The cost to produce x units of wire is C = 35x + 500, while the revenue is R = 60x.
Find all intervals where the product will at least break even.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The inequality in interval notation is
B. The product will never break even.
Answers
Answer:
n order for the product to at least break even, the revenue must be equal to or exceed the cost. To solve for this interval we set R>=C. So,
45x>=20x+550. Once we solve this equation we get x>=22 so the interval where the product will at least break even
so the answer is B.
Related Questions
Find the area of the figure pictured below.
15 yd
10 yd
17 yd
5 yd
A
Answers
First find the area of the square, then the triangle.
15 times 17 = 255 sq. yd
Triangle:
(5 times 5)/2 = 12.5 sq. yd
Your answer is 267.5 sq. yd
Hope this helps.
The vector ⇀
= ⟨2, 3⟩ is multiplied by the scalar –4. Which statements about the components, magnitude, and direction of the scalar product –4⇀
are true? Select all that apply.
A. The component form of −4⇀
is ⟨–8, –12⟩.
B. The magnitude of −4⇀
is 4 times the magnitude of ⇀
.
C. The direction of −4⇀
is the same as the direction of ⇀
.
D. The vector −4⇀
is in the fourth quadrant.
E. The direction of −4⇀
is 180° greater than the inverse tangent of its components.
Answers
Answer:
Therefore, the correct statements are A, B, and E.
Explanation:
Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.
To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀
.
- The component form of −4⇀
is obtained by multiplying each component of ⇀
by –4. Therefore, −4⇀
= ⟨–8, –12⟩. This means that statement A is true.
- The magnitude of −4⇀
is obtained by multiplying the magnitude of ⇀
by 4. The magnitude of ⇀
is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀
is 4√13. This means that statement B is true.
- The direction of −4⇀
is opposite to the direction of ⇀
because the scalar –4 is negative. This means that statement C is false.
- The vector −4⇀
is in the third quadrant because its components are both negative. This means that statement D is false.
- The direction of −4⇀
is 180° greater than the inverse tangent of its components because it is opposite to ⇀
. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀
is 180° + tan^(-1)(3/2). This means that statement E is true.
Therefore, the correct statements are A, B, and E.
Here is a rectangle.
9 cm
7 cm
Work out the perimeter of the rectangle.
Answers
Answer:
P=32cm
Step-by-step explanation:
Answer: 32
Step-by-step explanation: 9+9 =18
7+7= 14
14+18=32
Kendall is starting a new small business and working everyday to make it a success. She earned $952 in 7 days. Assume she will continue to earn money as the same rate and write this rate as a fraction with 30 in the denominator.
Answers
Answer:
$4080 / 30days
Step-by-step explanation:
In 7 days, Kendall earns $952
In 1 day, she will earn $952 ÷ 7 = $136
Therefore, the rate (r) at which she earns is $136/day. i.e
r = $136/day ---------------(i)
To write the rate as a fraction with 30 in the denominator, we multiply both the numerator and denominator of equation (i) by 30 as follows;
r = $(136x30) / 30 day
r = $4080/30days
1) Rick had to borrow $35,000 to buy a brand new
car. He has to pay 10% interest for 5 years. How
much interest will he have to pay?
80
Answers
On solving the provided question we can say that the total interest he pay in 5 year is = $17500.
How much is interest?The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money. The basic interest formula is as follows: Interest is equal to P, R, and T. P is the principal sum (the beginning balance). Interest rate, R (usually per year, expressed as a decimal). T = Number of intervals of time (generally one-year time periods).
Money required to borrow new car is $35,000.
and Rick pay 10% interest per year
so, interest he pay in one year = $35000 x 10% = $3500
total interest he pay in 5 year is = $17500
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Find the error. Select choice options are step 1, 2, 3 and x-coordinates and y-coordinates
Answers
Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.
What is the slope?
In mathematics, the slope is a measure of the steepness of a line.
The solution provided involves three steps to find the slope of the line that passes through two points: (-2, 8) and (4, 6).
Step 1 involves finding the change in y-coordinates, which is the difference between the y-coordinate of the second point and the y-coordinate of the first point. In this case, the second point has a y-coordinate of 6 and the first point has a y-coordinate of 8.
Therefore, the change in y-coordinates is 6 - 8 = -2.
Step 2 involves finding the change in x-coordinates, which is the difference between the x-coordinate of the second point and the x-coordinate of the first point. In this case, the second point has an x-coordinate of 4 and the first point has an x-coordinate of -2.
Therefore, the change in x-coordinates is 4 - (-2) = 6.
Step 3 involves dividing the change in y-coordinates by the change in x-coordinates to find the slope of the line. In this case, the change in y-coordinates is -2 and the change in x-coordinates is 6, so the slope is -2/6 or -1/3.
Since all the steps are correct and properly executed, there is no error.
Therefore, the slope of the line that passes through (-2, 8) and (4, 6) is -1/3.
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PLS HELP!! A student randomly guesses the answers to two true-false questions. Describe and correct the error in finding the probability of the student guessing both answers correctly. The student can either guess two incorrect answers, two correct answers, or one of each. So the probability of guessing both answers correctly is 1/3
Answers
Answer:
The student was wrong. The probability is actually 1/4.
Step-by-step explanation:
Let's say you have question A and question B. You could have incorrect on A, and incorrect on B. Or, you could have incorrect on A, but a correct on B. Or, you could have an incorrect on B, but a correct on A. Or, both could be correct. Since there are 4 different possibilities, the actual probability is 1/4.
need help writing a function
Answers
n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.
What is a linear equation in mathematics?
A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.
A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.
Roots : -3(mult . 2), 4(mult.2)
the function is given as
f(n) = (n + 3)² (n - 4)²
= (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)
= (n² + 6n + 9) (n² - 8n + 16 )
= n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1
collecting like term,
f(n) = n⁴ - 2n³ - 23n² + 24n + 144
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What is the median of the following Systolic Blood Pressure in mmHg: 121, 110, 114, 100 160, 130 130?
Answers
Answer:
121
Step-by-step explanation:
firstly you arrange the numbers in ascending order the number in the middle is considered to be the median
A partnership between two companies calls for company A to get a flat fee of $25,000 from Company B each month, plus 15% of all sales for the jointly developed product sold by company B. If Company B sells a total of $1,200,000 of the jointly developed product in the first twelve months, what will be the total amount owed Company A by Company B?
Answers
Answer:
no idea what the answer is, good luck!
Step-by-step explanation:
PLEASE HELP find mQT and m
Answers
Answer:
\(.x1 - 4 { {0.36 + + \times 4xx { {052. < < }^{?} }^{2} }^{?} } \gamma eee} \)
Eli has 3 cups of m&m's. He wants to separate them into 1/4 cups bags to share with his friends how many friends can Eli give a 1/4 bag of m&m's to?
Answers
Answer:
the answer would be 12 friends
Step-by-step explanation:
you would take the 3 and multiply it by the denominator which is the 4. so 3 × 4 = 12
2x + y = 7
x + y = 1
Answers
The solution to the system of equations is x = 6 and y = -5, which is the same as we obtained using the elimination method.
What is the system of equations?A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:
2x + y = 7 ---(1)
x + y = 1 ---(2)
To solve this system, we can use the method of elimination or substitution.
Method 1: Elimination
In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.
Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:
-2(x + y) = -2(1) --
Multiplying equation
(2) by -2-2x - 2y = -2
Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:
2x + y = 7(-2x - 2y = -2)0x - y = 5
We now have a new equation in which y is isolated.
To solve for y, we can multiply both sides by -1:
-1(-y) = -1(5)y = -5
Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6
Therefore, the solution to the system of equations is (x,y) = (6,-5).
Method 2: Substitution
In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.
From equation (2), we can solve for y in terms of x:y = 1 - x
We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6
Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5
Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.
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There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
How many people use at least two
facilities?
Answers
Answer:
he total number of people who use at least two facilities is 4 + 45 = 49
Step-by-step explanation:
To find the number of people who use at least two facilities, we can find the number of people who use all three facilities and add the number of people who use only two facilities.
The number of people who use all three facilities is 4, and the number of people who use only two facilities is 27 + 23 + 31 - 3 * 4 = 45.
Therefore, the total number of people who use at least two facilities is 4 + 45 = 49.
Prove the following statement by mathematical induction:
\(\sum_{i=1}^{n+1}{i*2^i = n * 2^{n+2} + 2}\) for all integers n ≥ 0.
Answers
The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.
What is mathmetical induction?Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.
The process involves two steps:
Base case: Prove the statement is true for some initial value, usually n = 1 or n = 0.Inductive step: Assume the statement is true for an arbitrary value of n, and use this assumption to prove that the statement is also true for the next value, n + 1.Here,
First, we need to prove the statement is true for the base case n=0,
When n=0, we have,
\(\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2\)
and
\(n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2\)
Therefore, the statement is true for n=0.
Next, we assume the statement is true for some arbitrary integer k, meaning:
\(\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2\)
We want to show that the statement is also true for n=k+1,
\(\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2\)
We can rewrite the left-hand side of the equation as,
\(=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2\)
This last step used the assumption that the statement is true for n=k.
Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.
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Look at the tape diagram below for the number of boys and the number of girls in a school. Find total number of students in the school.
Answers
Write an exponential growth equation for the following graph (i’ll give brainliest)
Answers
The exponential growth equation that passes through the given points is \(y = 6 \times 1.5^x\)
How to find an exponential growth equation ?
An exponential growth equation that passes through the given points. We aretaking the equation takes the form \(y = a×b^x \) where a is the initial value and b is the growth factor. We can use the three given points to form a system of equations.
It is clear that the equation passes through points ( -1,4), (0,6), (1,9)
So,
\(4 = ab^{-1} \\ 6 = ab^0 \\ 9 = a \times b^1\)
We are dividing the second equation by the first equation,
\( \frac{6}{4} = \frac{(ab^0)}{(ab^{-1})}\)
1.5 = b
Next, we can use this value of b in the third equation to find a,
9 = a×1.5¹
a = 6
Therefore, the exponential growth equation that passes through the given points is \(y = 6 \times 1.5^x\)
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Carter shared his post with 10 friends, who each share with only 2 people each day. Carter shared his post with 10 friends, who each share with only 2 people each day.
write an exponential function to represent the spread of carters social media post.
Answers
The exponential function will be equal to y = 20ˣ.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Carter shared his post with 10 friends, who each share with only 2 people each day.
The exponential function will be written as,
y = abˣ
y = 10(2)ˣ
y = 20ˣ
Therefore, the exponential function will be equal to y = 20ˣ.
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Answer:
f(x) = 10(2)^x
Step-by-step explanation:
Rule for solving: The first number is the first part of the equation, and the second number is in parenthesis.
1. what is the difference when (-6) is subtracted from (-3)?
Please give solutions
Answers
Answer:
(-3) - (-6) = -3+6 = 6-3 = 3
Step-by-step explanation:
Step-by-step explanation:
= -6 - (-3)
= -6 + 3
= -3
-6 change into -3
HELP ASAP (6 + 9m) + (- 4y - 5) + (7m + 6y)
Answers
Answer:
Simplify the expression
16m+2y+1
PLEASE HELP FAST!!! **20 POINTS**
Answers
Answer: constant of proportionately is 0.66 repeating. (I think)
Please help fast!!!!!!!
Answers
Answer: 156.38 m
Step-by-step explanation:
Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)
A mini fruit juice box contains 4 fluid ounces of juice. You need 2 1/2 quarts of fruit juice. How many mini fruit juice boxes will you need?
Answers
Answer:
1 3/5, hope I helped!
Step-by-step explanation:
4 divided by 2 1/2
4/1 divided by 5/2
4/1 times 2/5
8/5
1 3/5
8/5 mini fruit juice boxes will be needed
It is given that a mini fruit juice box contains 4 fluid ounces of juice, we need to find how many mini fruit juice boxes will be needed for 2 1/2 quarts of fruit juice.
