If the overall percentage of the defective panels from the two plants is 5% then plant B produced 4000 panels in total.
This question can be solved by formulating the problem into the form of a linear equation having two variables. Linear equation in two variables can be represented in the form of ax+by+c=0 where a, b and c are real numbers and x, y are variables or the coefficients, and a, b ≠ 0.
Let the production from plant A be x, and according to the question x=10000.
Also, let the production from plant B be y.
Now, as 3% of products are found defective from plant A and 10% of products are found defective from plant B and overall defective products is 5%.
Thus, 0.03x+0.1y=0.05(x+y)
As x=10000 then
0.03×10000+0.1y=0.05(10000+y)
300+0.1y=500+0.05y
0.05y=200
=>y=4000
Thus, the total number of panels produced by plant B is equal to 4000.
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Is a = 8 a solution to 6 = a/4 + 2
A water bottle holds 120oz. Each time Anna takes a sip she drinks 10oz.a) Write a function to represent the scenario
b) How many sips can Anna take before she needs to refill?
c) Create a graph to represent this situation.
d) What is the domain of the function?
From the situation described, we have that:
a) The linear function is: f(s) = 120 - 12s.
b) She can take 10 sips before she needs to refill.
c) The graph is given at the end of the answer.
d) The domain is: 0 ≤ s ≤ 10.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the parameters are given as follows:
m = -12, b = 120.
Hence the function is:
f(s) = 120 - 12s.
She can take sips until f(s) = 0, hence:
120 - 12s = 0
12s = 120
s = 10.
She can take 10 sips before she needs to refill, and hence the domain(set that contains the input values for the function) is 0 ≤ s ≤ 10.
The graph is given at the end of the answer.
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Two dozen eggs and a loaf of bread cost K4.94. Half a dozen eggs and two loaves of bread cost K2.32. Find the cost of a dozen eggs.
The cost of a dozen of eggs is $3.
Given two dozen eggs and a loaf of bread cost K4.94 and
Half a dozen of bread cost K2.32
Cost of a dozen of eggs = ?
we know that, 24E ₊ B = 8.50 and
6E ₊ 2B = 6.50
multiply the first equation by 2 and substract
48E ₊ 2B = 17
6E ₊ 2B = 6.50
after solving both equations we get:
42E = 10.50
we are searching for the value of a dozen eggs, which is 12E
multiply 42E = 10.50 by 12/42 = 6/21
and you get
12E = 10.50 × (6/21) \\ 10.50 = 21/2
12E = (21×6)/(2×21)
12E = 3
so a dozen eggs cost 3 dollars.
Hence we get the cost of a dozen of eggs as $3
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After the point Y (-4, -9) is translated along the vector <-6, 2>, the image will be located at point
The image of the coordinates of the resulting point are Y'(x, y) = (- 10, - 7).
How to find the coordinates of the image of a given point
In this problem we have the coordinates of a original point and a translation vector, the coordinates of the image is obtained by using the following formula:
Y'(x, y) = Y(x, y) + T(x, y)
Where:
Y(x, y) - Coordinates of the original pointY'(x, y) - Coordinates of the resulting pointT(x, y) - Translation vectorTo learn more on Y(x, y) = (- 4, - 9) and T(x, y) = (- 6, 2), then the coordinates of the resulting point are:
Y'(x, y) = (- 4, - 9) + (- 6, 2)
Y'(x, y) = (- 10, - 7)
The image of the coordinates of the resulting point are Y'(x, y) = (- 10, - 7).
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A quadrilateral with one right angle must be a rectangle
Answer:
false
Step-by-step explanation:
Can someone please find x ?
Answer:
Step-by-step explanation:
Write an algebraic expression that represents the following situation: An Uber driver earn $15 per hour driving per day, but also spends $20 a day on gas. Let h represent the number of hours driven in a day. Write an expression for the amount of profit an Uber driver earns in one day.
Answer:
h * $15 - $20
Step-by-step explanation:
h - number of hours per day
$15 - earnings per hour
$20 cost per day
h * $15 - gross earnings per day
h * $15 - $20 - net earnings per day
Can anybody please help me
Answer:
7x+2/x² +x +2
that's my answer
Some college advisors noticed the following breakdown of majors for the incoming freshman at their school: 3% math, 22% nursing, 16% psychology, 11% criminal justice, and 48% business. Suppose a first-year student was chosen at random. Which of the following is the probability distribution for that student’s major?
