To find the number of items, x, for which the total daily cost, C, of each machine will be the same, we can set up an equation and solve for x. The number of items x for which the total daily cost C of each machine will be the same is 20. For 20 items produced, the total daily cost per machine is $60.
Explanation:To find the number of items, x, for which the total daily cost, C, of each machine will be the same, we can set up the following equation:
40 + 1x = 30 + 1.5x
Simplifying, we get:
0.5x = 10
Dividing both sides by 0.5, we find:
x = 20
Therefore, the number of items x for which the total daily cost C of each machine will be the same is 20.
To find the total daily cost per machine for this number of items, we can substitute x = 20 into the equations for each machine:
Machine A: C = 40 + 1(20) = 60
Machine B: C = 30 + 1.5(20) = 60
So, for 20 items produced, the total daily cost per machine is $60.
The lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel. If $\angle BAE=54^{\circ}$ and $\angle DCE=25^{\circ}$, what is the measure of $\angle AEC$?
Use an asymptote convertor if needed:
[asy]
size( 200 ) ;
pair A = (0,0) ;
pair B = (0,2) ;
pair C = (3,0.5) ;
pair D = (3,2.5) ;
pair ptE = extension( A , A+dir(90-54) , C , C+dir(90+25) ) ;
draw( (0,-0.5)--(0,3) , linewidth(1.3) ) ;
draw( (3,-0.5)--(3,3) , linewidth(1.3) ) ;
draw( A--ptE--C ) ;
dot(Label( "$A$" , A , W )) ;
dot(Label( "$B$" , B , W )) ;
dot(Label( "$C$" , C , E )) ;
dot(Label( "$D$" , D , E )) ;
dot(Label( "$E$" , ptE , N )) ;
label( "$54^{\circ}$" , A , 5dir(70) ) ;
label( "$25^{\circ}$" , C , 8dir(100) ) ;
[/asy]
Answer:
79°
Step-by-step explanation:
Label the intersection of AE and CD point F. Then angle CFE is an alternate interior angle with angle BAE, so is congruent. The angle of interest is an exterior angle to triangle CFE, so is the sum of remote interior angles CFE (54°) and DCE (25°). That sum is ...
m∠AEC = 54° +25° = 79°
Based on the definition of alternate interior angles, the measure of ∠AEC is: 79°
What are Alternate Interior Angles?Interior angles that are alternating each other on a transversal are congruent, and are called alternate interior angles.
Thus:
m∠AEC = m∠BAE + m∠FCE
Substitute
m∠AEC = 54° + 25°
m∠AEC = 79°
Therefore, based on the definition of alternate interior angles, the measure of ∠AEC is: 79°
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The sale price of a sweater is $48. The price is 20% less than the original price. What was the original price.
The original price of the sweater, before a 20% discount, was found to be $60. This was calculated by dividing the sale price of $48 by 0.80, as the sale price represents 80% of the original price.
Explanation:The student is asking how to find the original price of a sweater given that the sale price is $48 and this sale price represents a 20% discount from the original price.
To find the original price, we need to understand that the sale price is 80% of the original price (100% - 20% discount). Let's denote the original price as P. We can set up the equation P * 0.80 = $48. Solving for P, we get P = $48 / 0.80
The calculation will give us the original price which is $60. The original price of the sweater was $60 before the 20% discount was applied.
Final answer:
The original price of the sweater was $60.
Explanation:
Let x be the original price of the sweater.
According to the given information, the sale price of the sweater is $48, which is 20% less than the original price.
So, we can set up the equation as follows-
Original Price - Discount = Sales Price
x - 0.2x = $48
Simplifying:
0.8x = $48
Dividing both sides by 0.8, we get:
x = $60
Therefore, the original price of the sweater was $60.
Shawn's father gave him $168. Shawn bought 10 books, each of which cost $10. How much money does Shawn have left?
will make brainliest
Answer:
68$
Step-by-step explanation:
cost of 10 book= 10$ * 10= 100$
now,
Remaining money= 168$-100$
=68$
Answer:
$68
Step-by-step explanation:
If each of the 10 books costs $10, you must multiply $10 x 10 to get $100. Then, you do $168 - $100 and get $68.
20 business cards are placed in a hat, 10 belong to women, 10 belong yo men If 2 cards are drawn at once. what's the probability that the first is a Man's card and the Second, A woman's card?
5/19
14/19
1/4
9/10
Answer:
First choice:
[tex]\large\boxed{\large\boxed{5/19}}[/tex]
Explanation:
The probability that the first is a man's card and the second, a woman's card is calculated as the product of both probabilities, taking into account the fact that the second time the number of cards in the hat has changed.
In spite of it is said that the cards are drawn at once, since it is stated a specific order for the cards (first is a man's card and the second, a woman's card) you can model the procedure as if the cards were drawn consecutively, instead of at once.
1. Probability that the first is a man's card
Number of cards in the hat = 20 (the 20 business card)Number of man's card in the hat: 10Probability = favorable oucomes / possible outcomes = 10/20 = 1/2.2. Probability that the second is a woman's card
Number of cards in the hat = 19 (there is one less card in the hat)Number of wonan's card in the hat: 10Probability = favorable oucomes / possible outcomes = 10/19.3. Probability that the first is a man's card and the second, a woman's card
(1/2) × (10/19) = 5/19That is the first choice.
Answer:
5/19
Step-by-step explanation:
I know this isn't as good as the other persons answer but I wanted to reassure you that it was correct and my proof is that I took a test on this and got it right with this answer. I hope I helped! :>
total area of the trapezoid
meters. What is the length of
2 The trapezoid below is made up of a square and a triangle. The total area of the
is 57.5 square meters. The area of the triangle is 32.5 square meters. What is the
a side of the square?
A 5 meters
B 25 meters
C 90 meters
D Not enough information is given.
Answer:
A 5 meters
Step-by-step explanation:
57.5 - 32.5 = 25
25 cubed is 5
is 28 √6 rational or irrational
Answer:
68.58571279792898674952395409176495897504652945838676359611.....
Irrational
Step-by-step explanation:
Answer:
It is irrational
Step-by-step explanation:
28sqrt6=sqrt(28^2*6)=sqrt(784*6)=sqrt(4704)=68.5857128...
Since the decimals go on forever, 28sqrt6 is irrational
Hope this helped!
Questions 32 help plz with explanation. 15 points!!
Answer:
The man's son
Step-by-step explanation:
"Brothers and sisters I have none, but that man's father is my father's son" the part where he says "that man's father is my father's son" implies that he is looking at his son.
What is the range of the equation ?
Option D:
all real numbers
Solution:
Definition of domain:
The domain of the function is the set of all possible
x-values (independent variable).
Definition of range:
The range of a function is the set of all possible resulting values
of y-values (dependent variable).
i.e The range of a function is the resulting y-values we get after substituting all the possible x-values.
Given function: [tex]y=\log_8x[/tex]
Domain of y: (0, ∞) (or) {x | x > 0}
Range of y: (–∞, ∞) (or) {y | y > R}
i.e all real numbers
Option D is the correct answer.
Hence the range of y is all real numbers.
in the rectangle below ac=48 units what is de
Answer:
24
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The diagonals of a rectangle are congruent, thus
DB = AC = 48
The diagonals also bisect each other, thus
DE = 0.5DB = 0.5 × 48 = 24 → B
if ABCD is a rombus with side length 15 mm and if BD=24 mm, then find the length of the other diagonal, AC. Draw a diagram and show work.
Answer:
AC = 18 mm
Step-by-step explanation:
See the attachment for a diagram.
Since length BD = 24 mm, length BO = 12 mm. Then ΔBOC is a right triangle with one leg 12 and hypotenuse 15. The other leg (OC) is given by the Pythagorean theorem:
OC² +OB² = BC²
OC = √(BC² -OB²) = √(225 -144) = √81
OC = 9
Diagonal AC is twice the length of OC, so is ...
AC = 2·9 = 18 . . . . mm
_____
It can save a little time if you recognize that the given sides of triangle BOC have the ratio 4:5. This suggests you're dealing with a 3:4:5 right triangle, and that side OC is (3/5)·(15 mm) = 9 mm.
18.
[Algebra - Expansion]
Expand 3(x + 2)
Answer:
Step-by-step explanation:
3(x + 2) = 3*x + 3*2
= 3x + 6
Help help help help
Answer:
b=[tex]\frac{t-5}{4}[/tex]Step-by-step explanation:
4b+5=t
First, you must get the variable alone! Substract 5 from both sides!
4b+5=t
-5 -5
The 5 cancels out because 5-5=0
The new equation is 4b=t-5
You must divide by 4 to get the variable alone since your solving for b!
4b=t-5
4 4
b= [tex]\frac{t-5}{4} \\[/tex]
This is your answer!
The school that Julia goes to is selling tickets to the annual dance competition. On the first day
of ticket sales the school sold 5 adult tickets and 13 child tickets for a total of $159. The school
took in $51 on the second day by selling 1 adult ticket and 5 child tickets. What is the price each
of one adult ticket and one child ticket?!
We have a system of equations in two variables, namely, a and c. Use the substitution to find a and c.
Answer:
The price of 1 adult ticket is $11, while the price of one child ticket is $8.
Step-by-step explanation:
Let's identify what we already know:
1) On the first day of ticket sales, the school sold $159 worth of tickets.
2) On the first day, they sold 5 adults tickets, and 13 adult tickets.
3) The school sold $51 worth of tickets on the second day.
4) The school sold 1 adult ticket, and 5 child tickets.
Let's create two formulas:
(5 times x) + (13 times y) = $159
(1 times x) + (5 times y) = $51
Which value of n makes the equation true? 6n − 2(4n + 7) + 4 = -2
Answer:
n = - 4
Step-by-step explanation:
Given
6n - 2(4n + 7) + 4 = - 2 ← distribute and simplify left side
6n - 8n - 14 + 4 = - 2
- 2n - 10 = - 2 ( add 10 to both sides )
- 2n = 8 ( divide both sides by - 2 )
n = - 4
To solve the equation 6n - 2(4n + 7) + 4 = -2, we apply the distributive property and combine like terms to simplify. The solution is n = -4.
To solve the equation 6n - 2(4n + 7) + 4 = -2, we need to apply the distributive property and combine like terms to simplify.
Distribute the -2 to both terms inside the parentheses: -2(4n + 7) = -8n - 14.Combine like terms: 6n - 8n - 14 + 4 = -2.Combine like terms again: -2n - 10 = -2.Next, we isolate the variable n by adding 10 to both sides: -2n - 10 + 10 = -2 + 10.Simplify: -2n = 8.Finally, solve for n by dividing both sides by -2: n = 8 / -2.Therefore, the value of n that makes the equation true is n = -4.
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The graph at the right shows the relationship between distance and time for a car driven at a constant speed.
1. What is the speed?
2. Is this a function relationship?
3. If this is a function, write a rule to represent it.
Answer:
1. 60 miles per hour
2. Yes, linear
3. Y=60x
Step-by-step explanation:
1. Speed is 60 miles per hour.
2. A function relationship is a relationship between two variables.
3. The rule to represent the function is Distance = 60t.
1. What is the speed?
The speed of the car is the rate at which it is traveling. It is calculated by dividing the distance traveled by the time taken to travel that distance.
Speed = Distance / Time
From the graph, we can see that the car travels 120 miles in 2 hours. Therefore, the speed of the car is:
Speed = 120 miles / 2 hours = 60 miles per hour
2. Is this a function relationship?
A function relationship is a relationship between two variables where each input value has only one output value. In other words, for every value of the independent variable (in this case, time), there is only one corresponding value of the dependent variable (in this case, distance).
We can see from the graph that the distance traveled by the car increases linearly with time. This means that there is a one-to-one relationship between the two variables, and therefore the relationship is a function.
3. If this is a function, write a rule to represent it.
A rule for a function is a mathematical expression that shows how the dependent variable is related to the independent variable. In this case, the rule for the function would be:
Distance = Speed * Time
Substituting the speed of the car into the rule, we get:
Distance = 60 miles per hour * Time
Therefore, the rule to represent the function is:
Distance = 60t
where t is the time in hours.
Widget Wonders produces widgets. They
have found that the cost, o(x), of making x
widgets is a quadratic function in terms of x.
The company also discovered that it costs
$20.50 to produce 3 widgets. $60.50 to
produce 7 widgets, and $133 to produce 12
widgets.
What is the total cost of producing nine widgets
Answer please! True or false!
Answer:
a. False
b. False
c. False
d. True
e. False. (any number above 14.5 is a solution).
Step-by-step explanation:
12 + 6y > 99
6y > 87
y > 14.5.
Can you please help me with the problem in the image below?
Given data:
m∠P = m∠R and TP = SR
To prove that ΔQTP ≅ ΔQSR:
Consider ΔQTP and ΔQSR,
m∠P = m∠R (given angle)
TP = SR (given side)
m∠Q = m∠Q (common angle)
∴ ΔQTP ≅ ΔQSR (by ASA congruence rule)
Hence ΔQTP and ΔQSR are congruence triangles by Angle - Side - Angle congruence rule.
The Indian Ocean is 2/10 of the area of the world’s oceans. What fraction represents the area of the remaining oceans that make up the world’s ocean? Wrote in simplest form
Answer I believe it would just be 8/10
Step-by-step explanation:
You have 2/10 of the worlds ocean which = Indian Ocean
So Your remaining ocean (10-2 = 8)
Also known as 8/10
The remaining oceans make up 4/5 of the world's oceans after subtracting the 1/5 that represents the Indian Ocean.
If the Indian Ocean covers 2/10 (or 1/5 when simplified) of the world's oceans, then the fraction representing the remaining oceans is found by subtracting this fraction from the whole (1, as the whole represents all of the world's oceans).
So, the calculation to find the fraction of the area of the remaining oceans would be:
1 - 2/10 = 1 - 1/5 = 5/5 - 1/5 = 4/5
Therefore, the remaining oceans make up 4/5 of the area of the world's oceans.
a teacher has 64 students to divide into small groups greater than 2 with no remaimder. how many ways can this be done?
To divide 64 students into small groups greater than 2 with no remainder, you would use the concept of combinations, specifically 62C3, resulting in 3,992 possible ways.
Explanation:A teacher has 64 students to divide into small groups greater than 2 with no remainder. To solve this, we can use the concept of combinations, denoted as nCr, where n is the total number of students and r is the size of each group. In this case, the calculation would be 62C3, which equals 3,992 ways of dividing the students into groups.
The first mechanic charged $95 per hours, and the second mechanic charged $70 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2,000. How long did each mechanic work?
Answer:
Step-by-step explanation:
Let a represent the hours put in my mechanic 1 and b represent that of mechanic 2.
a + b = 25, i.e. a = 25 - b
95a + 70b = 2000
Let's substitute the value of a in the second equation
95(25 - b) + 70b = 2000
2375 - 95b + 70b = 2000
2375 - 25b = 2000
-25b = 2000 - 2375
-25b = -375
b = 375/25
b = 15hrs
If b = 15hrs,
a + 15 = 25
a = 10hrs
7x + 2(6x + 9) = 170
Answer:
x = 8
Step-by-step explanation:
7x + 2(6x + 9) = 170
2(6x + 9) = 12x + 18
7x + 12x + 18 = 170
19x = 152
152/19 = 8
x = 8
Is 0,3 a solution to 2x-y=-3
Answer:
Yes, (x, y) = (0, 3) is a solution
Step-by-step explanation:
You can determine whether a given ordered pair is a solution by substituting those values into the equation, then checking to see if the resulting statement is true.
For x=0 and y=3, the equation becomes ...
2·0 -3 = -3 . . . . . a true statement
(0, 3) is a solution to the equation
1/2 = 1/3 − |x−3/6 +x|
Answer:
No solution exist!
Step-by-step explanation:
Answer:
It is impossible to have an arithmetic answer. No Solutions, or ø
Evaluate the expression when x=3 and y= -2
Answer:
-11
Step-by-step explanation:
To evaluate an expression with variables, replace the variables with what the question tells you to.
Replace "x" with 3. Replace "y" with -2.
-x + 4y
= -(3) + 4(-2) Multiply 4 and -2 first to get -8
= (-3) + (-8) Add normally. -3 + (-8) is the same as (-3) - 8.
= -11 Answer
Therefore the solution is -11.
Suppose a population has a doubling time of 25 years. By what factor will it grow in 25 years? 50 years? In 100 years?
A population with a doubling time of 25 years will grow by a factor of 2 in 25 years, by a factor of 4 in 50 years, and by a factor of 16 in 100 years, based on the exponential growth rule.
Explanation:If a population has a doubling time of 25 years, by what factor will it grow in various timeframes? Let's calculate this using the rule of exponential growth.
In 25 years, the factor by which the population will grow is 2, because the definition of doubling time implies that the population doubles every 25 years.
In 50 years, which is two doubling periods, the population will grow by a factor of 2^2 (2 raised to the power of 2), which is 4.
In 100 years, which is four doubling periods, the population growth factor will be 2^4 (2 raised to the power of 4), which equals 16.
Thus:
After 25 years, growth factor = 2After 50 years, growth factor = 4After 100 years, growth factor = 16help asap please!!!!!!!
Answer:
VW=30, WX=20, YW=30,ZX=20
Step-by-step explanation:
how do you do number 5 please.
Answer:
2.4 kg
Step-by-step explanation:
Given
dog eats 0.3 kg of dog food each day
hence we can say that the unit rate is 0.3 kg per day
1 day ------> eats 0.3 kg
8 days -------> eats 0.3 kg x 8 = 2.4 kg
Answer:
2.4 kilogram
Step-by-step explanation:
If
1 day = 0.3kg
8day =
0.3 multiply by number of days
0.3kg * 8= 2.4kg
Find a pair of numbers that is a member of both y=-3x-27 and y=5+x
Answer:
(x, y) = (-8, -3)
Step-by-step explanation:
If all you want is a quick solution, I find a graphing calculator to be very handy. The one used in the attachment shows the solution to be (x, y) = (-8, -3).
_____
You can use one equation to substitute for y in the other equation:
-3x -27 = 5 +x
-32 = 4x . . . . . . add 3x-5 to both sides
-8 = x . . . . . . . . divide by 4
y = 5 +(-8) = -3 . . . . . use the second equation to find y
The pair of numbers that satisfies both equations is ...
(x, y) = (-8, -3)
what is 1% of 12.54?
Answer:
0.1254
Step-by-step explanation:
(Divide by 100 to get 1%)
Answer:
Step-by-step explanation:
0.1254