A company discovers that to produce x=700 new electronic parts, it will cost y=$61100. To produce 620 new electronic parts, it will cost $54460
Answers
Answer:
The cost increases at a rate of $83 per item.
Step-by-step explanation:
Given two points, use the following to determine the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Given the points (700,61100) and (620, 54460), substitute and compute for the slope:
[tex]\begin{gathered} m=\frac{61100-54460}{700-620} \\ m=\frac{}{}83 \end{gathered}[/tex]The cost increases at a rate of $83 per item.
Related Questions
The admission fee at an amusement park is $2.75 for children and $4.80 for adults. On a certain day, 312 people entered the park, and the admission fees collected totaled $1104. How many children and how many adults were admitted?
Answers
Let the number of children admitted be x and let the number of adults admitted be y.
It is given that the total number of 312 people were admitted, this implies that the sum of the number of children and adults is 312:
[tex]x+y=312[/tex]It is given that the admission fee for children is $2.75, this implies that the total fees collected for x children are:
[tex]x\cdot2.75=2.75x[/tex]It is also given that the admission fee for adults is $4.80, this implies that the total fees collected for y children are:
[tex]y\cdot4.80=4.80y[/tex]Since the admission fees collected totaled $1104, it follows that:
[tex]2.75x+4.80y=1104[/tex]Hence, the following system of equations is formed:
[tex]\begin{cases}x+y=312{} \\ 2.75x+4.80y={1104}\end{cases}[/tex]Solve the system of equations:
Solve the first equation for x:
[tex]x=312-y[/tex]Substitute this for x in the second equation:
[tex]\begin{gathered} 2.75\left(−y+312\right)+4.8y=1104 \\ \text{ Simplify both sides of the equation:} \\ \Rightarrow-2.75y+858+4.8y=1104 \\ \Rightarrow-2.75y+4.8y+858=1104 \\ \Rightarrow2.05y+858=1104 \\ \text{ Subtract }858\text{ from both sides:} \\ \Rightarrow2.05y+858−858=1104−858 \\ \Rightarrow2.05y=246 \\ \text{ Divide both sides by }2.05: \\ \Rightarrow\frac{2.05y}{2.05}=\frac{246}{2.05} \\ \Rightarrow y=120 \end{gathered}[/tex]It follows that the number of adults admitted is 120.
Substitute y=120 into the equation x=312-y to find the value of x:
[tex]\begin{gathered} x=312-120 \\ \Rightarrow x=192 \end{gathered}[/tex]Hence, the number of children admitted is 192.
Answer: 192 children and 120 adults were admitted.
3. Which situation could be represented by the graph shown?3027242118A. Garrett buys limes for $0.80 each.B. Sophia buys 12-packs of soda for $1.75 each.C. Jacob buys packs of gum for $1.50 each.D. Allison purchases lemons for $0.75 each.15129631 2 3 4 5 6 7 8 9 10
Answers
Find the slope of the graph, use 2 points on the line (0,0) and (4,3)
[tex]m=\frac{3-0}{4-0}=\frac{3}{4}=0.75[/tex]The equation of the graph is y=0.75x, it represents the situation in option D. Allison purchases lemons for $0.75 each
Which situation can be represented by the equation y = 9x?Question 3 options:Michael drove x amount of hours in his car. This is 9 times the amount of miles as y.Michael drove x amount of miles in his car. He drove y amount of hours in 9 miles.Michael has y amount of miles to drive. This amount is 9 times x, the amount of miles to drive in hours.Michael has x amount of hours. This amount is 9 times y, the amount of miles to drive in hours.
Answers
Solution:
Given:
[tex]y=9x[/tex]This is a linear equation that relates distance, speed, and time.
where;
[tex]undefined[/tex]is 0.5 a integer but not a whole number
Answers
...
Natural Numbers are the numbers 1 through infinity.
Whole numbers.
So, they start from 1 and go on...
1, 2, 3, 4, .....
Now, Whole numbers are very same just that they start from 0, so it would be:
0, 1, 2, 3, ....
Integers would include the negatives fo the naturals and 0, so they would be:
...-2, -1, 0 , 1, 2, ....
We want a number NOT natural but integer, that would be 0.
So,
Natural Numbers = 1, 2, 3, 4, 5, ....
Whole Numbers = 0, 1, 2, 3, 4, 5, .....
Integers = ...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
Parallelogram ABCD is below. m
Answers
The consecutive angles of a parallelogram are supplementary. therefore:
[tex]\begin{gathered} m\angle A+m\angle B=180 \\ 41+x+8.5=180 \\ x+49.5=180 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=180-49.5 \\ x=130.5 \\ x\approx131 \end{gathered}[/tex]A car travels at a steady speed of 40 mph. How far will it go in 15 minutes?
Answers
The distance travelled by the car in 15 minutes can be determined as,
[tex]\begin{gathered} D=s\times t \\ D=40\text{ mph}\times15\text{ min}\times\frac{1\text{ h}}{60\text{ min}} \\ D=10\text{ miles} \end{gathered}[/tex]Thus, the required distance is 10 miles.
The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in NYC each year between 2000 and 2013. A line was fit to the data to model the relationship. Which of these linear equations best describes the given model?A) ŷ = ⅖x + 800B) ŷ = 40x + 800C) ŷ = 800x + ⅖D) ŷ = 800x + 40Based on the equation, use this equation to estimate the average rent in 2020.Round your answer to the nearest dollar.$___.
Answers
From the graph, we can conclude:
[tex]\begin{gathered} b=y-intercept_{}\approx800 \\ m\approx\frac{900-800}{3-0}\approx33.33\approx40 \end{gathered}[/tex]So, the linear equation that best describes the given model is:
[tex]\hat{y}=40x+800[/tex]Therefore, for 2020 or x = 20:
[tex]\begin{gathered} \hat{y}(20)=40(20)+800 \\ \hat{y}(20)=1600 \end{gathered}[/tex]what is the intermediate in the form (x+a)^2=b as a result of completing the square for the following equation?Answer:()^2=
Answers
Step 1: Write out the equation
[tex]x^2-12x+32=4[/tex]Step 2: Subtract 32 from both sides of the equation
[tex]\begin{gathered} x^2-12x+32-32=4-32 \\ x^2-12x=-28 \end{gathered}[/tex]Step 3: Complete the square by adding 1/2 of the square of the coefficient of x to both sides
That is
[tex]x^2-12x+(-6)^2=-28+(-6)^2[/tex]This implies that
[tex](x-6)^2=-28+36=8[/tex]Hence the intermediate step is (x - 6)² = 8
7/8 of a watermelon weight is water. if the watermelon weighs 24 kilograms, how many of the kilograms come from water?
Answers
ANSWER
21 kg of the watermelon are water.
EXPLANATION
We have to divide the weight of the watermelon by 8 and then multiply by 7 - or in other words, multiply by 7/8:
[tex]24\times\frac{7}{8}=\frac{24}{8}\times7=3\times7=21[/tex]21 of the 24 kilograms of the watermelon are from water.
Graph the line from the table you found in (5). Remember to scale and label your axes!
Answers
We are asked to draw a line by using the values given in the table.
Let x denotes the first column of values and y denotes the second column of values
So, the (x, y) ordered pairs are
(0, 4), (2, 0), (1, 2), (3, -2), (-1, 6)
Let us plot these points on the graph then we would draw a line connecting these points.
Therefore, this is how the graph of the line looks like.
The y-intercept of the line is the point where the line intersects the y-axis.
From the above graph, we see that the line intersects the y-axis at y = 4
Therefore, the y-intercept of the line is 4
The slope of the line is given by
[tex]slope=\frac{\text{rise}}{\text{run}}[/tex]The rise is the vertical distance between the two points on the line.