Answer:
The correct answer is B, I took the test :)
You just turn the percentages into decimals
The probability distribution table is formed clearly in the answer part.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
The probability for all the elements in the sample space can be shown in one table known as distribution table.
Suppose X be the event of choosing a major.
Then, its probability can be given as P(X).
Here, the percent value of a given event is equivalent to their probability.
It can be represented in the form of table as,
X (Major chosen by student) P(X) (Probability)
Math 3% = 0.03
Nursing 22% = 0.22
Psychology 16% = 0.16
Criminal justice 11% = 0.11
Business 48% = 0.48
This table is known as the probability distribution table.
Hence, the probability distribution table is formed by calculating the probability for each of the events.
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describe the translation from figure A to figure B
Answer:
The figure A is translated from the third quadrant to the second quadrant thus the formula used is P(x,y) = T(a,b) = Image of P(x+a, y+b). The object A and its image B are congruent and the direction and magnitude of the displacements are given by the direction and magnitude of translation vector t = ( a,b ). Where, a is the horizontal displacement ( along x-axis ) and b is the vertical displacement ( along y-axis ).
Evaluate this 5 2/3 + 11/12 =
pls tell me the answer ASAP
Answer:
6[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Another way to write 5 2/3 is to change this into an improper fractions. Another names for 1 is 3/3. I am going to add 5, 3/3 to 2/3
3/3 + 3/3 + 3/3 + 3/3 + 3/3 + 2/3 = 17/3
We want to add this to 11/12, but to do that we need a common denominator. I need to make an equivalent fraction of 17/3 where 12 is the denominator
[tex]\frac{17}{3}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{68}{12}[/tex] Now we can add the two fractions together.
[tex]\frac{68}{12}[/tex] + [tex]\frac{11}{12}[/tex] = [tex]\frac{79}{12}[/tex] = 6[tex]\frac{3}{4}[/tex]
A party rental company has chairs and tables for rent. The total cost to rent 9 chairs and 7 tables is $86. The total cost to rent 3 chairs and 5 tables is $52. What is the cost to rent each chair and each table
Answer: ok here is ur answer The cost for 1 chair is $2.75 and the cost for 1 table is $8.75
Use the elimination method of linear equations to find your answer.
Our equations for this problem are:
3c+5t=52 and 9c+7t=86
1. Multiply the entire first equation by -3.
-3(3c+5t=52)
2. Simplify the equation from above:
-9c-15t=-156
3. Stack the two equations on top of each other and add/subtract:
-9c-15t=-156
9c+7t=86
4. You should be left with -8t=-70. Simplify this to find the value of t:
t=8.75
5. Plug the value of t into any of the original equations and solve for c.
3c+5(8.75)=52
6. Simplify the equation above:
3c+43.75=52
7. Subtract 43.75 from both sides of the equation:
3c=8.25
8. Divide both sides by 3 to get your c value:
c=2.75
Step-by-step explanation: i really hope this helps pls lmk if i am wrong (:
Eli runs a distance of 3 miles in 2/5 of an hour. Jess runs a distance of 4/5 mile in 1/10 of an hour. Who had the faster speed? show your work.
Jess had the faster speed than Eli.
We have the relation connecting Distance travelled, Time taken to travel and the speed given by,
Distance Travelled = Speed x Time taken
Here, we need to find the speed of Eli and Jess to find out who was faster.
So we use the formula, Speed = Distance travelled / Time taken
Distance travelled by Eli = 3 miles
Time taken by Eli = 2/5 hour
Speed of Eli = Distance / Time taken
= 3/(2/5)
= 15/2 = 7.5 miles per hour
Distance travelled by Jess = 4/5 mile
Time taken by Jess = 1/10 hour
Speed of Jess = Distance / Time taken
= (4/5)/(1/10)
= 8 miles per hour
Comparing the speeds of Eli and Jess, Jess had the faster speed of 8 miles per hour.
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A principal has given a class $75 to help pay for a field trip to a zoo. The students in the class are selling pies for
$5 each to earn the rest of the money they need. The field trip will cost a total of $386.
Which inequality can be used to findp, the number of pies the class needs to sell in order to earn enough money to
pay for the field trip?
A 5p+75 ≤ 386
B 5p+752 386
C 75p+52 386
D 75p+5≤ 386
I'd say its A because:
5x#of pies + the money the principal pitched in (75) is less than or equal to 386 dollars (their goal for the field trip).
The inequality equation is given by 5p + 75 ≤ 386 , where p is the number of pies the class sells
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality relation be represented as A
Let the number of pies the class sells be p
Now , the equation will be
The total amount for the field trip = $ 386
The amount given to the students = $ 75
The cost of 1 pie = $ 5
So , the cost of p pies = 5p
Now , the total amount with the students = cost of p pies + amount given to the students
Substituting the values in the equation , we get
5p + 75 ≤ 386
Therefore , the value of A is 5p + 75 ≤ 386
Hence , the inequality relation is 5p + 75 ≤ 386
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There are 31 horses competing in a show, how many ways can the blue,red,and yellow ribbons be awarded
If there are 31 horses competing in a show, then the blue, red, and yellow ribbons can be awarded in 26970 different ways.
As per the question statement, 31 horses are competing in a show.
We are required to calculate the number of ways in which the blue, red and yellow ribbons can be awarded.
To solve this question, first, we need to know a basic rule of horse shows, which is the 1st place or the winner is awarded with a blue ribbon, the second place or the runners-up is awarded with a red ribbon and the third place or the second runners-up is awarded with a yellow ribbon.
That is, in simpler terms, we have to calculate the number of different ways, in which the first, second and third places can be achieved between 31 different horses, each having equal probability of winning.
To solve this question, we just need to know the formula of permutation which goes as [tex][(nPr)=\frac{n!}{(n-r)!} ][/tex], i.e., we are to select an ordered set or "r" from a set of "n".
As per our question, (n = 31) and (r = 3), and using these in the above mentioned formula of permutation, we get
[tex](31C)=\frac{31!}{(31-3)!}=\frac{31!}{28!} =\frac{28!*29*30*31}{28!}=(28*29*30)=26970.[/tex]
That is, the blue, red and yellow ribbons can be awarded in a show with 31 horses as contestants in 26970 different ways.
Probability: In mathematics, probability of an event is the extent to which it is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.Permutation: In mathematics, a permutation of a set is an arrangement of its members into a particular sequence, or if the set is already ordered, a rearrangement of its elements.To learn more about permutations, click on the link below.
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Find and simplify the difference quotient
f(x) = -x²+2x+5
f(x+h)-f(x)
————————
h
w an example
=
Get more help
f(x+h)-f(x)
——————
h
h#0 for the given function
Given difference quotient is f(x) = -x²+2x+5.
Simplified version is (f(x + h) - f(x))/h = 1.
What is difference quotient?If f(x) = x - 5, then
f(h) = h - 5
f(x + h) = (x + h) - 5
(f(x + h) - f(x))/h = (((x + h) - 5) - (x - 5))/h
(f(x + h) - f(x))/h = (x + h - 5 - x + 5)/h
(f(x + h) - f(x))/h = h/h
(f(x + h) - f(x))/h = 1
since h ≠ 0.
The average rate of change of the function over an interval is measured by the difference quotient (in this case, an interval of length h). The instantaneous rate of change is hence the limit of the difference quotient (i.e., the derivative).
The slope of secant lines can be calculated using the difference quotient. Almost identical to a tangent line, a secant line traverses at least two points on a function.
That equation is known as a difference quotient because both the numerator and denominator are differences.
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[tex]-\sqrt[4]{324}[/tex]
y+1-x when x=4 and y=5
Answer:
2
Step-by-step explanation:
Y = 5
x = 4
Substitute
5 + 1 - 4
6 - 4
2
Answer:
Given that x = 4 and y = 5,
[tex]\sf 5 + 1 - 4\\(5 + 1) - 4\\5 + 1\\= 6\\= 6 - 4\\= 2[/tex]
Therefore, the answer is 2.
The kinetic energy T units of a moting body (of constant mass) varies as the square of its speed vm/s. If T = 800 units when v= 20m/s: Calculate V when T= 1800.
The kinetic energy T units of a motion body (of constant mass) varies as the square of its speed v m/s. If kinetic energy T = 800 units when speed v= 20m/s: Calculate V when T= 1800.
If T=1800 then V=30m/s.
kinetic energy is nothing but The energy an object has as a result of motion is known as kinetic energy.
Given that,
If T = 800 units when v= 20m/s
Kinetic energy formula is
[tex]T=\frac{1}{2}mv^{2}[/tex]
Here, T is kinetic energy , m is mass and v is speed
Now,
[tex]800=\frac{1}{2}m(20)^{2} \\800\times2=m(400)\\\frac{1600}{400}=m\\ m=4[/tex]
We got mass m as 4
Now, when T= 1800 find v=?
[tex]1800=\frac{1}{2}\times4\times v^{2} \\1800\times2= v^{2} \\ v^{2} =900\\v=30[/tex]
Therefore, we got speed v=30m/s when the kinetic energy T=1800.
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The sum of 8 and three times a number is 41
Answer:
The number is 11
Step-by-step explanation:
First turn this into a mathematical equation
8+3x=41
subtract 8 from both sides
3x=33
divide both sides by 3
x=11
Question 3 of 10
A triangle has two sides of lengths 6 and 9. What value could the length of
the third side be? Check all that apply.
A. 10
B. 12
C. 4
D. 15
E. 7
F. 2
SUBIT
The third side of the triangle have to greater than the difference of the two provided sides.
A triangle is polygon with 3 edges and 3 vertices.
x > (9-6) so x > 3x < (9+6) so x < 15So possible answers could be:
A. 10B. 12C. 4E. 7he mean life of a tire is 30,000 km. The standard deviation is 2000 km.
Then, 68% of all tires will have a life between ___________ km and __________ km.
The conclusion is that 68% of all tires will have a life between 28000 km and 32000 km.
How to use the Empirical Rule of statistics?
The empirical rule in statistics states that for a normal distribution,
68% of the distribution are within one standard deviation from the mean.95% are within two standard deviation from the mean.99.7% are within three standard deviations from the mean.We are given;
Mean (μ) = 30000 km
Standard deviation (σ) = 2000 km
Using the empirical rule of 68% which lies within one standard deviation from the mean, we have;
μ ± σ = 30000 ± 2000 = (28000, 32000)
Thus, we conclude that 68% of all tires will have a life between 28000 km and 32000 km.
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How many chicks will hatch from 4,500 eggs if on average 87 chicks hatch from 100 eggs?
Answer:
33915
Step-by-step explanation:
87% is the average, so you have to find 87% of 4500.
Jade is stranded downtown with only $10 to get home. Taxis cost $0.75 per mile, but there is an additional $2.35 "hire" charge. Write a formula and use it to calculate how many miles Jade can travel with her money.
Find the area of a parallelogram whose altitude is 17 inches and whose base is 12 inches.
Answer:
A= 204 in²
Step-by-step explanation:
The base is 12 in, and the height is 17 in.
A=b h=12·17=204 in²
it it right
Did Cameron beat his best golf score
Answer: i do not know
Step-by-step explanation:
cause i do not know
Is the product of 3/6 times 5/4 equal to the the product of 3/4 times 5/6? Explain
Answer:
Step-by-step explanation:
Yes the product is equal because even though the numbers may have changed places they did not change the position(numerator to denominator) vice versa.meaning the product of what is in the numerator is equal irrespective of the positions for an e.g in numerator part ion the first terms we have 3*5=15 and in the second scenario we have of course 3*5=15 same applies to the denominators 3*5=5*3Find unit rate $602 for 20 hours of work
Helpp please I don’t understand :(
Answer:
s = 2 1/3 + 1/2
t = 2/3 + 3/2
We have to find the sum of both s and t.
2 1/3 + 1/2 = 2 2/6 + 3/6 = 2 5/6
2/3 + 3/2 = 4/6 + 9/6 = 13/6 = 2 1/6
If we look at the number lines, we can see that c matches with both points.
Amanda is framing her pool for resurfacing. The pool began with 14,340 gallons of water and it is draining at a rate of 880 gallons per hour. How long has the pool been draining if currently there are 8,840 gallons in the pool.
The number of hours that the the pool been draining if currently there are 8,840 gallons in the pool is 6.25 hours.
How to calculate the time?Let the time taken be represented by h.
Therefore, the appropriate expression will be:
14340 - 880h= 8840
Collect like terms
880h = 14340 - 8840
880h = 5500
h = 5500/880
h = 6.25 hours
The number of hours is 6.25 hours.
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