9 = 27
2<-2x+6 or -18>-2x+6
x < 2 and x > 12 are the answers to the inequality expressions supplied.
What is an inequality expression
An algebraic inequality is a mathematical statement that uses the inequality sign to connect an expression to a value, a variable, or another expression. One-variable inequalities can have solutions that can be graphed on a number line or on a coordinate plane.
Given the inequality expressions below:
2<-2x+6 or -18>-2x+6
Solve individually;
2 < -2x + 6
2- 6 < -2x
-4 < -2x
-2x > -4
x < 4/2
x <2
For the inequality -18>-2x+6
-18 - 6 > -2x
-24 > -2x
-2x < -24
x > 24/2
x > 12
Hence the solution to the given inequality expressions are x < 2 and x > 12
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PLS HELP!!
Cruz had d $10 bills and 4 fewer $20 bills than he has $10 bills. Enter an algebraic expression to represent how much money Cruz has in dollars. Simplify the expression, if possible.
Answer:Here's the basic equation
m(d) = 10d + 20(d - 2) (the money total is the 10 dollar bills plus the 20 dollar bills (which are two less than the 10 dollars))
Step-by-step explanation:
To simplify it, start by distributing the 20:
m(d) = 10d + 20d - 40
add like terms
m(d) = 30d - 40
Help me please I dont know
Your friend asks you to help him study and will pay you 5 dimes the first time you help him. You agree to help if he multiplies your payment by 5 for each study session. After 2 study sessions, you will receive 25 dimes, and after 3 study sessions, you will receive 125 dimes.
Complete and solve the equation that finds the number of dimes he will pay you after the 7th study session
The equation that finds the number of dimes he will pay you after the 7th study session [tex]a_7=5\times5^{7-1}[/tex].
Given that, Your friend asks you to help him study and will pay you 5 dimes the first time you help him.
What is a geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
The formula to find nth term of the geometric sequence is [tex]a_n=ar^{n-1}[/tex].
According to the question,
The geometric sequence is 5, 25, 125,.....
So, r=25/5 =5
Now, [tex]a_7=5\times5^{7-1}[/tex]
= 5×15625
= 78125 dimes
Therefore, the equation that finds the number of dimes he will pay you after the 7th study session [tex]a_7=5\times5^{7-1}[/tex].
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If f(x) = 4x+9 and g(x) = x-6, what is f(x) times g(x)?
A.) x^2 - 15x + 8
B.) 4x^2 - 15x - 54
C.) x^2 - 54x - 15
D.) 4x^2 + 8x -54
Answer:
B.) 4x^2 - 15x - 54
Step-by-step explanation:
You want the product f(x)·g(x) when f(x) = 4x+9 and g(x) = x-6.
Binomial multiplicationThe distributive property can be used to find the product. Each term of one binomial is multiplied by every term of the other, and like terms are combined.
f(x)·g(x) = (4x +9)·(x -6)
= 4x(x -6) +9(x -6)
= 4x² -24x +9x -54 = 4x² +(-24 +9)x -54
f(x)·g(x) = 4x² -15x -54 . . . . . . . . . . matches choice B
__
Additional comment
The product of two binomials is sometimes described using the mnemonic FOIL, for First, Outer, Inner, Last. These refer to the locations of the terms involved in the four products
(4x +9)·(x -6) — First(4x +9)·(x -6) — Outer(4x +9)·(x -6) — Inner(4x +9)·(x -6) — LastThese products are the same as the ones we show above.
The FOIL mnemonic is only helpful for two binomials. Any polynomials can be multiplied using the distributive property.
helppppp meeee
-1+|x+4,5|=-6,2
Answer:
x= 2.7,-11.7 (sorry if im wrong) :'C
help due a week ago!!!!!!!!!!!!!!!!!!!
Answer:
5+0.1x=3-0.9x
2=-0.10x
1=-0.5x
x=-2
Answer is B good luck comrade<33!!
What is the standard deviation for the set of data { 6,7,8,9,10}? Find the standard deviation by completing the table.
Standard deviation for the given set of data { 6,7,8,9,10} is equal to √2.
As given in the question,
Given set of data is equal to :
{ 6,7,8,9,10}
[tex]x_{i}[/tex] = { 6,7,8,9,10}
Here total number of observation 'N' is equal to 5.
