A manufacturing plant earned 4000 pesos per man-hour of labor when it opened. Each year, the plant earns an additional 6% per man-hour. What expression gives the amount the plant earned per man-hour of labor 3 years after it opened?
Answer:
866.16??????
Step-by-step explanation:
The amount is 4,494.40 plant earned per man-hour of labor 3 years after it opened.
It is required to find the amount the plant earned per man-hour of labor 3 years after it opened.
What is a geometric sequence ?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant. where r is the common ratio between successive terms.
Given:
A manufacturing plant earned 4000 pesos per man-hour of labor.
Rate= 6% per man-hour.
Time=3 years
We can consider the geometric sequence formula
[tex]A_{n} = A_{1} r^{n-1}[/tex]
[tex]A_{1}[/tex]= 4000
r = 1.06/1 = 1.06
n = 3
Substitute:
[tex]A_{3} = 4000(1.06)^{3-1} \\A_{3} = 4000(1.06)^{2}\\A_{3}= 4000(1.1236)\\A_{3} = 4,494.40[/tex]
Therefore, the amount is 4,494.40 plant earned per man-hour of labor 3 years after it opened.
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Find the surface area of the composite figure. 12 cm 11 cm 5 cm 7 cm 3 cm 4 cm 4 cm 12 cm SA = [?] cm? Enter
Answer:
116cm2
Step-by-step explanation:
ddyjjhffyyyttyu
find the length of UT
Answer:
I think it would be
A .39
I hope that it helps you
factorise the following 1. x²-2x+15.... 2. y²-19y+90
Answer:
1. x²-2x+15
This can't be factored, I've tried multiple ways now, but it just can't be factored.
2. y²-19y+90
Let's factor y^2−19y+90
y^2−19y+90
The middle number is -19 and the last number is 90.
Factoring means we want something like
(y+_)(y+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -19
Multiply together to get 90
Can you think of the two numbers?
Try -9 and -10:
-9+-10 = -19
-9*-10 = 90
Fill in the blanks in
(y+_)(y+_)
with -9 and -10 to get...
(y-9)(y-10)
Answer:
(y−9) (y−10)
You invest $5000 into an account that has a 2.7% annual interest rate and is compounded quarterly. Approximately how long will it take until you have $7,500 in your account?
Since the interest is compounded, we will have to use the compound interest formula.
We Weill plug 7500 in for A, because that's the amount of money that we want to have at the end of some amount of time.
5000 will go in for P because that's the starting amount.
2.7% will be converted into a decimal percentage form. You can do this by dividing by 100, which you will get .027, and then plug that in for r, the rate.
Since the interest is compounded quarterly, n = 4.
After a bit of number crunching, you will get to the point where you have to solve for an exponent. You can easily do this by using the natural log ln(). One property of logarithm is that you can take the exponent and place it in front of the log. Now you can divide both sides to separate and solve for t.
It take 10.5 years for the investment to grow to $7,500 in the account with a 2.7% annual interest rate compounded quarterly.
Given:
P = $5000
r = 2.7% = 0.027 (as a decimal)
n = 4 (quarterly compounding)
A = $7500
The formula for compound interest:
[tex]\[ A = P\left(1 + \frac{r}{n}\right)^{nt} \][/tex]
Substituting these values into the formula
[tex]\[ 7500 = 5000\left(1 + \dfrac{0.027}{4}\right)^{4t} \][/tex]
Dividing both sides of the equation by $5000, we have:
[tex]1.5 = (1.00675)^{(4t)[/tex]
Assuming a natural logarithm (ln), we have:
ln(1.5) = [tex]ln((1.00675)^{(4t))[/tex]
Using the logarithm property,[tex]ln(a^b) = b * ln(a)[/tex], simplify the equation:
[tex]ln(1.5) = 4t * ln(1.00675)[/tex]
Now, dividing both sides of the equation by 4 * ln(1.00675):
t = ln(1.5) / (4 * ln(1.00675))
t = 10.5 years.
Therefore, it will take 10.5 years for the investment to grow.