The run is the horizontal distance between the two points on the line.
As you can see, we selected two points on the line. (you may select any two points)
The two points are (2, 0) and (3, -2)
The vertical distance is -2 (negative because it is going down) and the horizontal distance is 1
[tex]slope=\frac{\text{rise}}{\text{run}}=\frac{-2}{1}=-2[/tex]Therefore, the slope of the line is -2
Given the standard restricted domains, which of the following relationships does not hold for x=-1? (Assume angles are in radians.)
Answers
Answer:
[tex]D:\text{ arccos\lparen cos\lparen-1\rparen\rparen= 1}[/tex]Explanation:
From the restricted domain, we want to check for the relationship that does not hold
All we have to do here is to substitute the value -1 for x, after which we evaluate each of the given equations
We proceed as follows:
[tex]\begin{gathered} a)\text{ sin\lparen}\sin^{-1}(-1))\text{ = -1} \\ b)\text{ arcsin\lparen sin\lparen-1\rparen\rparen = -1} \\ c)\text{ cos\lparen arc cos \lparen-1\rparen\rparen = -1} \\ d)\text{ arc cos\lparen cos\lparen-1\rparen\rparen = 1} \\ e)\text{ tan\lparen arc tan\lparen-1\rparen\rparen = -1} \\ f)\text{ arctan\lparen tan\lparen-1\rparen\rparen = -1} \end{gathered}[/tex]The correct option is thus D
2) The mass of a radioactive element decays at rate given by m(t) = m0e^-rt, where m(t) is the mass at any time t, m0 is the initial mass, and r is the rate of decay.Uranium-240 has a rate of decay of .0491593745. What is the mass of U-240 left after 10 hours, if the initial mass is 50 grams? (Use e = 2.71828.]A) 28.54387 gB) 30.58254 gC) 32.14286 gD) 32.68034 g
Answers
Solution
- We are given the following formula:
[tex]\begin{gathered} m(t)=m_0e^{-rt} \\ \text{where,} \\ r=\text{decay rate} \\ t=\text{time} \\ m_0=\text{ Initial mass} \\ m=\text{mass after time t} \end{gathered}[/tex]- We are told that the Initial mass is 50g, the decay rate is .0491593745, time (t) is 10 hours, and e = 2.71828.
- With the above information, we can proceed to substitute the values given into the formula and get the mass of Uranium after 10 hours.
- This is done below:
[tex]\begin{gathered} m=50\times2.71828^{-(0.0491593745)\times10} \\ \\ m=50\times0.611651003817 \\ \\ \therefore m=30.5825\ldots\approx30.58254g \end{gathered}[/tex]Final Answer
The answer is 30.58254g (OPTION B)
Calculate the distance between the points G=(-2,-6) and N=(-9, 2) in the coordinate plane.Give an exact answer (not a decimal approximation).
Answers
To find the diatance between two points you use the next formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]For the given two points:
[tex]\begin{gathered} d=\sqrt[]{(-9-(-2))^2+(2-(-6))^2} \\ \\ d=\sqrt[]{(-7)^2+8^2} \\ \\ d=\sqrt[]{49+64} \\ \\ d=\sqrt[]{113} \end{gathered}[/tex]Then, the distance between points G and N is the square root of 113
Michael Run 3 times last week who are the destinations human
Answers
Given the distances Michael ran each day, add them up in order to obtain the total distance, as shown below
[tex]7+16.9+8.48=32.38[/tex]Therefore, the answer is 32.38km
Use the formula P(B\A)=n(A and B)÷n(A) to find the probability P(kinglface card) when a single. card is drawn from a standard 52 card deck. P(king face card)=
Answers
In a deck of 52 cards, there 4 faces of Kings. These are the King of Hearts, King of Diamonds, King of Spades, and King of Clubs. Therefore, the chance of drawing a king face card in a deck of cards would be 4 out of 52 or 1 out of 13.
Answer: P(king face card) = 1/13
For positive acute angles A and B, it is known that sin A= 7/25 and cos B= 21/29. Find the value of sin(A + B) in simplest form.
Answers
Answer
sin A = 7/25
cos B = 21/29
To find sin(A + B), we use double angle formula.
sin(A + B) = sin A cos B + sin B cos A
sin A = 7/25 , cos B = 21/29
From trigonometric identity, sin²θ + cos²θ = 1
cos A = √(1 - sin²A) = √(1 - (7/25)²)
cos A = √(1 - (49/25))
cos A = √(576/625)
cos A = 24/25
Also, sin B = √(1 - cos²B) = √(1 - (21/29)²)
sin B = √(1 - (441/841))
sin B = √(400/841)
sin B = 20/29
Recall that sin(A + B) = sin A cos B + sin B cos A
sin (A + B) = (7/25 x 21/29) + (20/29 x 24/25)
sin (A + B) = (147/725 + 480/725)
sin (A + B) = (147 + 480)/725
sin (A + B) = 627/725
[tex] |4x - 5 \leqslant 7| [/tex]here's my absolute value equation
Answers
2.
The inequation is given as,
[tex]\lvert4x-5\rvert\leq7[/tex]Consider the analogy,
[tex]\lvert a\rvert\leq b\Rightarrow-b\leq a\leq b[/tex]Applying this analogy to the given inequality,
[tex]-7\leq4x-5\leq7[/tex]Now, we just need to obtain the solution set for this inequality.
Add 5 to each term,
[tex]\begin{gathered} -7+5\leq4x-5+5\leq7+5 \\ -2\leq4x\leq12 \end{gathered}[/tex]Divide by 4 each term of the inequality,
[tex]\begin{gathered} \frac{-2}{4}\leq\frac{4x}{4}\leq\frac{12}{4} \\ -0.5\leq x\leq3 \end{gathered}[/tex]Thus, the solution set to the given inequation is obtained as,
[tex]-0.5\leq x\leq3[/tex]2. The following is a graph of the function f(x) = 2^x. Graph thetransformation f(x+3) on the blank coordinate axis.yy
Answers
Explanation:
The transformation f(x+3) indicates that we have to translate the graph of f(x) 3 units to the left.
In the graph of f(x) the y-intercept is at y = 1. For f(x+3) this point is moved 3 units to the left, so it is (-3, 1).
Answer:
The graph of f(x+3) is
TWO-Variable SystemsThe two lines graphed below are parallel. How many solutions are there to thesystem of equations?O A. TwoO B. ZeroO C. OneO D. Infinitely manyPREVIOUS
Answers
Answer:
B. Zero
Explanation:
The solutions of a system of equations are the points where the graphs intersect. If the lines are parallel, the lines will not intersect, so there will be no solutions to the system.
Therefore, the solutions to the system of two parallel lines are
B. Zero
The average amount of water used per person each day in a country is 45 gallons. How much water does the average person use in one year?
Answers
Proportions
It's assumed the amount of water consumed by one person is proportional to the time.
The contant of proportionality is given as 45 gal/day.
Since one normal year has 365 days, then we use the same proportion to calculate the water used in one year as follows:
Water used = 45 * 365 = 16,425 gallons.
The average person uses 16,425 gallons.of water in one year
As the number manu fucture increase from soo+200. manufactute (ost increase from 350 to 650 birr. Assume that the given data establishes relationship between Cost. cand number of units made. Q and asume that the the relation This is linear. Assuum the thice unit is birr 13.
Answers
y = 3x + 50 is the linear equation relating the total cost to the number of units produced.
We know that a linear equation is of the form
y = mx + b
Where m is the slope (rate of change of y with respect to x) and b is the value when x is 0.
With the given information, the cost increased by
$650 - $350 = $300
When the number of units produced increased by 200 - 100 = 100.
So the rate of change of cost (y) with respect to x (number of units) is 300/100=3.
So the equation is of the form
y = 3x + b
Use one of the two given data points to determine b.
When the production was 100, the total cost was $350:
So,
350 = 3(100) + b
350 = 300 + b
b = 50
Hence the answer is y = 3x + 50 is the linear equation relating the total cost to the number of units is produced.
To learn more about linear equations click here https://brainly.com/question/26310043
#SPJ9
Use the intercepts to graph the equation. y = -6 x-intercept: Enter as a coordinate: such as (a, b). If there is no x-intercept, enter DNE. Enter as a coordinate: such as (a, b). If y-intercept: there is no y-intercept, enter DNE. 8 6 5 4 ربا
Answers
Answer:
x -intercept: DNE
y-intercept: (-6, 0)
Explanation:
The x-intercept is the point where the line intersects the x-axis.
The y-intercept is the point where the line intersects the y-axis.
Now when we draw the line y = -6, we get
We see that the red line does not intersects the x-axis at any point; thereffore, the x-intercept does not exist.
x -intercept: DNE
The red line intersects the y-axis at y = -6; therefore, the y-intercept is the point (0, -6)
An arithmetic sequence has a 10th term of 15 and 14th term of 35. show that the equation (y=mx+b) of this graph equals an =-30+(n-1)5.
Answers
The arithmetic sequence follows
[tex]a_n=-30+(n-1)5[/tex]Lets see if the 10th term is 15 by replacing the n for 10
n=10
[tex]a_{10}=-30+(10-1)5[/tex][tex]a_{10}=-30+(9)5=-30+45=15[/tex]Now, Lets see if the 14th term is 35 by replacing the n for 14
n=14
[tex]a_{14}=-30+(14-1)5[/tex][tex]a_{14}=-30+(13)5=-30+65=35[/tex]Then so, the sequence follows the equation an =-30+(n-1)5.Find the diameter of a circle with a circumference of 28.26 centimeters. Use 3.14 for π.
Answers
Answer:
The diameter of the circle is 9.0 cm.
[tex]d=9.0\text{ cm}[/tex]Explanation:
Given that the circumference of the circle is 28.26 centimeters.
[tex]C=28.26\text{ cm}[/tex]Recall that the formula for the circumference of a circle is;
[tex]\begin{gathered} C=2\pi r=\pi d \\ d=\frac{C}{\pi} \end{gathered}[/tex]Substituting the given values;
[tex]\begin{gathered} d=\frac{28.26\text{ cm}}{3.14} \\ d=9.0\text{ cm} \end{gathered}[/tex]Therefore, the diameter of the circle is 9.0 cm.
[tex]d=9.0\text{ cm}[/tex]If X = 7 units, Y = 11 units, Z = 14, and H = 4 units, what is the surface area of the triangular prism ?
Answers
we know that
The surface area of a triangular prism is equal to
SA=2B+PL
where
B is the area of the triangular face
P is the perimeter of the triangular face
L is the length of the prism
step 1
Find the area B
B=(1/2)*y*h
substitute the given values
B=(1/2)*11*4
B=22 units^2
step 2
Find teh value of P
P=X+X+y
substitute the given values
P=7+7+11
P=25 units
step 3
Find the surface area
SA=2*22+25*14
SA=394 units^2Find and graph the intercepts of the following linear equation: x-4y=16
Answers
The given function is:
[tex]x-4y=16[/tex]The x-intercept is the value of x when y = 0.
[tex]\begin{gathered} x-4(0)=16 \\ x=16 \end{gathered}[/tex]The y-intercept is the value of y when x = 0.
[tex]\begin{gathered} (0)-4y=16 \\ -4y=16 \\ \text{ Dividing both sides of the equation by }-4 \\ y=-4 \end{gathered}[/tex].
what is 7/8 - 3 1/5? i cant firgure it out
Answers
Answer:
-93/40 or -2 13/40
Step-by-step explanation:
7/8 - 16/5
Adjust based on the LCM
35/40 - 128/40
35-128/40
7. Solve this riddle. I am an even number. I am between 10 and 20. And when I am divided by 7, I have no remainder. What number am I?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
solve the riddle = ?
Step 02:
We must analyze the exercise to find the solution
a. even number
b. 10 ----- 20
c. x / 7 ===> no remainder
11 , 13 , 15 , 17 , 19 ===> even numbers
Help meeee please!!!!
Answers
The coordinates of B' are (1, 0) after transforming the parallelogram down 4 units and right 3 units.
What are coordinates?Coordinates are distances or angles, represented by numbers, that uniquely identify points on surfaces of two dimensions or in space of three dimensions. These are the set of values that shows the exact position. Coordinates are the set of points, or numbers, that locates a point on a line, on a plane, or in space. The points at the coordinates are called coordinate points. The coordinate plane has two axes. Those are horizontal and vertical axes. The two axes intersect each other at a point called the origin. Coordinate axes are one of the fixed reference lines of a coordinate system. It is a two-dimensional number line. It is used to locate the position of any point.
From the graph, the coordinates of B are (-2, 4).
Translating 4 units down means the value of the y-axis is changing. Therefore, new coordinates will be
(-2-0, 4-4)
=(-2, 0)
Then the parallelogram is translated to 3 units to the right. So, the x-axis is changing to a positive end.
The coordinates of B' will be
(-2+3, 0+0)
= (1,0)
To know more about coordinate, visit:
https://brainly.com/question/19187448
#SPJ1
y = x2 + 5x - 10y=-x² + 2x + 10
Answers
Since in both given equations, the variable y is already clear, then you can equal the two equations and then solve for x. So, you have
[tex]\begin{cases}y=x^2+5x-10\text{ (1)} \\ y=-x^{2}+2x+10\text{ (2)}\end{cases}[/tex][tex]\begin{gathered} x^2+5x-10=-x^2+2x+10 \\ \text{ Add }x^2\text{ to both sides of the equation} \\ \text{ Subtract 2x to both sides of the equation} \\ \text{ Subtract 10 to both sides of the equation} \\ x^2+5x-10+x^2-2x-10=-x^2+2x+10+x^2-2x-10 \\ 2x^2+3x-20=0 \end{gathered}[/tex]To solve for x you can use the quadratic formula, that is,
[tex]\begin{gathered} \text{ For }ax^2+bx+c=0\text{ where a}\ne0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In this case
a=2
b=3
c=-20
So,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{(3)^2-4(2)(-20)}}{2\cdot2} \\ x=\frac{-3\pm\sqrt[]{9+160}}{4} \\ x=\frac{-3\pm\sqrt[]{169}}{4} \\ x=\frac{-3\pm13}{4} \\ x_1=\frac{-3+13}{4}=\frac{10}{4}=\frac{5}{2}=2.5 \\ x_2=\frac{-3-13}{4}=\frac{-16}{4}=-4 \end{gathered}[/tex]Now you can plug in the solutions found in any of the given equations to find their respective y-coordinates.
For the first solution, you have
[tex]\begin{gathered} x_1=\frac{5}{2} \\ y_{}=-x^2+2x+10\text{ (2)} \\ y_1=-(\frac{5}{2})^2+2(\frac{5}{2})+10 \\ y_1=-\frac{25}{4}+5+10 \\ y_1=\frac{35}{4} \\ y_1=8.75 \\ \text{ Then} \\ (2.5,8.75) \end{gathered}[/tex]For the second solution, you have
[tex]\begin{gathered} x_2=-4 \\ y=-x^2+2x+10\text{ (2)} \\ y_2=-(-4)^2+2(-4)+10 \\ y_2=-16-8+10 \\ y_2=-14 \\ \text{Then} \\ (-4,-14) \end{gathered}[/tex]Therefore, the solution set of the given system of equations is
[tex]\mleft\lbrace(-4,-14),(2.5,8.75)\mright\rbrace[/tex]