Mean [tex]\bar{x}[/tex] = ∑x / n
= ( 6+ 7+ 8 + 9 + 10 ) / 5
= 40 /5
= 8
[tex]\sum (x_{i} -\bar{x})^{2}[/tex] = ( 6- 8)² + (7-8)² + (8 - 8)²+ ( 9 -8)² + (10 - 8)²
= 4 + 1+ 0 + 1+ 4
= 10
Standard deviation = [tex]\sqrt{ \frac{\sum (x_{i} -\bar{x})^{2}}{N}[/tex]
= √10/5
= √2
Therefore, standard deviation for the given set of data { 6,7,8,9,10} is equal to √2.
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The shop teacher wrote down how many picture frames the students made last week.
Making picture frames
******
xxxx-
x
xx
ххххххх
0 1 2 3
4
Picture frames made
How many students made at least 3 picture frames?
students
9 students made at least 3 picture frames.
What is Box- whisker plot?An illustration of variation in a set of data is called a box and whisker plot. A histogram analysis usually gives an adequate display, but a box and whisker plot can add more detail while enabling the display of different sets of data on the same graph.
Given:
The plot shows picture frames made by students last week.
Number of Frames Number of students
0 6
1 4
2 1
3 2
4 7
So, the students made at least 3 picture frames
= 2+ 7
= 9
Hence, 9 students made at least 3 picture frames.
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a researcher finds a 95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25). what is the correct interpretation of this interval?
By using the concept of confidence interval, it is obtained that
We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.
Second option is correct
What is Confidence interval?
Let the quantity which is to be estimated is [tex]\theta[/tex]. A confidence interval for the parameter θ, with confidence level [tex]\alpha[/tex] is the interval (a, b), where
P(a < [tex]\theta[/tex] < b) = [tex]\alpha[/tex], P is the probability
Here the average commute time in minutes ([tex]\mu[/tex]) is to be calculated
95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25)
This means that it is 95% confident that the interval (15.75, 28.25) contains the population mean commute time in minutes using public transit
So the correct interpretation is
We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.
Second option is correct
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Complete Question
A researcher finds a 95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25). What is the correct interpretation of this interval?
A) There is a 95% chance commute time in minutes using public transit is between 15.75 and 28.25 minutes.
B) We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.
C) We are 95% confident that all commute time in minutes for the population using public transit is between 15.75 and 28.25 minutes.
D) We are 95% confident that the interval 15.75 < μ < 28.25 contains the sample mean commute time in minutes using public transportation.
a population has a mean of 75 and a standard deviation of 10. samples of size 50 are chosen and the sample means are recorded. what is the expected value of the sample mean?
A population has a standard deviation of 10 and a mean of 75.
The sample mean has a standard deviation of 5 and an expectation of 100.The empirical rule states that there is a 68% probability of being between 95 and 105 (within one standard deviation of its expected value) if it is approximately normal.
What is meant by a standard deviation?
A measure of how dispersed the data are in relation to the mean is called the standard deviation (or ).Data with a low standard deviation are grouped around the mean, while data with a high standard deviation are more dispersed.
How can I determine the standard deviation?
Step 1: Locate the mean. Step 2: Find the square of the distance from the mean for each data point. Step 3: Sum the results of Step 2's values. Step 4: Divide by how many data points there are.
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can someone help me?
Answer:
B
Step-by-step explanation:
1.20x + 3.60 < 9.60
1.20x < 9.60 - 3.60
1.20x < 6
x < 6 ÷ 1.20
x < 5
which of the following are true about the chi-square goodness of fit test?a. It is common to use one-sided alternative hypotheses when performing the chi-square goodness of fit test
b. The chi-square test statistic follows a Poisson null distribution
c. It compares an observed frequency distribution with an expected frequency distribution
d. The null hypothesis is that there is no difference between the observed and expected values
e. The degrees of freedom are k - 1, where k is the number of classes
f. The nature of the expected frequency distribution depends on the probability model on which it is based
Option c, d, f are true about the chi-square goodness of fit test.
Explanation:
a. It is common to use one-sided alternative hypotheses when performing the chi-square goodness of fit test.
FALSE, there is no such thing as one sided in chi-square goodness of fit test.
b. The chi-square test statistic follows a Poisson null distribution.
FALSE, chi square is a distribution of its own more like normal distribution.
c. It compares an observed frequency distribution with an expected frequency distribution.
TRUE, because this is what is done in chi-square test.
d. The null hypothesis is that there is no difference between the observed and expected values.
TRUE
e. The degrees of freedom are k - 1, where k is the number of classes.
FALSE, because k is the number of parameters and not the number of classes.
f. The nature of the expected frequency distribution depends on the probability model on which it is based.