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You move down 5 units and up 5 units. You end at (1,3). Where did you start?
Answer:
(1, 3)
Step-by-step explanation:
Since up and down are opposites, the point didn't move at all.
I hope this helps!
pls ❤ and mark brainliest pls!
An investor has an account with stock from two different companies. Last year, his
stock in Company A was worth $6600 and his stock in Company B was worth $3500.
The stock in Company A has increased 7% since last year and the stock in Company B
has increased 1%. What was the total percentage increase in the investor's stock
account? Round your answer to the nearest tenth (if necessary).
If the graph of y=|x| is translated so that the point (1,1) is moved to (4,1) what is the equation of the new graph?
This question is solved using translation concepts, and doing this, it is found that the equation of the new graph is:
[tex]y = |x - 3|[/tex]
--------------------------
When a function f(x) is translated a units to the left, we get f(x - a).
--------------------------
In this question:
The original function is [tex]y = |x|[/tex]
Point (1,1) is moved to (4,1), that is, 3 is added to the x-coordinate, meaning that the function was shifted 3 units to the left.
Thus, the new equation is:
[tex]y = g(x) = f(x - 3) = |x - 3|[/tex]
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Point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid. The distance between the two points is _____.
There are no answer choices just that question.
Answer:
d = 1.1 units
Step-by-step explanation:
Since the x- coordinates of the 2 points are equal, both 3, then they lie on a vertical line. The distance between the 2 points is the difference in the y- coordinates, that is
d = | 2.4 - 1.3 | = | 1.1 | = 1.1 units
Answer:
Answer is "1.1"
Step-by-step explanation:
.......................
Verbal expression
25(6+x)
Answer:
25(6+x) = (25×6) + (25×x)
= 150+25x
Step-by-step explanation:
i hope it helps
⇛25(6 + x)
⇛150 + 25x
[tex] [/tex]
Ayuda por favor Por favor
Answer:
the answer is 1 and 1/2
Step-by-step explanation:
Find the area of ABCD
Answer:
Applying Heron's Formula
[tex]s=\frac{2.89+4.3+6.81}{2}[/tex]
[tex]s_1=7[/tex]
[tex]A_1=\sqrt{7(7-2.89)(7-4.3)(7-6.81)}[/tex]
[tex]A_1=10.56[/tex]
Now, [tex]s_2=\frac{6.81+8.59+7.58}{2}[/tex]
[tex]s_2=11.49[/tex]
[tex]A_2=\sqrt{11.49(11.49-6.81)(11.49-8.59)(11.49-7.59)}[/tex]
[tex]A_2=24.69[/tex]
Total Area:
[tex]10.56+24.69[/tex]
[tex]=35.25[/tex]
OAmalOHopeO
Solve this for me please it would be very much appreciated
Answer:
x= 8
Step-by-step explanation:
Right angled triangle :
Use Pythagorean theorem,
Base² + altitude² = hypotenuse²
x² + ( 2x - 1)² = (2x +1)²
(2x + 1)² - (2x-1)² -x² = 0
[tex]\boxed{(a+b)^{2}-(a-b)^{2}=4ab}[/tex] {here, a = 2x and b = 1}}
4*2x*1 - x²= 0
8x - x² = 0
x(8 - x) =0
x = 0 {Ignore} or 8 - x= 0
-x = -8
x = 8
x = 8
Which number is in the middle of -7 and 15?
Answer:
the answer os eleven
Step-by-step explanation:
As oyu see the half way number is 4 higher that 7 and 4 lower than 15.
A pet shop owner buys large bags of dry cat food that contain 10kg. He wants to make up bags that contain 200g of cat food. How many 200g bags of cat food can he make from one large bag?
Answer:
50 bags
Step-by-step explanation:
1 kg = 1000 grams
10 kg * 1000g/ 1kg = 10000 g
Divide 10000 grams by 200 g
10000g / 200g = 50
What x 1/4 = 2
? X 1/4 = 2
It’s an equation
the sum of 5 consecutive even numbers is 130. find the numbers.
