Answer:
The labor cost per shirt of the American factory is 0.36 times the labor cost per shirt of the foreign company.
Step-by-step explanation:
A textile factory in the United States plays 300 workers a total of $9 million each year to produce 4.5 million shirts.
Therefore, the labor cost per shirt will be
[tex]\frac{9 \times 10^{6}}{300 \times 4.5 \times 10^{6}} = 0.0067[/tex]
Again, a foreign factory employs 225 workers at a total cost of $1,050,000 to produce 2,500,00 shirts.
Therefore, the labor cost per shirt will be
[tex]\frac{1050000}{250000 \times 225} = 0.01867[/tex]
Therefore, the labor cost per shirt of the American factory is 0.36 times (Approximate) the labor cost per shirt of the foreign company. (Answer)
Who do you answer this question?
Answer:
1
Step-by-step explanation:
Using the rule of exponents
[tex]a^{0}[/tex] = 1
Thus
[tex](75x^2z^12)^{0}[/tex] = 1
Answer:
1
Step-by-step explanation:
any non-zero expression raised to the power of 0 equals 1
1/4 is to 1 1/4 as 2 is to b
Answer:
b=22
Step-by-step explanation:
11/4 divided by 1/4 equals 11. 11*2 =22
Answer:
The answer is actually 10
Step-by-step explanation:
b = 10
is 4.9+0.03 = to 4.093 yes or no
Answer:
No, the correct answer of 4.9+0.03 would be 4.93
Good morning,
Answer:
No
Step-by-step explanation:
4.9+0.03=4.93
and 4,93≠4.093.
:)
The first term in this sequence is -1. Write the function that represents the sequence
Answer:
[tex]a_{n}[/tex] = 2n - 3
Step-by-step explanation:
Note the difference in consecutive terms is constant, that is
1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2
This indicates that the terms are an arithmetic sequence with
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 1 and d = 2, thus
[tex]a_{n}[/tex] = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3
A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 100 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 10 to year 20.
The crop yield increased by 200 pounds per acre from year 10 to year 20.
The crop yield increased by 100 pounds per acre from year 10 to year 20.
The crop yield decreased by 10 pounds per acre from year 10 to year 20.
The crop yield decreased by 0.1 pounds per acre from year 10 to year 20.
Answer:
The average rate of change = -10
The crop yield decreased by 10 pounds per acre from year 10 to year 20.
Step-by-step explanation:
A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function [tex]f(x) =-x^2 + 20x + 100[/tex] models the crops in pounds per acre over x years.
The average rate of change can be calculated using formula
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
In your case,
[tex]a=10\\ \\b=20,[/tex]
then
[tex]f(a)=-10^2+20\cdot 10+100=-100+200+100=200\\ \\f(b)=-20^2+20\cdot 20+100=-400+400+100=100[/tex]
and the average rate of change is
[tex]\dfrac{100-200}{20-10}=\dfrac{-100}{10}=-10[/tex]
This means the crop yield decreased by 10 pounds per acre (negative rate of change) from year 10 to year 20.
Answer:
'The crop yield decreased by 10 pounds per acre from year 10 to year 20.'
Step-by-step explanation:
i got it right on the test =)
The function f(x) = 1.50x + 12.50 relates how much kelsey pays for digital service, f(x), to the number of movies, x, she streams a month. what is the value and meaning of f(18)
f(18) = 39.50
This gives the monthly cost Kelsey will pay if she streams 18 movies in a month
Step-by-step explanation:
Given function is:
[tex]f(x) = 1.50x+12.50[/tex]
Here x is the number of movies
so for f(18), this means that the total number of movies will be 18
Solving
[tex]f(18) = 1.50(18)+12.50\\f(18) = 27+12.50\\f(18) = 39.50[/tex]
Hence,
f(18) = 39.50
This gives the monthly cost Kelsey will pay if she streams 18 movies in a month
Keywords: functions, Domain,range
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A typewriter types 840 words in 2.4 hours. Working at the same rate, how many words will he type in 3.6 hours?
Answer:
1260 words
Step-by-step explanation:
if you divide 840 by 2.4 you would get 350 then multiply by 3.6
With the same rate the number of words typed in 3.6 hour is 1260.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, a typewriter types 840 words in 2.4 hours.