TRUE, this is a fact line because the model whose hypothesis testing we are following we will follow expected frequency of that model only.
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Module 10 Honors Assignment – Geometry
Use the area of the shapes to determine the geometric probability for each problem.
Suppose a dart is thrown at a regular hexagon dartboard with the design
shown. (Reminder: regular polygons have congruent sides and congruent
angles). Find the probability that a dart hits one of the shaded areas. The
white figure is a rectangle. Be sure to show all work.
The probability that a dart hits one of the shaded areas is 1/6 when a dart is thrown at a regular hexagon dartboard with the design shown.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions.
Here,
angle of hexagon=360/6=60°
using trigonometric ratios,
area of triangle=bh/2
=(h*h√3/2)/2
=h²√3/4
area of hexagon=6*area of triangle
=6*(h²√3/4)
=3√3*h²/2
area of rectangle=bh
=h*h√3
=h²√3
area of shaded region,
=3√3*h²/2-h²√3
=h²√3/2
area of 1 shaded region=(h²√3/2)/2
=h²√3/4
Probability of hitting one shaded area,
=(h²√3/4)/(h²3√3/2)
=1/6
When a dart is thrown at a standard hexagonal dartboard with the pattern shown, the likelihood that it will land in one of the shaded areas is 1/6.
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A fish is swimming at a constant rate towards the ocean floor. The equation y = -5x – 9 can be used to represent this situation, where y is the depth of the fish in meters below sea level and x is the number of seconds the fish has been swimming. Which statement best describes the depth of the fish, given this equation? Answer
The statement best describes the depth of the fish is that from starting position of 9 meters below sea level, the fish is descending 5 meters per second
How to determine the statement that best describes the depth of the fish?
In order to know which statement best describes the depth of the fish, we have to first understand what the equation means:
Given: the equation y = -5x – 9
This can be likened to the equation of a straight line, which is of the form y =mx +c,
where m is the slope and c is the y-intercept
Comparing the given equation with the equation of a line :
y = -5x – 9
Slope(m) = -5 and y-intercept(c) = -9
The y-intercept represents the starting while the slope is the rate of descend
Therefore, what this means is that from starting position of 9 meters below sea level, the fish is descending 5 meters per second.
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481.5712 Find the digits in the tens place, in the tenths place, and in the ten thousandths place for the following number.
Answer:
Tens place: 8
Tenths place: 5
Ten thousandths place: 2
Answers:
tenths place = 5
ten-thousandths place = 2
======================================================
Explanation:
Refer to the place value chart shown below.
The 5 is in the tenths place which is one spot to the right of the decimal point. The ten-thousandths place is four spots to the right of the decimal point.
HELP PLS
Find the y-intercept of the line on the graph.
Enter the correct answer.
Answer:
-4
Step-by-step explanation:
The line intercepts at the y axis on exactly -4.
Answer:
The y-intercept is (0,-4).
Step-by-step explanation:
You can see that for the y-axis, that is the first point the line passes through. Hope this helps! Good luck! I am up doing math too. -_- Don't mark me brainliest, I just like to help.
Need help with this please
Answer:
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
7. What is the dependent variable for the function g(t)=-t-10?
Ot
10
O-t
09
A
The dependent variable in the function g(t) = - t - 10 is g .
In the given function g(t) = - t - 10 , we have t which is the independent variable. It makes up the domain of the function.
The independent variable is the one whose value is mapped by all and any particular t.
And 10 is the constant.
Dependent variables get their name since their values are examined throughout an experiment under the assumption or requirement that they are likewise dependent on the value of the dependent variable pursuant to some regulation .
Independent variables are those that, in relation to anything having to do with the experiment in question, are not considered to be reliant on any other factors.
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the product of 5 and the sum of 3 times a number and 4
Answer:
it is written as 5(3x+4)
4 students have different heights. Their average is 64.5 inches. The shortest is 62 inches and the tallest is 68 inches. If the middle two have the SAME height, how tall are each of them?
Please help, 50 points. Show your work!!! I need it or I wont get a mark.
The height of each of the two students is 64
What is the mean of data?The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values. It’s the most commonly used measure of central tendency and is often referred to as the “average.”
Let the heights of each of the two students be x,
so that x, x, 68 and 62 are the heights of the four students
Average height which is 64.5 = [tex]\frac{x + x + 62 + 68}{4}[/tex]
[tex]\frac{x + x + 62 + 68}{4}[/tex] = 64.5
by cross multiplying,
x + x + 62 + 68 = 4 x 64.5
2x + 130 = 258
collecting like terms,
2x = 258 - 130
2x = 128
x = 128/2
x = 64 inches
In conclusion the height of each of the 2 students with equal height is 64 inches.