Answer:
22, 24, 26, 28, 30
Step-by-step explanation:
If the sum of 5 numbers is 130, that means the average of these numbers is 26.
If it is the average then it is the middle, or the third number. The two numbers before it would then be 22 and 24 by subtracting twos, and the two numbers after it would be 28 and 30 by adding twos.
22, 24, 26, 28, 30
Answer:
22,24,26,28,30
Step-by-step explanation:
I call the unknown number x
I write consecutive numbers in terms of x.
x+ (x+2) + (x+4) + (x+6) + (x+8) = 130
5x + 20 = 130
5x = (130 - 20)
5x = 110
x = 22 = smallest even number
x + 2 = 24 = second even number
x +4 = 26
x + 6 = 28
x + 8 = 30
please help me guys its important
Answer:
1441.08in^3
Step-by-step explanation:
The number of pounds of one-dollar-a-pound
coffee needed to mix with 80 pounds of 70¢ a
pound coffee to make a mixture worth 84¢ a
pound is
(A) 70
(B) 80
(C) 95
(D) 65
Answer:
A
Step-by-step explanation:
Let's say we need x pounds of one-dollar-a-pound coffee . The coffee must average out to 84 cents a pound, and the formula for average is
sum of cost of coffee / number of pounds of coffee, so we have
0.84 = total cost of coffee / (x+80) . The total cost of coffee can be found to be the sum of the cost of $1 coffee and 70 cent coffee, so we have
0.84 = (cost of $1 coffee + cost of 70 cent coffee) / (x+80)
The cost of $1 coffee can be found by adding $1 for each pound of one dollar coffee, or $1 * x. Similarly, the cost of 70 cent coffee is equal to 0.70 * 80, so we have
0.84 = (1*x+0.7*80)/(x+80)
0.84 = (x+56)/(x+80)
multiply both sides by (x+80) to remove a denominator
0.84(x+80) = x+56
0.84x + 67.2 = x+56
subtract both sides by 56 and 0.84x to isolate the x and its coefficients
11.2 = 0.16 x
divide both sides by 0.16 to isolate x
11.2/0.16 = x = 70
The number of pounds of a constituent in a mixture given the cost of the
mixture and the cost and mass of the other constituent can be calculated
by using an equation to model the system
The correct option for the number of pounds of one-dollar- pound coffee needed is option A
(A) 70 pounds
The procedure for arriving at the correct option is as follows:
The given parameters are;
The cost of the the coffee for which the mass in the mixture is to be determined = One-Dollar a pound = 100 ¢ a pound
The mass of the coffee 70¢ a pound coffee to be mixed = 80 pounds
The cost per pound of the mixture = 84 ¢ a pound
The required parameter;
The number of pounds of the one-dollar-a-pound (100 ¢ a pound) coffee in the mixture
Method:
Let x (pound) represent the number of pounds of the one-dollar-a-pound coffee in the mixture, we have;
Mass of mixture = Mass of the one-dollar-a-pound in the mixture, x + Mass of 70 ¢ a pound in the mixture, 80
∴ Mass of mixture in pounds = x + 80
Cost = Cost per pound × Number of pound
Find solution by applying the equation;
Cost of the constituents = Cost of the mixture
Where;
Cost of the constituents = $1 × x + 70 ¢ × 80 = 100 ¢ × x + 70 ¢ × 80
Cost of the mixture = 84 ¢ × (x + 80)
Therefore;
100 ¢ × x + 70 ¢ × 80 = 84 ¢ × (x + 80)
The above can be expressed as 100·x + 70×80 = 84 × (x + 80)
Expanding, evaluating and collecting like terms gives;
100·x + 5,600 = 84·x + 6,720
100·x - 84·x = 6,720 - 5,600 = 1,120
16·x = 1,120
x = 1,120/16 = 70
The number of pounds of one-dollar- pound coffee needed, x = 70 pounds
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Geometry, please answer question ASAP
Answer: I think it would be C
Step-by-step explanation:
Answer:
the correct answer is C because its the only polygon with a caved in feature
In the figure below j ll h find the values of x and y
Answer:
26
Step-by-step explanation:
Given: Lines J and H are parallel lines. O intersects both lines equally.