Now, number of words typed in 1 hour is
840/2.4
= 350
Now, the number of words typed in 3.6 hour is
350×3.6
= 1260
Therefore, with the same rate the number of words typed in 3.6 hour is 1260.
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Indicate the equation of the line, in standard form, that passes through (2, -4) and has a slope of 3/5.
The equation of the line in standard form is 3x - 5y = 26
Step-by-step explanation:
Let us revise the forms of the linear equation
The slope intercept form is y = mx + b, where m is the slope of the line and b is the y-interceptThe point-slope form is [tex]y-y_{1}=m(x-x_{1})[/tex] , where m is the slope of the line and [tex](x_{1},y_{1})[/tex] is a point on the lineThe standard form is Ax + By = C, where A, B, and C are constantThe general form is Ax + By + C = 0, where A, B, and C are integers∵ The line passes through point (2 , -4)
∵ The slope of the line is [tex]\frac{3}{5}[/tex]
- Let us using the point-slope form and then change it to the
standard form
∵ [tex]x_{1}[/tex] = 2 and [tex]y_{1}[/tex] = -4
∵ m = [tex]\frac{3}{5}[/tex]
- Substitute these values in the form of the equation below
∵ [tex]y-y_{1}=m(x-x_{1})[/tex]
∴ [tex]y-(-4)=\frac{3}{5}(x - 2)[/tex]
∴ [tex]y+4=\frac{3}{5}(x - 2)[/tex]
Let us change it to standard form
- Multiply each side my 5 to cancel the denominator in the
right hand side
∴ 5(y) + 5(4) = 3(x - 2)
- Simplify the two sides
∴ 5y + 20 = 3x - 6
- Add 6 to both sides
∴ 5y + 26 = 3x
- Subtract 5y from both sides
∴ 26 = 3x - 5y
- Switch the two sides
∴ 3x - 5y = 26
The equation of the line in standard form is 3x - 5y = 26
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3. Let F(x)=(2/3)^x
Complete each statement.
Answer:
See explanation
Step-by-step explanation:
Let [tex]F(x)=\left(\dfrac{2}{3}\right)^x.[/tex] Plot the graph of this function. From the graph:
A. The domain of the function is [tex]x\in (-\infty,\infty).[/tex]
B. The range of the function is [tex]y\in (0,\infty).[/tex]
C. The y-intercept of the graph of F(x) is [tex](0,1).[/tex]
D. The horizontal asymptote is x-axis.
E. The graph of the function F(x) is decreasing from left to right.
F. The value [tex]\frac{2}{3}[/tex] determines that the graph of the function is decreasing from the left to the right.
Answer:
what he said above me
Step-by-step explanation:
The distance traveled, in meters, of a coin dropped from a tall building is modeled by the equation d(t) = 4.9t2 where d equals the distance traveled at time t seconds and t equals the time in seconds. What does the average rate of change of d(t) from t = 3 to t = 6 represent?
The coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.
The coin falls down with an average speed of 14.7 meters per second from 3 seconds to 6 seconds.
The coin falls down with an average speed of 44.1 meters per second from 3 seconds to 6 seconds.
The coin travels an average distance of 14.7 meters from 3 seconds to 6 seconds.
PLEASE HELP!!
The average rate of change of d(t) from t = 3 to t = 6 represent: A. The coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.
In Mathematics and Geometry, the average rate of change (ARoC) of a function f(x) on a closed interval [a, b] can be calculated by using this mathematical equation (formula):
Average rate of change (ARoC) = [tex]\frac{f(b) - f(a)}{(b - a)}[/tex]
Based on the given quadratic function, we can reasonably infer and logically deduce the following:
[tex]d(t)=4.9t^2\\\\d(3)=4.9(3)^2[/tex]
f(a) = d(3) = 44.1
[tex]d(t)=4.9t^2\\\\d(6)=4.9(6)^2[/tex]
f(a) = d(3) = 176.4
Next, we would determine the average rate of change (ARoC) of the function over the interval [3, 6]:
Average rate of change (ARoC) = [tex]\frac{176.4 - 44.1}{(6 - 3)}[/tex]
Average rate of change (ARoC) = 44.1 meters.
In this context, we can logically deduce that the coin travels an average distance of 44.1 meters from 3 seconds to 6 seconds.