What is 1 quart?
A unit of US customary system used in liquid measure, equal to 2 pints or 32 ounces
4 divided by 2 1/2
4 divided by 5/2
4 × 2/5
8/5
Therefore 8/5 mini fruit juice boxes will be needed for 2 1/2 quarts of fruit juice
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What is the approximate area, in square units, of the circle shown below?
Answers
9514 1404 393
Answer:
50.3 square units
Step-by-step explanation:
The circle has a diameter of 8 units, so a radius of 4 units. The area formula is ...
A = πr²
A ≈ 3.14159(4²) ≈ 50.265
The area of the circle is about 50.3 square units.
Find the volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0). Slices perpendicular to the x-axis are semicircles. Enter answer using exact values.
Answers
The volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0) is 25π/12 cubic units.
What is a triangle?
A triangle is a closed geometric shape that is formed by connecting three line segments. These line segments are called sides, and the points where they meet are called vertices. A triangle has three sides, three angles, and three vertices.
To start, let's graph the triangle to get a better understanding of the problem:
(0,3) *
|\
| \
| \
| \
| \
(0,0) *-----*-----> x
(5,0)
The height of this slice is given by the line from the point (x,0) to the point (0,3), which has equation y = 3/5 * x + 0. The radius of the semicircle is half the height of the slice, which is given by the equation r = 3/10 * x.
The area of a semicircle is πr²/2, so the volume of this slice is:
V(x) = π * (3/10 * x)² / 2 * dx
To find the total volume of the solid, we need to integrate this expression over the range of x values that covers the entire base of the solid, which is from x=0 to x=5:
V = ∫₀₅ π * (3/10 * x)² / 2 dx
V = π/20 * ∫₀₅ x² dx
V = π/20 * [x³/3] from 0 to 5
V = π/20 * (5³/3)
V = π/4 * (25/3)
V = 25π/12
Therefore, the volume of the solid is 25π/12 cubic units.
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(x>0,
|x - 5 > 2x +1.
Answers
The exact form is
X=5,-1/2
Decimal form
X=5,-0.5
OZ
Find 4 consecutive odd integers such that the sum of the first and the last is the same as 9 less than the third
Answers
9514 1404 393
Answer:
-11, -9, -7, -5
Step-by-step explanation:
Let x represent the third of the odd integers. Then the first is (x -4) and the last is (x +2). We are told their sum is ...
(x -4) +(x +2) = x -9
2x -2 = x -9
x = -7 . . . . . . . . . . add 2-x
The integers are -11, -9, -7, -5.
The length of a rectangle is 10m greater than the width. The area is 24m^2
Answers
Answer:
length: 12m
width: 2m
Step-by-step explanation:
24 = a*w
a = w+10
then:
24 = (w+10)w
24 = w*w + 10*w
24 = w² + 10w
0 = w² + 10 - 24
w = {-10±√((10²)-(4*1*-24))} / (2*1)
w = {-10±√(100+96)} / 2
w = {-10±√196} / 2
w = {-10±14} / 2
only positive numbers:
w = {-10+14}/2
w = 4/2
w = 2m
a = w+10
a = 2 + 10
a = 12m
Check:
24 = 12*2
Rewrite x - 3y = 6 in slope-intercept form.
А
X= 3y +6
В
y=x - 2
С
у = 3х -6
D
Зу = 6-х
Answers
Answer:
use formula y=mx+c
\(x - 3y = 6 \\ x - 6 = 3y \\ x - \frac{6}{3} = y \\ x - 2 = y \\ y = x - 2\)
so the answer is B
find the x and y intercepts of the following linear function and draw the graph: 2x-8y=-18
Answers
Answer:
Step-by-step explanation:
2x - 8y = - 18
- 8y = - 2x - 18
y = ¼x + 2¼
y intercept occurs when x = 0, so b = 2¼ (0, 2¼)
x intercept occurs when y = 0
0 = ¼x + 2¼
¼x = - 2¼
x = -9 (-9, 0)
