Assume that an economy has 1,000 workers, each working 2,500 hours per year. if the average real output per worker-hour is $20, then total output, or real gdp, will be
Answer:
$50,000,000
Step-by-step explanation:
You want to know the total output (real gdp) of 1000 workers, each working 2500 hours producing real output of $20 per hour.
GDPThe output, called "gross domestic product" or GDP, is the total output of all workers for the hours they work:
(1000 worker) × (2500 hours/worker) × ($20/hour) = $50,000,000
The GDP will be $50,000,000 or 50 million dollars.
Which transformations could have been used to create A'B'C'? Choose all that apply.
a 180° rotation about the origin and then a translation 3 units up and 1 unit left
a translation 3 units up and 1 unit left and then a 180° rotation about the origin
a 90 degree clockwise rotation about the origin and then a reflection over the Y axis
a 90° counterclockwise rotation about the origin and then a reflection over the X axis
A translation through you to down and one unit right and then I 108° rotation about the origin
The correct transformation is a rotation of 180° around the origin followed by a translation of 3 units up and 1 unit to the left.
Which transformation is used to get A'B'C'?
To analyze this we can only follow one of the vertices of the triangle.
Let's follow A.
A starts at (3, 4). If we apply a rotation of 180° about the origin, we end up in the third quadrant in the coordinates:
(-3, -4)
Now if you look at A', you can see that the coordinates are:
A' = (-4, -1)
To go from (-3, -4) to (-4, -1), we move one unit to the left and 3 units up.
Then the complete transformation is:
A rotation of 180° around the origin, followed by a translation of 3 units up and 1 unit to the left.
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Answer:
A. a 180degree rotation about the origin and then a translation 3 units up and 1 unit left
E. a translation 3 units down and 1 unit right and then a 180degree rotation about the origin
If f(x)=(4x-3) / 2 and g(x) =(2x+3) / 4, which of the following is true?
A f(g(x)) =1
B f(g (x)) = 0
C f(g(x))=-1
D f(g(x)) = x
Answer:
f(g(x))= x
Step-by-step explanation:
f(x)=(4x-3)/2
g(x) =(2x+3)/4
f(g(x)) means use the value obtained from g(x) in the equation defined by f(x). Since g(x) =(2x+3)/4, we can substitute (2x+3)/4 in place of the x in f(x).
If f(x)=(4x-3)/2 then use the expression (2x+3)/4 in place of "x" in (4x-3)/2
f(x) = (4x-3)/2
g(x) = (2x+3)/4
f(g(x))=(4((2x+3)/4)-3)/2
f(g(x))=(((8x+12)/4)-3)/2
f(g(x))= (2x+3-3)/2
f(g(x))= 2x/2
f(g(x))= x
solve x - 23 = 57 ⅔ x = 7
Step-by-step explanation:
[tex]x - 23 = 57 \\ x = 57 + 23 \\ x =80 \\ \\ \frac{2}{3}x = 7 \\ ( \frac{3}{2}) \frac{2}{3}x = 7( \frac{3}{2}) \\ x = \frac{21}{2} [/tex]
You need to invest $1000 in a bank account and are give two options. The first option is to earn $50 every month you leave the money in the account. The second one is to earn 3% interest each month. Describe each of these two functions and make a table of values for each for several months. Which account would you choose?
Answer:
Option 1Earn $50 every month.
Let x = number of months the money is left in the accountLet y = the amount in the accountInitial amount = $1,000[tex]\implies y = 50x + 1000[/tex]
This is a linear function.
Option 2Earn 3% interest each month.
(Assuming the interest earned each month is compounding interest.)
Let x = number of months the money is left in the accountLet y = the amount in the accountInitial amount = $1,000[tex]\implies y = 1000(1.03)^x[/tex]
This is an exponential function.
Table of values[tex]\large \begin{array}{| c | l | l |}\cline{1-3} & \multicolumn{2}{|c|}{\sf Account\:Balance} \\ \cline{1-3} & \sf Option\:1 & \sf Option\:2 \\\sf Month & \sf \$50\:per\:mth & \sf 3\%\:per\:mth \\\cline{1-3} 0 & \$1000 & \$1000 \\\cline{1-3} 1 & \$1050 & \$1030 \\\cline{1-3} 2 & \$1100 & \$1060.90 \\\cline{1-3} 3 & \$1150 & \$1092.73 \\\cline{1-3} 4 & \$1200 & \$1125.51 \\\cline{1-3} 5 & \$1250 & \$1159.27 \\\cline{1-3} 6 & \$1300 & \$1194.05 \\\cline{1-3} 7 & \$1350 & \$1229.87 \\\cline{1-3}\end{array}[/tex]
From the table of values, it appears that Account Option 1 is the best choice, as the accumulative growth of this account is higher than the other account option.
However, there will be a point in time when Account Option 2 starts accruing more than Account Option 2 each month. To find this, graph the two functions and find the point of intersection.
From the attached graph, Account Option 1 accrues more until month 32. From month 33, Account Option 2 accrues more in the account.
ConclusionIf the money is going to be invested for less than 33 months then Account Option 1 is the better choice. However, if the money is going to be invested for 33 months or more, then Account Option 2 is the better choice.
Which point is on the circle centered at the origin with a radius of 5 units?
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
(2, StartRoot 21 EndRoot)
(2, StartRoot 23 EndRoot)
(2, 1)
(2, 3)
i been asking for help since yesterday
Use the graph above to complete problems 1 - 5.
Mary is planning a costume party. She spent $375.00 as shown on the graph. How much of the money was spent, to the nearest dollar, on the following items?
1) On decorations?
2) On food?
3) On party hall rental?
4) On prizes?
5) On invitations?
Which is not a function?
Can give brainliest!!
Answer:
Number #1
Step-by-step explanation:
#1 isn't a function
Answer:
Choice 3 is not a function.
Step-by-step explanation:
Reason: It has points (1,3) and (1,7). X cannot repeat otherwise it is not a function.
Hope this helps!
If not, I am sorry.
If you rolled two dice, what is the probability
that you would roll a sum of 4?
Give your answer as a simplified fraction.
Answer:
1/36.
Step-by-step explanation:
A total number of possible outcomes = 36.
To get a sum of 12 the possible outcomes are just 6,6.
Are the two triangles similar? How do you know? (image attached)
Answer:
no
Step-by-step explanation:
they're not same because no angles are mentioned and sides are diff too
1) A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect prefer comic books?
x
A. 10
B. 20
C. 60
D. 80
E. 100
help please
Answer:
First send the graph then we can help you in your answer
Answer:
D. 80
Step-by-step explanation:
The graph shows that about 3/8 ( 37.5% ) of the students enjoy comic books.
200 × .375 = 75
75 rounded to the nearest tens value is 80
For anyone wondering, the graph was on a different question that this person asked.
A cone and a cylinder have the same base and height, as shown below.
The volume of the cylinder is 84 rin.3 What can be concluded about the volume of the cone? Check all that apply.
1
The volume of the cone is the volume of the cylinder.
The volume of the cylinder is 2 times the volume of the cone.
The volume of the cone is less than the volume of the cylinder.
Answer:
The volume of the cone is less than the volume of the cylinder.
Step-by-step explanation:
please help me (show ur solution)
Answer:
See below ~
Step-by-step explanation:
Q9
x = 200° (arc measure = central angle measure)The inscribed angle y is half of the arc length xy = 1/2xy = 1/2(200°)y = 100°Q10
x + 112 = 180x = 68°y + 81 = 180y = 99°Answer:
9. x = 200 and y = 100
10. x = 68 and y = 99
Step-by-step explanation:
Question 9
The measure of an arc is the measure of its central angle.
⇒ x = 200
This is a non-cyclic quadrilateral as not all its vertices touch the circumference of the circle.
The angle at the center is twice the angle at the circumference.
⇒ y = 200 ÷ 2
⇒ y = 100
Question 10
This is a cyclic quadrilateral as all its vertices touch the circumference of the circle.
The opposite angles in a cyclic quadrilateral add up to 180°.
⇒ x + 112 = 180
⇒ x = 68
⇒ y + 81 = 180
⇒ y = 99
At a diner, the lunch special gives you three choices. For the starter, you can pick from 3 choices (soup or salad or fries) For the main item, you can pick from 2 choices (burger or sandwich) For the drink, you can pick from 2 choices (coke or pepsi) If the staff chooses all items for you randomly, figure these probabilities.
1. Probability of getting (soup, burger, coke)
2. Probability of getting (fries, burger, any drink)
Answer:
1/12; 1/6
Step-by-step explanation:
1. the chance of getting soup is 1/3, the chance of getting a burger is 1/2, and the chance of getting coke is 1/2, multiply these chances to get (1/3) *(1/2) * (1/2) = 1/12
2. the chance of getting fries is 1/3, the chance of getting a burger is 1/2, and the chance of getting any drink is 1, multiply these chances to get (1/3) * (1/2) * 1 = 1/6
Zack has 2 feet of balsa wood. he needs twice that amount to finish a project. the cost is $0.05 per inch. how much will the balsa wood cost zack.
Answer:
$1.2
Step-by-step explanation:
There is 12 inches in a foot, and if he needs twice the amount he already has which is 4 then you would multiply 0.05 times 24 and you would get $1.2
Answer: $1.20 for 2 feet of balsa wood
Step-by-step explanation: There are 12 inches in 1 foot, and 24 inches in 2 feet. The cost per inch is 0.05, multiplying 24 (inches) x 0.05 (the cost per inch) would equal $1.20
Someone help me with this
combine like terms to simplify 3x + 5 - 2x
Step-by-step explanation:
3x and 2x are like terms so,
3x + 5 - 2x
3x - 2x + 5 = x + 5
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression
[tex]\star~~\large\pmb{3x+5-2x}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Combine like terms.The like terms here are: 3x-2x; let's combine them:
[tex]\star~\large\pmb{x+5}[/tex]
We can't simplify this any further, because x and 5 are not like terms.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{Variables\:and\;numbers\;are\;not\;like\;terms}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
Which of the following proves ABC= DEF?
Answer: A
Step-by-step explanation:
In the diagram, we see that we have two pairs of congruent angles, so it is going to be either ASA or AAS congruence.
To determine if it is ASA or AAS congruence, we can use the fact that for ASA, the side is included between the congruent angles, whereas in AAS, the side isn't.
Since the congruent side is included between the two angles, there is ASA congruence.
Find the area of the complex figure
What is the value of y?
log^464 = y
OA. 16
OB. 8
OC. 3
OD. 4
The value of y in the given logarithmic equation is 3. The correct option is C. 3
Evaluating Logarithmic equationFrom the question, we are to determine the value of y in the given logarithmic equation
The given equation is
[tex]log_{4}64=y[/tex]
By applying one of the laws of logarithm, we get
[tex]64 = 4^{y}[/tex]
Now, express 64 in index form,
[tex]4^{3} = 4^{y}[/tex]
Since the bases are equal, we can equal the powers to get
3 = y
∴ y = 3
Hence, the value of y in the given logarithmic equation is 3. The correct option is C. 3
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Find the distance between the points (-6,-4) and (-6,-18)
Answer:
The answer is 16 units.
Step-by-step explanation:
Now we have to use the distance formula i.e distance between two points =root under (x2-x1)^2+(y2-y1)^2
Answer:
22 is the distance between the points
2. Use the figures below for parts a through c.
B
45°
15
90% C
105°
120%
105°
W
80
(a) Are the corresponding angles in figures ABCD and WXYZ congruent? (1 pt)
Circle or highlight one:
Yes
No
(b) Are the corresponding sides in figures ABCD and WXYZ proportional? (1 pt)
Circle or highlight one:
Yes
No
Show your work for part b below. (2 pts)
(c) Are figures ABCD and WXYZ similar? (1 pt)
Circle or highlight one:
Yes
45°
No
110
150
120%
Z
90% Y
40
Answer:
see the attachment photo!
Identify the angle of depression.
Answer:
4
Step-by-step explanation:
An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line.
An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line.
∠3 is an angle of elevation because it is formed by the line of sight that is above the horizontal line.
∠4 is an angle of depression because it is formed by the line of sight that is below the horizontal line.
∠5 is neither an angle of depression nor an angle of elevation because it is not formed by the horizontal line and the line of sight.
∠6 is an angle of elevation because it is formed by the line of sight that is above the horizontal line.
Therefore, the angle of depression is ∠4.
How many solutions are there to the equation?
2x + 3 = 2x + 7
Answer:
this equation has no solutions.
Step-by-step explanation:
2x+3 = 2x+7
3=7
please help I need this done today
Answer: 45 degrees
Step-by-step explanation:
90-45 = 45
Kyle recorded his height, in inches, from age 6 to age 18. The graph below shows the data that he recorded as a function of his height over time. Kyle plotted many of the points from memory, but has some accurate data from old medical records. His two most accurately plotted points occurred at age 6 with a height of 45 inches and at age 18 with a height of 75 inches. Use these two data points to determine the equation for the line of best fit for Kyle's data.
Answer:
you probably moved on, but for everyone else:
y= 5/2x + 30
Step-by-step explanation:
(HELP FAST) I need help with this geometry question
Answer: no
Step-by-step explanation:
The ratio of the shorter sides is 27/5, which is equal to 3.4.
The ratio of the longer sides is 78/9, which is about 8.7.
Since the ratio of the longer sides is not equal to the ratio of the shorter sides, it is not a dilation.
A certain planet has a day length of 24 hours. the planet is totally covered in water,
except for one small island. at hour 0, the island has 100% light with the planet's star
in the top of the sky. at hour 12, the island has 0% light and is in total darkness.
write an equation that models the amount of light in the sky on the island in terms
of hours passed.
Answer:
above
Step-by-step explanation:
the entire method for the question is linked above :)
the ratio of new airplanes to old air planes in a fleet of 720 planes of which 240 are old airplanes
Answer:2
Step-by-step explanation:(720-240)/(240)
Picture has the choices
Answer: 4th option, 28 = 28
Step-by-step explanation:
Cross multiplying means we will multiply the numerator of the first fraction by the denominator of the second. Then we will multiply the denominator of the first by the numerator of the second.
-> See attached for a visual example and my work.
28 = 28, so the fractions are equal.
Answer:
Step-by-step explanation:
2/7=4/14 because 7x4=28 and 2x14=28. so you're gonna see which equals 28. but for example, if it's 10, you do 10/1.