Multiply.use estimation to check your answer. 4 × 1.2
7.5 × 18. 0.34 × 0.83.
0.04 × 0.6
Answer:
4.8, 135, 0.2822, 0.024
Step-by-step explanation:
4*1.2=4.8
7.5*18=135
0.34*0.83=0.2822
0.04*0.6=0.024
65 Divided by 3459 what is it?
Answer: 53.2
Step-by-step explanation:
Answer:
0.01879
Step-by-step explanation:
The answer to 3.x + 14x
How to calculate the mode of this data?
1.7 8.9 3 5.9 3.2 4.1 6.6 0.7
Answer:
there is no mode
Step-by-step explanation:
The mode is the value that appears most frequently in a data set. In this set of numbers none appear more than once. There is no mode.
In a nursery class of 18 pupils, the average is
[tex]4 \frac{1}{2} [/tex]
years. What is the sum of the ages of pupils?
Answer:
The sum of the age of pupils is 81
Step-by-step explanation:
Let sum of age of 18pupils = x
Average ages = 4.5
Average = total/no. of pupil
4.5 = x/18
x = 81
Answer:
The sum of the age of pupils is 81
The lengths of the triangle's sides are 5, 12, and 13. What is the measure of the angle opposite to side 13?
Answer:
90°
Step-by-step explanation:
5, 12 and 13 are the sides of a right triangle ( Pythagorean triple )
13 is the measure of the hypotenuse whose opposite angle is 90°
Answer:
90°
Step-by-step explanation:
5^2+ 12^2 = 13^2
25 + 144 = 169
The Converse Pythagorean Theorem (Egyptian triangle) states that if the length of the sides of a triangle, say a, b, and c, satisfy a^2 + b^2 = c^2, then this is a right triangle with a right angle opposite to side c.
And since 5^2 + 12^2 = 13^2 satisfies the statement a^2 + b^2 = c^2, c (which is 13) is opposite to a 90° angle.
Please help me with this math problem I don’t know it I need to pass this class !!!!!!
The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]
Step-by-step explanation:
Given
Length of box = l = ab
Width of box = w = a+5b
Height of box = h = 2b^2
The volume of a box is given by:
[tex]V = Length*Width*Height\\V = l*w*h[/tex]
Putting the values
[tex]V = (ab)(a+5b)(2b^2)\\ = (ab)(2b^2)(a+5b)\\=(2ab^3)(a+5b)\\Distributive property\\=(2ab^3*a) + (2ab^3*5b)\\=2a^2b^3 + 10ab^4[/tex]
Hence,
The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]
Keywords: Volume, Polynomials
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A 6000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $189600?
Answer:
4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were sold
Step-by-step explanation:
Given:
Tickets are sold at price [tex]\$28[/tex] and [tex]\$40[/tex].
Let Number of tickets sold at price [tex]\$28[/tex] be [tex]x[/tex].
Let Number of tickets sold at price [tex]\$40[/tex] be [tex]y[/tex].
Theater has maximum capacity of 6000 seat.
Hence,
[tex]x+y=6000 \ \ \ \ equation \ 1[/tex]
Total revenue to be generated is [tex]\$189600[/tex]
[tex]\therefore 28x + 40y= 189600 \ \ \ \ equation \ 2[/tex]
Now Multiplying equation 1 by 40 we get,
[tex]x+y=6000\\40x+40y=240000\ \ \ \ equation \ 3[/tex]
Now Subtracting equation 2 by equation 3 we get,
[tex](40x+40y=240000)- (28x + 40y= 189600)\\12x=50400\\\\x=\frac{50400}{12}=4200[/tex]
Now substituting value of x in equation 1 we get,
[tex]x+y=6000\\4200+y=6000\\y=6000-4200= 1200[/tex]
Hence a total of 4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were sold
To generate a total revenue of $189,600, 4200 tickets should be sold at $28 and 1800 tickets should be sold at $40.
Explanation:To find the number of tickets to be sold at each price, we can set up a system of equations. Let's assign variables:
Let x be the number of tickets sold at $28.
Let y be the number of tickets sold at $40.