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Steve drives an electric car. He can drive 425 kilometres before he needs to stop and re-charge his car. It takes 10 minutes to charge 50 kilometres. How long does Steve have to wait for his car to fully charge?
Answer:
Step-by-step explanation:
The question is asking how many times does 50 go into 425?
or 450/50 = ?
my calculator says it's 9 . What does your calculator say?
since we now know it's 9 times, we can just multiply 9 * 10 minutes
by observation of 9*10, I get the answer, what answer do you get?
-2f-3.7<2.3 inequality?
The solution to the inequality expression is f >-3
How to determine the solution to the inequality expression?From the question, we have the following parameter that can be used in our computation:
-2f - 3.7 < 2.3
Add 3.7 to both sides of the expression
This gives
-2f < 6
Divide both sides of the expression by -2
So, we have the following representation
f >-3
Hence, the solution is f >-3
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Wyatt went to the grocery store and bought bottles of Soda and bottles of juice. Each bottle of Soda has 30 grams of sugar and each bottle of juice has 40 grams of sugar. Wyatt purchased 2 more bottles of juice than bottles of Soda and they all collectively contain 430 grams of sugar. Write a system of equations that could be used to determine the number of bottles of Soda purchased and the number of juice purchased. Define the variables that you used to write the system.
Answer:
soda=30g
juice=40g
2 juice than soda=430g
Step-by-step explanation:
Since Keven bought 12 total drinks, we have the equation S + J = 12. We also know how much sugar is in each drink, as well as the total amount of sugar in all the drinks purchased. The equation 30S + 40J = 450 represents this scenario in terms of S and J. Now we have two equations with two unknowns (S and J) that make up the following linear system of equations:
S+J =12
30S+40J =450
We can solve this system by using either elimination or substitution (I will use substitution here):
S+J = 12
S=12- J
Now we can substitute the expression 12- J in for S in the second equation, and then solve for J:
30(12- J) +40J = 450
360- 30J +40J = 450
10J = 90
J = 9
Finally, we can substitute 9 in for J in either of the two original equations to solve for S:
S + 9 = 12
S = 3
So Keven bought three bottles of soda and nine bottles of juice. Hope this helps. Let me know if you have any questions.
The system of equations that could be used to determine the number of bottles of Soda purchased will be J=S+2 and 30S+40J =430, while the number of juice purchased will be 7.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, each bottle of juice contains 40 grams of sugar, compared to 30 grams per bottle of soda. Wyatt bought 2 more bottles of juice than soda, and they all have 430 grams of sugar in total.
If Wyatt purchased 2 more bottles of juice than bottles of Soda
J =2+S ------------(1)
J-S=2
Each bottle of Soda has 30 grams of sugar and each bottle of juice has 40 grams of sugar and they all collectively contain 430 grams of sugar.
30S+40J =430
Substitute the value of J in equation 2 as
30S+40(2+S)=430
30S+80+40S=430
70S=430-80
70S=350
S=5
The number of juice is,
J=S+2
J=5+2
J=7
Thus, the system of equations that could be used to determine the number of bottles of Soda purchased will be J=S+2 and 30S+40J =430, while the number of juice purchased will be 7.
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Write 3 x √3 as a single power of 3
Answer:
[tex]3^{1.5}[/tex]
Step-by-step explanation:
[tex]3 = 3^1[/tex]
[tex]\sqrt{3} = x^{0.5}[/tex]
[tex]3*\sqrt{3} = 3^{1} * 3^{0.5} = 3^{1 + 0.5} = 3^{1.5}[/tex]
Work out the percentage increase in her total hours from Weekend 1 to Weekend 2
Answer:
Step-by-step explanation:
weekend 1 : 3+2= 5
weekend 2 : 5.5+3.5=9
difference: 9-5=4
increase/initial value [times] 100
4/5(100)= 80%
I need help solving with an explanation please
Answer:
a = 1b = 0c = 0d = 1Step-by-step explanation:
[tex]\left[\begin{array}{cc}2&7\\1&3&\end{array}\right] \left[\begin{array}{cc}-3&7\\1&-2&\end{array}\right] =\left[\begin{array}{cc}2(-3)+7(1)&2(7)+7(-2)\\1(-3)+3(1)&1(7)+3(-2)&\end{array}\right] =\left[\begin{array}{cc}1&0\\0&1&\end{array}\right][/tex]