There are 245 gallons of antifreeze solution required.
What is Percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Here, Let 60% antifreeze solution volume = x
15% antifreeze solution volume = 15%
Final concentration 50%
Process
0.6x + 0.15(70) = 0.5(70 + x)
Simplification
0.6x + 10.5 = 35 + 0.5x
0.6x - 0.5x = 35 - 10.5
0.1x = 24.5
x = 24.5/0.1
x = 245 gallons
Thus, There are 245 gallons of antifreeze solution required.
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Use the sequence 1, 5, 9, 11, 13, ...
Find the 150th term of the sequence.
Answer: 597
Step-by-step explanation:
The common difference is 5-1=4, so the explicit formula is [tex]a_{n}=1+(n-1)(4)[/tex]
Substituting in n=150,
[tex]a_{150}=1+(150-1)(4)=\boxed{597}[/tex]
A firm that sells e-books - books in digital form downloadable from the Internet - sells all e-books relating to do-it-yourself topics (home plumbing, gardening, and so on) at the same price. At present, the company can earn a maximum annual profit of $ when it sells copies within a year's time. The firm incurs a -cent expense each time a consumer downloads a copy, but the company must spend $ per year developing new editions of the e-books. The company has determined that it would earn zero economic profits if price were equal to average total cost, and in this case it could sell copies. Under marginal cost pricing, it could sell copies.
Part 2
In the short run, to the nearest cent, what is the profit-maximizing price of e-books relating to do-it-yourself topics? $
enter your response here.
Part 3
At the profit-maximizing quantity, to the nearest cent, what is the average total cost of producing e-books? $
enter your response here.
The profit-maximizing price of e-books relating to do-it-yourself topics is $5.35 and the average total cost of producing e-books is $4.35.
Profit-maximizing price and average total costa. Profit-maximizing price
The maximum that the firm can earn is $35,000 at a quantity of 35,000 copies
Fixed cost FC = $140,000
Variable cost vc=$0.35 per book
Total Revenue TR =P XQ
Total Revenue TR= P x 35,000
Total Cost TC = FC + VC XQ
Total Cost TC = 140,000 + (0.35×35,000)
Total Cost TC = 140,000 +$12,250
Total Cost TC = $152,250
Profit = TR- TE
35,000 = 35,000P- $152,250
35,000P=187,250
P=187,250/35,000 copies
P=$5.35
b. Average total cost
Average total cost=Total cost/Quantity
Average total cost= $152,250/35,000 copies
Average total cost=$4.35
Therefore the profit-maximizing price of e-books relating to do-it-yourself topics is $5.35 and the average total cost of producing e-books is $4.35.
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The complete question is:
A firm that sells e-books - books in digital form downloadable from the Internet - sells all e-books relating to do-it-yourself topics (home plumbing, gardening, and so on) at the same price. At present, the company can earn a maximum annual profit of $35,000 when it sells 35,000 copies within a year's time. The firm incurs a 35-cent expense each time a consumer downloads a copy, but the company must spend $140,000 per year developing new editions of the e-books. The company has determined that it would earn zero economic profits if price were equal to average total cost, and in this case it could sell 40,000 copies. Under marginal cost pricing, it could sell 120,000 copies.
In the short run, to the nearest cent, what is the profit-maximizing price of e-books relating to do-it-yourself topics?
At the profit-maximizing quantity, to the nearest cent, what is the average total cost of producing e-books?
Question 18 25
f(x) = 2x
g(x) = 4x + 1
Find
() (2). Include any restrictions on the domain.
A.
(4) (x) = 477³¹, x ≥ 0
○ B. ( 4 ) (x) = ¹⁄⁄², ¤ / 0
4c-1
x
O c. (1) (₂) -
O D. (5)(x) =
✓/2T
55-1
2,² / 1
2 / -4
Answer: D
Step-by-step explanation:
[tex]\left(\frac{f(x)}{g(x)} \right)=\frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{4x+1}[/tex].
This eliminates A and B.
Also, the domain excludes when the denominator equals 0, which in this case, makes the answer D
CON PROCESOS POR FAVOR
Answer:
[tex] \dfrac{149}{40} [/tex]
[tex] \dfrac{38}{15} [/tex]
Step-by-step explanation:
[tex] (\dfrac{7}{8} + \dfrac{4}{5}) - (\dfrac{9}{20} + \dfrac{-5}{2}) = [/tex]
[tex] = (\dfrac{7}{8} \times \dfrac{5}{5} + \dfrac{4}{5} \times \dfrac{8}{8}) - (\dfrac{9}{20} + \dfrac{-5}{2} \times \dfrac{10}{10}) [/tex]
[tex] = (\dfrac{35}{40} + \dfrac{32}{40}) - (\dfrac{9}{20} + \dfrac{-50}{20}) [/tex]
[tex] = \dfrac{67}{40} - (-\dfrac{41}{20}) [/tex]
[tex] = \dfrac{67}{40} + \dfrac{41}{20} \times \dfrac{2}{2} [/tex]
[tex] = \dfrac{67}{40} + \dfrac{82}{40} [/tex]
[tex] = \dfrac{149}{40} [/tex]
[tex] (-\dfrac{6}{4} + \dfrac{3}{2}) + (\dfrac{6}{5} + \dfrac{4}{3}) = [/tex]
[tex] = (-\dfrac{3}{2} + \dfrac{3}{2})+ (\dfrac{6}{5} \times \dfrac{3}{3} + \dfrac{4}{3} \times \dfrac{5}{5}) [/tex]
[tex] = 0 + \dfrac{18}{15} + \dfrac{20}{15} [/tex]
[tex] = \dfrac{38}{15} [/tex]
To prove triangles similar, we only need to prove corresponding angles congruent OR corresponding sides are proportional. However, with a quadrilateral we need to prove corresponding angles congruent AND corresponding sides are proportional. Explain in your own words why it takes more to prove that quadrilaterals are similar. Include examples demonstrating how “just angles” or “just sides” is not enough.
It takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc.
What is a quadrilateral?It should be noted that a quadrilateral simply means a shape that has four sides and four angles.
In orde to prove that triangles are similar, we only need to prove corresponding angles congruency.
On the other hand, it takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc. This makes them more elaborate.
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if the relationships below are given in the form(input, output) which paring always describes a function
The function among the given option is height of a building in feet, height of the building in inches , Option B is the correct answer.
What is a Function ?
A function is a law that relates a dependent and an independent variable.
The options mentioned below needs to be studied to determine which forms a function.
Option A , C and D doesn't really form a function ,
For two variables need to be a function then they have to be dependant on each other and have only one output for a given input.
height of a building in feet, height of the building in inches
Height of building in feet = (height of building in inches/12)
so this is a function
Therefore Option B is the right answer.
The missing options are
If the relationships below are given in the form (input, output), which pairing always describes a function?
A) (number of doors in a car, number of cup holders in the car)
B) (height of a building in feet, height of the building in inches)
C) (beverage charge on a bill, total meal charge on the bill)
D) (distance from home during a trip, time elapsed during the trip)
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can someone please help mee
Answer:
[tex]f(z) = z^2-3z+2[/tex]
[tex]f(x+1) = x^2-x[/tex]
[tex]f(\sqrt{2}+1) = 2-\sqrt{2}[/tex]
Step-by-step explanation:
[tex]f(x+1) = x^2+2x+1-3x-3+2[/tex]
[tex]f(\sqrt{2}+1) = 2+2\sqrt{2}+1-3\sqrt{2}-3+2[/tex]
Can someone help me with this?
Answer:
A
Step-by-step explanation:
In this case you have to show that 1 + 2 = 180
This way when you show that 2 + 3 = 180, that proves 1 & 3 are congruent.
Answer:
A. 2. ∡1 is supplementary to ∡2 (linear pair theorem)
Step-by-step explanation:
Given the following proof so far, we have:
1. Line a and line b intersect => given
2. ? => ?
3. ∡3 is supplementary to ∡2 => linear pair theorem
4. ∡1 ≅ ∡3 => congruent supplements theorem
Now let's take a look at the reasoning for statement 4, which says that angle 1 and 3 are congruent due to congruent supplements theorem.
In this theorem, if 2 angles are supplementary (add up to 180 degrees) to the same angle, it means those 2 angles are congruent.
Why does this work?
________________________________________________________
Let's say x + y = 180, and z + y = 180
By transitivity (if a = b and b =c, then a=c), x + y is equal to z + y
x + y = z + y
Subtract y from both sides
x = z
________________________________________________________
Statement 3 says ∡3 is supplementary to ∡2, and because of congruent supplements theorem being our last reason (where ∡1 and ∡3 are congruent), we need to make statement 2 also have ∡1 being supplementary to ∡2, (∡2 is like y in the example above - it's the angle that ∡1 and ∡3 are both supplementary to).
This will eliminate choices B (which has ∡1, but also ∡4 which isn't necessary), C ( ∡which mentions nothing about ∡1), and D (which also doesn't mention anything about ∡1, and which also isn't necessary as we have statement 3 essentially saying the same thing), leaving A as the correct answer.
John invested $4,500 at 5.5% annual simple interest. His maturity value of his investment was $5,545. How long did John invest the money? Round to the hundredth.
John invested the money at simple interest for 4.22 years.
We have,
Invested amount = $ 4500
Rate of interest = 5.5 %
Time = t years
Maturity value = $ 5545
So,
Total interest earned = $ 5545 - $ 4500 = $ 1045
And,
Simple interest = (Principal × Rate × Time ) / 100
So, Using the mentioned formula,
1045 = ( 4500 × 5.5 × t ) /100
1045 = 45 × 5.5 × t
⇒
t = (1045) / (45 × 5.5)
⇒ t = 4.22 years
Therefore, John invested the money at simple interest for 4.22 years.
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Need help with this geometry question
2) [tex]\overline{EK} \cong \overline{KG}, \overline{HK} \cong \overline{KF}[/tex]
3) Opposite sides of a parallelogram are congruent.
4) [tex]\triangle EF \text{ }K \cong \triangle GHK[/tex]
Maria rides her bicycle to school at a constant speed of 15 miles per hour.If the distance to school is 6 miles,how many minutes will it take Maria to get to school?EXPLAIN PLEASE
E. 10
F.15
G.24
H.30
Answer:
24 minutes
Explanation:
Given:
speed: 15 miles/hdistance: 6 milesFormula:
time taken = distance/speed
Applying the formula:
time taken = 6/15 = 0.4 hours = 24 minutes
Now
Speed=Distance/TimeTime=Distance/SpeedTime =6/15=0.4h=24minwhat is the value of x
let's name the vertices of the triangle as A B C and D as the image shown above
In triangle ABC
sin 60° = AB/AC
√3/2 = 8√2/ AC
AC = 16√2/√3
In triangle ACD
sin 45° = AC/AD
1/√2 = 16√2/ 3 AD
AD = 16/3 x = 16/3Select the correct answer.
A system of equations and its solution are given below.
System A
x + y = 8
4x - 6y = 2
Solution: (5,3)
Choose the correct option that explains what steps were followed to obtain the system of equations below.
System B
x + y = 8
10x = 50
Answer:
B will be the answer...
Step-by-step explanation:
The second equation in system B is only in terms of y, so we need to use elimination to eliminate the x term from the second equation in system A.
To do that, we need to multiply the first equation by 5.
5 (-x − 2y = 7)
-5x − 10y = 35
Add to the second equation. Notice the x terms cancel out.
(-5x − 10y) + (5x − 6y) = 35 + (-3)
-16y = 32
Combining this new equation with the first equation from system A will get us system B.
-x − 2y = 7
-16y = 32
Answer:
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution to system A.
Step-by-step explanation:
exact answer
An angle measures 37*. What is the measure of its supplement?
Answer:
143°
Step-by-step explanation:
supplementary angles are angles that combine to form a straight line (and we know that a straight line = 180 degrees)
you can think of an angle as needing another angle to "supplement" it into being a full line.
So, we know that one angle = 37°
And that: one angle + supplementary angle = 180 degrees
37° + x = 180°
- 37 -37
x = 143
So, the measure of this angle's supplement is 143°
hope this helps!!
Answer:
143 degrees
Step-by-step explanation:
180 - 37 = 143
Which trig expression can be used to find the height on the tree where the top guy wire attaches if the base of the wire is four feet from the base?
The trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)
How to use trigonometric rations to find height?The height of the tree can be found using trigonometric ratios.
Therefore,
tan ∅ = opposite / adjacent
Hence,
for the higher wire
tan 75 = h / 4
4 tan 75 = h
This can be express as follows:
tan 75 = tan(45 + 30)
Hence,
4 × 3.73205080757 = 14.9282032303 ft = 14.9ft
Hence, the trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)
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boat traveled downstream a distance of 60 mi and then came right back. If the speed of the current was 6 mph and the total trip took 4 hours find the average speed of the boat relative to the water.
Answer:
7.5mph
Step-by-step explanation:
Let the average speed of the boat to be x mph.
Total Distance = Avg. Speed x Total Time
60 = ((x+6) + (x-6))(4)
60 = (x+6+x-6)(4)
(2x)(4)=60
2x=60/4
2x = 15
x = 15 /2
x = 7.5mph
Answer:
15 +√261 ≈ 31.155 mph
Step-by-step explanation:
The time for the trip can be found by dividing the distance by the speed.
__
setupThe relation between time, speed, and distance is ...
time = distance/speed
The speed for the downstream leg was the sum of the boat speed (b) and 6 mph. The speed for the upstream leg was the difference. So the total trip time was ...
4 = 60/(b +6) +60/(b -6) . . . total time is the sum of the times for the legs
__
solutionMultiplying by the product of the denominators, we have ...
4(b +6)(b -6) = 60(b -6) +60(b +6)
b² -36 = 30b . . . . divide by 4 and simplify
b² -30b = 36 . . . . put in a form useful for completing the square
(b -15)² = 36 +15² . . . . . complete the square
b -15 = √261 . . . . . . . . take the square root (negative root is extraneous)
b = 15 +√261 ≈ 31.155 . . . . add 15
The average speed of the boat was about 31.155 mph.
The measure of an interior angle of a regular polygon is 120°. What is the measure of each exterior angle? The polygon has how many sides?
Answer:
60°, arms 6
Step-by-step explanation:
let the total arms = n
total generated angles in a regular polygon is = (n-2)×180
now,
(n-2)×180 = 120 n
or, 180n - 360 =120n
or, 60n = 360
or, n = 6
The average car sold from Dealership A is $25,700. If the sales person receives 1.5% commission on price of car, how much commission is made on average per car sold?
Answer:
$385.50
Step-by-step explanation:
The amount of commission is found by multiplying the commission rate by the value of the sale.
1.5% × $25,700 = $385.50
A commission of $385.50 is made on an average car sold.
consider the graph of y= f(x), shown below
Answer: The domain is [tex]\boxed{(-4, 4)}[/tex] and the range is [tex]\boxed{[-4, 4]}[/tex].
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Marsha deposited $9,500 into a savings account 2 years ago. The simple interest rate is 2%. How
much money did Marsha earn in interest?
Substitute the values into the equation.
Interest=$years
Answer:
$380Step-by-step explanation:
GivenDeposit amount P = $9500Interest rate r = 2%Time t = 2 years
Use interest formula:
I = PrtSubstitute given values and calculate:
$9500*0.02*2 = $380Answer:
$ 380
Step-by-step explanation:
We can use the below formula to find the simple interest.
Simple interest = P r t ÷ 100
Here,
P ⇒ Principal ⇒ $ 9500
r ⇒ rate ⇒ 2%
t ⇒ time ⇒ 2 years
Let us solve it now.
Simple interest = P r t ÷ 100
Simple interest = 9500 × 2 × 2 ÷ 100
Simple interest = 38000 ÷ 100
Simple interest = $ 380
A linear function contains the following points. What are the slope and y-intercept of this function?
Answer:
slope: -1
y-intercept: 6
Step-by-step explanation:
y-intercept is when x is 0 so it's 8 and the slope can be found using the slope formula (y2-y1)/(x2-x1)
(6-8)/(0 - (-2)) = -2/2 = -1
Given that y is an integer, find all values of y such that y< 6
Answer:
Values: 3,4,5
Step-by-step explanation:
I hope this helps:)
DRaw the graph of f (x) = 1/2 x² -2x where -2 < x < 4
Answer:
Graphs Attached Below
Step-by-step explanation:
Hello!
Standard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]
From our Equation:
a = 1/2b = -2c = 0There are several values that are needed to drawing a parabola:
y - interceptAxis of Symmetry (AOS)Vertexx - interceptsY-interceptStandard form of a quadratic: [tex]ax^2 + bx + c= 0[/tex]
The y-intercept is the "c" value. Given that our equation has a "c" value of 0, the y -intercept is 0.
Axis of SymmetryA parabola is always symmetrical vertically. The line in which the fold happens is the Axis of Symmetry.
To calculate the AOS, we use the formula [tex]AOS = \frac{-b}{2a}[/tex], from the values of the equation.
Calculate
[tex]AOS = \frac{-b}{2a}[/tex][tex]AOS = \frac{-(-2)}{2(0.5)}[/tex][tex]AOS = \frac{2}{1}[/tex][tex]AOS = 2[/tex]The Axis of Symmetry is a vertical line, so the AOS is the line x = 2.
VertexThe vertex is the highest or lowest point on the graph of a parabola. It resides on the AOS of the graph.
To calculate the vertex, we simply have to find the y-value, given that we have the x-value from the AOS. We can find the y-value by plugging in the AOS for x in the original equation.
Calculate
[tex]f(x) = \frac12x^2 - 2x[/tex][tex]f(x) = \frac12 (2)^2 - 2(2)[/tex][tex]f(x) = 2 - 4[/tex][tex]f(x) = -2[/tex]The y-value is -2. The vertex is (2, -2).
X-interceptsThe x-intercepts are the points where the graph intersects the x-axis (y = 0).
Solve by Factoring
[tex]f(x) = \frac12 x^2 - 2x[/tex][tex]0 = \frac12x(x - 4)[/tex][tex]x = 0, x = 4[/tex]The roots are (0,0) and (4,0).
GraphNow we just draw the y-intercept, vertex, AOS, and the x-intercepts, and draw a curved line between them.
Image Attached
Domain RestrictionsThe Domain (x-values) are being restricted to all x-values that are greater than or equal to -2 and less than 4.
That means we remove the parts of the line that don't belong in that domain.
Image Attached
How much time do you actually save by speeding?
Of the following fractions3/7, 5/8, 7/13, and 11/19 Which is the largest
Answer:
5/8
Step-by-step explanation:
5/8=0.6.25
0.625> all the other numbers
determined about the triangle formed by the ground,
wall, and ladder? Check all that apply.
The triangle is isosceles.
The leg-to-hypotenuse
ratio is 1:√√2.
The leg-to-hypotenuse ratio is 1:√2.
The nonright angles are congruent.
The ladder represents the longest length in the
triangle.
(A,B,D,E)
Answer:
a² b² c² equals mc² and that is the answer
find the highest number of student of whom 125 apples, 150 oranges and 225 mangoes can be divided equally
Answer:
25
Step-by-step explanation:
find the greatest common factor (GCF) of the 3 quantities using prime factorisation.
125 = 5 × 5 × 5
150 = 2 × 3 × 5 × 5
225 = 3 × 3 × 5 × 5
Next, identify those prime factors that the 3 numbers have in common and multiply them.
the common factors are 5 × 5 = 25
then
125 ÷ 25 = 5
150 ÷ 25 = 6
225 ÷ 25 = 9
the 25 students each get 5 apples, 6 oranges and 9 mangoes
Taylor's computer randomly generate numbers between 0 and 4, as represented by the given uniform density curve.
A graph titled Random number generated by computer has random number on the x-axis. A horizontal line is at y = one-fourth from 0 to 4.
What percentage of numbers randomly generated by Taylor's computer are less than 0.5?
12.5%
25%
50%
87.5%
Picture posted below
12.5% is the percentage of numbers randomly generated by Taylor's computer that is less than 0.5.
An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).
The percentage of numbers randomly generated by Taylor's computer are less than 0.5 is given by
P(0≤X≤0.5)
=[tex]\int_{0}^{0.5}\frac{1}{4}dx[/tex]
[tex]=\frac{1}{4}x|^{0.5}_{0}[/tex]
[tex]=\frac{1}{4}(0.5-0)[/tex]
[tex]=0.25(0.5)[/tex]
= 0.125
That is 12.5%
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The radius of a circle is 4 millimeters. What is the circle's area? Use 3.14 for pi.
(The answer MUST BE ONE OF THE ANSWERS BELOW)
Answer:
50.24 mm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = 3.14 ( 4)^2
= 50.24 mm^2
Answer:
c. 50.24 square millimeters
Step-by-step explanation:
Radius of circle = 4 milimeters.
Area of a circle = πr²
Area = 3.14 × 4² (π = 3.14)
= 50.24 square millimeters
PLEASE HELP what does -4=<X<4 mean?
Suppose that the function fis defined for all real numbers as follows. Graph the function f. Then determine whether or not the function is continuous.
Answer:
the value of x is between -4 and 4