The total revenue from selling x tickets at $28 is 28x, and the total revenue from selling y tickets at $40 is 40y. Since the total revenue is $189,600, we can write the equation:
28x + 40y = 189,600
We also know that the total number of tickets sold is x + y = 6000.
We can solve this system of equations to find the values of x and y. One way is to multiply the second equation by 28 and subtract it from the first equation:
28x + 40y - 28x - 28y = 189,600 - 28(6000)
12y = 189,600 - 168,000
12y = 21,600
y = 21,600 / 12 = 1800
Substituting the value of y in the equation x + y = 6000, we get:
x + 1800 = 6000
x = 6000 - 1800 = 4200
Therefore, 4200 tickets should be sold at $28 and 1800 tickets should be sold at $40 to generate a total revenue of $189,600.
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Find all roots: x^3 + 7x^2 + 12x = 0
Show all work and check your answer.
Answer:
[tex]x=0,x=-4,x=-3[/tex]
Step-by-step explanation:
The given equation is
[tex]x^3 + 7x^2 + 12x = 0[/tex]
Factoring by x:
[tex](x^2 + 7x + 12)x = 0[/tex]
One of the root is x=0. Let's solve the parentheses.
Expanding the trinomial
[tex]x^2 + 4x+3x + 12=0[/tex]
Factoring
[tex]x(x + 4)+3(x + 4)=0[/tex]
Factoring
[tex](x + 4)(x+3)=0[/tex]
This will give us the two remaining roots
[tex]x=-4,x=-3[/tex]
Here is a link to a picture of a Math Question I need help with, It's the last question I need to answer, so please help.
Answer:
-2x+3y=15
Step-by-step explanation:
y=2/3x+5
y-2/3x=5
-2/3x+y=5
3(-2/3x+y)=3(5)
-2x+3y=15
A survey showed that 35% of the students prefer plain white milk over chocolate milk. If the school has 1200 students. How many students prefer chocolate milk?
780 students prefer chocolate milk.
Step-by-step explanation:
Let,
the total percentage = 100%
Students who prefer plain white milk = 35%
Students who prefer chocolate milk = 100 - 35 = 65%
Number of students = 1200
No. of students who prefer chocolate milk = 65% of total students
No. of students who prefer chocolate milk = [tex]\frac{65}{100}*1200[/tex]
No. of students who prefer chocolate milk = [tex]\frac{78000}{100}\\[/tex]
No. of students who prefer chocolate milk = 780
780 students prefer chocolate milk.
Keywords: percentage, subtraction
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Kara drew a picture of a monarch butterfly. A monarch butterfly has an average wingspan of 4 inches. In her picture, the butterfly had a wingspan of 22 inches. What scale did she use?
a school is taking 388 students on a field trip to the zoo, and they can rent buses that hold 30 students for $895 each or vans that hold 15 students for $450 each
how many buses would it take to get everyone to the zoo?
how many vans would it take to get everyone to the zoo?
would it be cheaper to rent the buses or the vans? why?
~~~~~~~~~~~~
please get this finished soon, it's due homework for tomorrow.
whilst this is being answered, I'm going to be doing other homework, so good luck answering this one
It would take 13 buses to get everyone to the zoo
It would take 26 vans to get everyone to the zoo
It would be cheaper to rent buses
Step-by-step explanation:
The given is:
A school is taking 388 students on a field trip to the zooThey can rent buses that hold 30 students for $895 eachThey can rent vans that hold 15 students for $450 eachWe need to find how many buses it would take to get everyone to the zoo, how many vans it would take to get everyone to the zoo, and would it be cheaper to rent
∵ The number of students is 388
∵ Each bus can hold 30 students
- Divide the number of students by 30 to find the number of buses
∴ The number of buses = 388 ÷ 30 = 12.92
- They must to rent 13 bus to hold all the students
∴ The number of buses is 13
It would take 13 buses to get everyone to the zoo
∵ The number of students is 388
∵ Each van can hold 15 students
- Divide the number of students by 15 to find the number of vans
∴ The number of vans = 388 ÷ 15 = 25.87
- They must to rent 26 vans to hold all the students
∴ The number of vans is 26
It would take 26 vans to get everyone to the zoo
Let us find the cost of rent of the buses and vans to find which of them is cheaper
∵ The cost of rent of each bus = $895
∵ The number of buses = 13
∴ The cost of rent the buses = 13 × 895 = $11635
∵ The cost of rent of each van = $450
∵ The number of vans = 26
∴ The cost of rent the buses = 26 × 450 = $11700
∵ $11635 < $11700
∴ The cost of rent the buses < the cost of rent the vans
∴ The buses is cheaper than the vans
It would be cheaper to rent buses
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If the original price was $19, and the item was reduced by 65%, what would the new price be.
Answer: 6.65
Step-by-step explanation:
19-(19×.65)
Answer:
$ 6.65
Step-by-step explanation:
100% - 65% = 35%
Hence, $19 x 35% = $6.65
solve for x. 9^x+15=3^7x
The solution is x = 6
Step-by-step explanation:
Let us revise some rules of the exponents
If [tex]a^{n}=a^{m}[/tex] , then n = m[tex](a^{n})^{m}=a^{nm}[/tex]∵ [tex]9^{(x+15)}=3^{7x}[/tex]
∵ 9 = 3 × 3
∴ 9 = 3²
- Substitute 9 by 3² in the equation above
∴ [tex](3^{2})^{(x+15)}=3^{7x}[/tex]
- Use the second rule above for the left hand side
∵ [tex](3^{2})^{(x+15)}=3^{2(x+15)}[/tex]
∴ [tex](3^{2})^{(x+15)}=3^{2x+30}[/tex]
∴ [tex]3^{2x+30}=3^{7x}[/tex]
- By using the first rule above
∴ 2x + 30 = 7x
- Subtract 2x from both sides
∴ 30 = 5x
- Divide both sides by 5
∴ 6 = x
The solution is x = 6
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Karen went to the farmers market
to buy a total of 17 papayas and pineapples. If papayas were 2.50 each, pineapples were $3
each and she spent a total of $48, how many of each fruit did she buy?!
Answer:
6 papayas and 11 pineapples
Step-by-step explanation:
So, we need to find an answer of how many papayas and pineapples she bought, and we only spent $48.
So, papayas are $2.50 each, and Pineapples are $3.00 each and we only bought 17 fruits total.
lets try 8 papayas, and 9 Pineapples.
$2.50 x 8 = $20.00 total on Papayas
$3.00 x 9 = $27.00 total on Pineapples.
That would only be $47 spent total.
Lets try 10 papayas and 7 pineapples.
$2.50 x 10 = $25.00
$3.00 x 7 = $21.00
That would only be a total of $26 spent.
Lets try 6 papayas and 11 pineapples.
$2.50 x 6 = $15.00
$3.00 x 11 = $33.00
This would be a total of $48 spent.
6. What is the result of multiplying the digit in the hundredths place by
the digit in the ten thousands place in the number below?
5,094,437.816
1 A.6
B.9
C.54
D.72
Answer:
B.9
Step-by-step explanation:
9*1=9
What three consecutive even integers have a sum of 24?
Answer:
6 + 8 + 10 = 24
Answer: 6, 8, and 10
Step-by-step explanation:
x-first number
x+2-second
x+4-third
x+x+2+x+4=24
3x=18
x=6
6, 8, and 10
What is 28 is 35% of what number
Answer:
80
Step-by-step explanation:
35/100X = 28
35X = 2800
2800/35=80
Answer: 80
Step-by-step explanation: To answer the question 28 is 35% off what number, we translate the question into an equation.
So we have "28 is" which means 28 = 35% which we need to write as a decimal. To write a percent as a decimal, we move the decimal point 2 places to the left so 35% can be written as the decimal .35. Next we have "of what number" which means times X.
Now we have the following equation.
28 = (.35) (x)
Now to solve for x since x is being multiplied by .35, we need to divide by .35 on both sides of the equation.
On the right side of the equation, the .35's cancel and we have x. On the left side of the equation, we have 28 ÷ .35 which is 80.
So 80 = x.
Therefore, 28 is 35% of 80.
Which is a y-intercept of the continuous function in the table?
(5,0)
(0, 1)
(0,5)
(1,0)
Answer:
(0, 5 )
Step-by-step explanation:
The y- intercept is the value of the y- coordinate where the function crosses the y- axis. At this point the x- coordinate is zero.
From the table when x = 0, y = 5
Thus (0, 5) is the y- intercept