Since two angles equal 180, that will be what (4y + 12) and 64 will be equal to.
(4y + 12) + 64 = 180
76 + 4y = 180
-76 -76
-------------------
4y = 104
y = 26
x and y is both 26 because they are vertical angles.
Hope this helped.
I need help ASAP!!! Please explain how to solve the problem I am stuck
Answer:
( x - 11 )^2 + ( y - 5 )^2 = 4^2
Step-by-step explanation:
The general form of equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2.
h and k are the co-ordinates of the center of circle and r is the radius
We have,
r=4
(h,k)=(11,5)
( x - h )^2 + ( y - k )^2 = r^2
or, ( x - 11 )^2 + ( y - 5 )^2 = 4^2
If you simplify,
x^2-22x+121+y^2-10y+25=16
or, x^2+y^2-22x-10y+146-16=0
or,x^2+y^2-22x-10y+130=0
Answer:
( x - 11 )^2 + ( y - 5 )^2 = 4^2
Step-by-step explanation:
You start with a given set of rules and conditions and determine something to
be true. What type of reasoning did you use?
O A. deductive
O B. inductive
C. logical
D. conditional
Answer:
i use logical reasoning
The bag contained 6 red marbles and 10 blue marbles. Bill removed a red marble. He then replaced it. What is the probability Bill will remove a blue marble on his next try?
Answer:
5/8
Step-by-step explanation:
There are 6 red marbles and 10 blue marbles. = 16 marbles
P( blue ) = number of blue marbles / total = 10/16 = 5/8
Answer:
5/8
Step-by-step explanation:
its just the chance of drawing a blue marble. the drawing of the red marble was independent to the current drawing of the blue marble, so the probability of drawing a blue marble is just the number of blue marbles over the total number of marbles. that is 10/16 or 5/8
Between which two numbers does 46 lie?
A.
between 8 and 9
B.
between 6 and 7
C.
between 5 and 6
D.
between 7 and 8
Answer:
So the sqrt(46) is between 6 and 7
Step-by-step explanation:
sqrt(46)
5*5 = 25
6*6=36
7*7=49
So the sqrt(46) is between 6 and 7
Tom has a job that pays £9.32 per hour. He worked for 40 hours last week . How much did he earns
Answer:
372.8
Step-by-step explanation:
Per hour = 9.32
Worked 40 hours
Total amount of money he earned last week = 40 x 9.32
= 372.8
Answer:
Tom has a job that pays £9.32 per hour. He worked for 40 hours last week . How much did he earns
9.32 x 40 = £372.80
Step-by-step explanation:
9.32 pounds times 40 hours
Is (3,-3)(3,−3)left parenthesis, 3, comma, minus, 3, right parenthesis a solution of the graphed system of inequalities?
Hi there!
»»————- ★ ————-««
I believe your answer is:
No.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
If we mark the point at (3, -3), the we can tell that the point does not lie in any shaded region. This means that it is NOT a solution to the system.See the graph attached.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
No, (3, -3) is not the solution to the graphed system of inequalities.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
From the graph,
The point of intersection is (2, 3).
This is the solution to the graphed system of inequalities.
But,
(3, -3) is given as the solution which is not true.
Thus,
(3, -3) is not the solution.
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Factorize this and solve no p, q, s, t, w
explanation:
all the questions are solved
in question no. s and t u need to divide the number in two different parts to slove
for no. w we can get two type of solution.
p and q u need to give the power of whole .
Which property is illustrated by the equation 3 (m n) = (3 m) n?
Answer:
The property illustrated by the equation 3(mn) = (3m)n is associative property of multiplication. This answer has been confirmed as correct and helpful.Answer:
associative
Step-by-step explanation:
What do you think happens to the graph
of f(x) = x2 if we multiply it by 3? Make a
guess. It undergoes a ...
I
A. Vertical Stretch
B. Vertical Shrink
Answer:
b. vertical shrink
Step-by-step explanation:
