A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 5 child bikes and 15 adult bikes in a week? (1 point)
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answers
The company can build 5 child bikes and 15 adult bikes in a week.
The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".
Linear Equations:Linear Equations are mathematical statements, which can be used to find an unknown quantity or any value in a given problem. Here we use variables like x, y .. etc. to represent unknown values.
Here we will use Linear Equations to solve the equations.
Here we have
One child bike requires 4 hours to build and 4 hours to test
Number of hours to build 'c' number of child bikes = 4c
Number of hours to test 'c' number of child bikes = 4c
One adult bike requires 6 hours to build and 4 hours to test.
Number of hours to build 'a' number of adult bikes = 6a
Number of hours to test 'a' number of adult bikes = 4a
Number of hours taken to build bikes in one week = 120
=> 4c + 6a ≤ 120 --- (1)
Number of hours taken to test the bikes in one week = 100
=> 4c + 4a ≤ 100 --- (2)
Assume that
The company can build 5 child bikes and 15 adult bikes in a week
Substitute c = 5 and a = 15 in (1) and (2)
(1) => 4(5) + 6(15) ≤ 120
=> 110 ≤ 120 [ which can be true ]
(2) => 4(5) + 4(15) ≤ 100
=> 80 ≤ 100 [ which can be true ]
From the above calculations,
Both (1) and (2) are satisfied
Therefore,
The company can build 5 child bikes and 15 adult bikes in a week.
The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".
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Related Questions
the area of a square is seasonal 25 cm Square calculate the length of a diagonal to one decimal place .
Answers
Answer:
The answer is 7.1cm to 1d.p
Step-by-step explanation:
Area of square =L²
25=L²
√L²=√25
L=5cm
hyp²=opp²+adj²
x²=5²+5²
x²=25+25
x²=50
√x²=√50
x=7.1cm to 1d.p
Jose weighs 12 pounds less than twice what his sister maria weighs. If w respesent maria weight. Which expression shows jose weight
Answers
Answer:
2w-12
Step-by-step explanation:
Jose = 2x(Maria's weight) -12
j = 2w -12
What is (-2/3)+(7/8)?
Answers
Answer: 5/24
Step-by-step explanation:
(-2/3)+(7/8)=
(-2/3)+(7/8)*24/24= ==> 24 is the LCM of 3 and 8
\(\frac{(-2*24)/3+(7*24)/8}{24}\)=
\(\frac{-2*24/3+7*24/8}{24}\)=
\(\frac{-2*8+7*3}{24}\)=
\(\frac{-16+21}{24}\)=5/24
help me pls! PLS PLS PLS I NEED IT
20 points
options are x, x^9, x^4, and x^6
Answers
Answer:
x^4
Step-by-step explanation:
The expression can be simplified to (x^2)^2. Using an exponent rule, you multiply the two exponents together to get 4. The answer is x^4
-4 2/3 x -1 1/2 with work shown pls
Answers
Answer:
g
Step-by-step explanation:
e
Enter the number that belongs in the green box
Answers
The number that belongs in the green box using sine rule is 13.96.
What is sine rule?The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
To calculate the number that belongs in the green box, we use the formula below
Formula:
SinA/a = SinB/b.................. Equation 1From the diagram,
Given:
A = 70°B = 61°b = 15a = xSubstitute these values into equation 1
Sin70°/15 = sin61°/xSolve for x
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What is the median of this data set 2 2 5 6 6 8 9 11?
A) 6
B)5
C)7
D) 8
Answers
Answer:
6 is your answer since its in the middle.
Step-by-step explanation:
Randy is starting a beehive so that he can have fresh
honey. He decides to check the current population of bees
in the hive by marking 160 bees. Later, Randy collects 240
bees and observes that 30 of them are marked. What is the
BEST estimate for the bee population?
Answers
Answer:
1,280
Step-by-step explanation:
the number 5 and 20 have a special relationship: 1/5 is equivalent to 20% and 1/20 is equivalent to 5% are there any other numbers that have a relationship like this? why does this relationship happen?
Please help
Answers
The other numbers are 2 and 50. These relationships are like this because the product of both numbers gives a 100
FractionsFraction is the ratio of two integers. It is written in the form a/bFrom the information given, we are to determine the other numbers like 5 and 20 that form the given relationship.
The other numbers that form this relationship are 2 and 50
Get their percentages1/2 * 100 = 50%
1/50 * 100 = 2%
Thesee relationships are like this because the product of both numbers gives a 100
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13. Consider the two repeating decimals shown
below.
0.31313131...
0.02020202...
a. By simply looking at the decimal
representations, what is the sum of these
two rational numbers? Write as a decimal
and as a fraction.
b.
Verify your answer by finding fractions that
represent each decimal. Add the fractions.
c. Write the difference of the two numbers as a
repeating decimal.
Answers
1) The decimal 0.31313131...as a fraction is; 310/990
2) The decimal 0.02020202 as a fraction is; 200/9990
3) The difference of the two numbers as a repeating decimal is; 0.29292929
How to change decimal to fractions?We are given the decimals as;
0.31313131...
0.02020202...
1) The decimal 0.31313131... is repeating decimal.
If we write it as;
x = 0.31313131...
Multiply both sides by 10 to get;
10x = 3.131313 --- (1)
Multiply both sides of initial equation by 1000 to get;
1000x = 313.131313 ----(2)
Subtract eq 1 from eq 2 to get;
990x = 310
x = 310/990
2) The decimal 0.02020202 is a repeating decimal.
If we write it as;
x = 0.02020202...
Multiply both sides by 100 to get;
10x = 2.020202 --- (1)
Multiply both sides of initial equation by 10000 to get;
10000x = 202.0202 02 ----(2)
Subtract eq 1 from eq 2 to get;
9990x = 200
x = 200/9990
3) The difference of the two numbers as a repeating decimal is;
0.31313131 - 0.02020202 = 0.29292929
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Classwork 12/6: Write a polynomial function
for each set of zeros.
1.) 5,-3, 12
2.) 4, 6, -1,0
3.) - 2/5,2
Answers
A polynomial function for each set of zeros is f(x) = (x - 5)(x+3)(x -12), f(x) = (x - 4)(x -6)(x +1),f(x) = (x +2/5)(x -2).
What is polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Suppose you are given that a polynomial f(x) has zeroes { a, b, c }
Then the polynomial, if it is known that it is cubic, is,
f(x) = (x - a)(x - b)(x - c)
For : 5,-3, 12
f(x) = (x - 5)(x+3)(x -12)
For : 4, 6, -1,0
f(x) = (x - 4)(x -6)(x +1)
For : - 2/5,2
f(x) = (x +2/5)(x -2)
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A polynomial function for each set of zeros is f(x) = (x - 5)(x+3)(x -12), f(x) = (x - 4)(x -6)(x +1),f(x) = (x +2/5)(x -2).
What is polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Suppose you are given that a polynomial f(x) has zeroes { a, b, c }
Then the polynomial, if it is known that it is cubic, is,
f(x) = (x - a)(x - b)(x - c)
For : 5,-3, 12
f(x) = (x - 5)(x+3)(x -12)
For : 4, 6, -1,0
f(x) = (x - 4)(x -6)(x +1)
For : - 2/5,2
f(x) = (x +2/5)(x -2)
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Help please I’ll mark brainiest
Answers
Answer:
h = 2.12 , c = 6.93
Step-by-step explanation:
To calculate h:
Apply the cosine identity
\(cos\ x =\frac{base}{hypotenuse}\\\\cos\ 45=\frac{h}{3}\\\\0.707=\frac{h}{3}\\\\h=3(0.707)\\h=2.12\\\)
To calculate c:
Apply the tangent identity
\(tan\ x=\frac{perpendicular}{base}\\\\tan\ 60=\frac{c}{4}\\\\1.732=\frac{c}{4}\\\\c=1.732(4)\\c=6.93\\\)
C=6.9
Double check my answers using the picture below or by the long way (Pythagorean’s)
I suggest you memorize the drawings by heart because the 30-60-90 and the 45-45-90 right triangles are considered special in geometry and they will keep testing you on them until you graduate from university !
Hope it helps.
If d(4)=68. Thus, joe travels 68 mi in 4 hours. How many mi does Joe travel in 45 min
Answers
Answer:
12.75 miles
Step-by-step explanation:
Changing hours to minutes
4 hours 4*60 = 240 minutes
Now we can use a ratio to solve
68 miles x miles
------------- = -----------------
240 minutes 45 minutes
Using cross products
68*45 = 240x
Divide each side by 240
68*45 /240 = x
12.75 miles
Answer:
12.75 MILES
Step-by-step explanation:
if he travels 68 miles in 4 we should find how many miles per hour
to find this we divide 68/4 which is 17
So if he is going 17 MPH then to find how far he travels in 45 min we should multiply by 3/4
17 x 3/4 is 12.75
12.75 MILES
What is the translation from
a) shape X to shape Z?
b) shape Z to shape X?
Answers
The translation form of each shape is given as follows:
a) X to Z: (x, y) -> (x + 5, y + 2).
b) Z to X: (x, y) -> (x - 5, y - 2).
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.For the composition of translations, we add the coordinates, hence:
-2 + 7 = 5.5 - 3 = 2.Hence the rule from X to Z is given as follows:
(x, y) -> (x + 5, y + 2).
From Z to X, we have the inverse rule, hence:
(x, y) -> (x - 5, y - 2).
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calculate the Geometric mean for the
distribution 8, 6, 3, 5 and 4
Answers
Answer:
Step-by-step explanation:
The geometric mean is the average of the 5 numbers
8 + 6 + 3 + 5 + 4 Just add.
Total = 26
There are 5 elements, so the average = 26/5 = 5.2
What is the slope of a line perpendicular to a line which has a slope of -2
Answers
Answer:
it is 1/2
Step-by-step explanation:
The product of a lines slope M and the slope K of a perpendicular is -1:
M*K=-1
This implies
K=-1/M
since
M * -1/M=-1
In our example we are given a line of slope M=-2 therefore the slope K of a line to perpendicular to this line is:
M*K=-1
-2*K=-1
K=-1/-2=1/2
Identify the like terms in the expression -12h²-4+9-3h
Answers
We are given the following expression:
\(undefined\)PLEASE HELP NOW!!!!!
Answers
The percentage for blue balls will be 56% and the percentage for red balls will be 44%.
What is the percentage for the colors of the gumball?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this situation, there are 4000 balls and 2240 of then are blue while 1760 area red.
The percentage for blue balls will be:
= Number of blue balls / Total balls × 100
= 2240 / 4000 × 100
= 56%
The percentage for red balls will be:
= Number of red balls / Total balls × 100
= 1760 / 4000 × 100
= 44%
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Given that A and I are the centers of the congruent circles shown below, compare the quantity in column A with the quantity in column B. Choose the best answer. The quantity in column A is greater. The quantity in column B is greater. The two quantities are equal. The relationship cannot be determined from the information given.
Answers
Answer: The two quantities are equal
Step-by-step explanation:
Edge2021
C. The two quantities are equal
Step-by-step explanation:
Edge 2020 2021
Find the value of each variable in the following parallelogram - show work
Answers
Answer: x=14 y=10
Step-by-step explanation:
what is the most effluence first step to isolate the variable term on one side of this equation -9x=-4x+5
Answers
if y=1/4x and x=-12 find y
Answers
Answer:
y=-3
Step-by-step explanation:
You have one red apple and three green apples in a
bowl. You randomly select one apple to eat now and
another apple for your lunch. Use a sample space to
determine whether randomly selecting a green apple
first and randomly selecting a green apple second are
independent events.
Answers
Answer: vvvvv
Step-by-step explanation:
Let R1 and G1 represent the red and green apples available for the first selection, respectively. Similarly, let R2, G2a, and G2b represent the red and two green apples available for the second selection, respectively. Then, the sample space for the two selections is:
{(R1, R2), (R1, G2a), (R1, G2b), (G1, R2), (G1, G2a), (G1, G2b)}
Out of these six outcomes, only two involve selecting a green apple first: (G1, R2) and (G1, G2a). And out of these two outcomes, only one involves selecting a green apple second: (G1, G2a).
Therefore, since the probability of selecting a green apple second changes based on whether a green apple was selected first, the events of selecting a green apple first and selecting a green apple second are dependent.
In APQR, what is the mZQ? Enter your answer in the box.
Answers
Answer:
∠Q = 105°
Step-by-step explanation:
(6x + 5) + (11x - 5) + x = 180°
combine like terms:
18x = 180°
x = 10°
∠Q = 11(10) -5 = 105°
How do we solve this?
Answers
Correct option is E, The roots of Auxiliary equation are √6 and -√6.
The solution of an nth-order differential equation or difference equation depends on an algebraic equation of degree n called the characteristic equation (or auxiliary equation) in mathematics.
The auxiliary equation, however, lacks true roots. Consider the simple harmonic equation y + y = 0, which has solutions and was given that name because of how it relates to the vibration of a musical tone. Y2(t) = cos t and Y1(t) = sin t. r2 + 1 = 0 is the auxiliary equation for the straightforward harmonic equation.
The Auxiliary form of the given equation is m² - 6 = 0
Using identity a² - b² = (a - b) (a + b),
⇒ The equation becomes (m - √6)(m+√6) = 0
⇒ either m = √6 or m = -√6
Hence, The roots of Auxiliary equation are √6 and -√6.
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45 points!!
solve question 9
Answers
Answer:
answer
A) 11.7²+X.6²
B) 7²+10² 0²
What is the cos A?Will give 15 points.
Answers
Answer:
Step-by-step explanation:
cos A = \(\frac{\sqrt{8} }{3}\)
Please solve
8-6(x-3) >-4x+12
Answers
Answer:
7 > x
Step-by-step explanation:
8-6(x-3) > -4x+12
Multiply 6 with the ones in the paranthesis:
8-6x+18 > -4x+12
Simplify numbers:
26-6x > -4x+12
Do the balance method:
12-26 > -6x+4x
-14 > -2x
Simplify to x:
-14/-2 > -2x/-2
7 > x
Answer:
Step-by-step explanation:
Here you go mate
Step 1
8-6(x-3) >-4x+12 Equation/Question
Step 2
8-6(x-3) >-4x+12 Simplify
-2x+26>12
Step 3
-2x+26>12 Subtract
-2x>-14
Step 4
-2x>-14 Divide
answer
x<7
2x - y=17 and x-y=10
Solve with substitution, show work?
Answers
Answer:
x = 7 y = -3
Step-by-step explanation:
x - y = 10 ⇒ x = 10 + y
Substitute x = 10 + y into 2x - y = 17:
2(10 + y) - y = 17
20 + 2y - y = 17
y = -3
Substitute the found value of y into x = 10 + y to find x:
x = 10 - 3 = 7
The following data set shows the number of project points each student in a class earned last week.
68, 84, 86, 74, 58, 82, 82, 96, 78, 96, 70, 78, 98, 80, 94, 96, 64, 82, 74, 78, 96. W
Which dot plot correctly displays this data?
Answers
Answer:
D
Step-by-step explanation:
I think its correct
Answer:
C.
Step-by-step explanation: