Answer:
It is proportional. When You graph it, it will go through the origin. The slope is 5. The y intercept is 0.
Step-by-step explanation:
When a linear function is proportional, the slope will be in the form of y/x.
So, say we put 2 in for x, then y would be 10. 2 is the x and 10 is the y. What is 10/2? 5 (the slope)
If we put in 6 for x, then y would be 30. 5 is the x and 30 would be the y. What is 30/5? 5 (the slope)
if we put in -3 for x, then y would be -15. -3 is the x and -15 would be the y. What is -15/-3? 5 (the slope).
We could not find the slope this way, if the line was not proportional.
For example, if the y intercept is not zero, like
y = 5x + 2. If I put 3 in for the x, then the y would be 17. Is 17/3 equal to 5? No, because the line is not proportional.
Question 8
Match each compound to its correct type.
8.1
CO
hydroxide
8.2
CO₂
carbonate
8.3
SO₂
8.4
CaCO
8.5
NaOH
oxide
trioxide
dioxide
The correct matching of each compound to its type:
8.1 CO - oxide
8.2 CO₂ - dioxide
8.3 SO₂ - dioxide
8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)
8.5 NaOH - hydroxide
8.1 CO - oxide
8.2 CO₂ - dioxide
8.3 SO₂ - dioxide
8.4 CaCO - carbonate
8.5 NaOH - hydroxide
Here is the correct matching of each compound to its type:
8.1 CO - oxide
8.2 CO₂ - dioxide
8.3 SO₂ - dioxide
8.4 CaCO - incorrect notation (needs a subscript for the number of atoms)
8.5 NaOH - hydroxide
Compound 8.4, CaCO, is not correctly represented. It should have a subscript to indicate the number of atoms present in the compound.
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Find the angle between A = 3i +2j - 6k and B = 4i- 3j+k
The angle between A and B is 90 degrees.
The angle between two vectors A and B, you can use the dot product formula:
A · B = [tex]|A| |B| cos(\theta)[/tex]
where A · B is the dot product of A and B, |A| is the magnitude of A, |B| is the magnitude of B, and theta is the angle between the two vectors.
First, let's calculate the dot product of A and B:
A · B = (3)(4) + (2)(-3) + (-6)(1)
= 12 - 6 - 6
= 0
Next, let's calculate the magnitudes of vectors A and B:
|A| = √((3)² + (2)² + (-6)²)
= √(9 + 4 + 36)
= √(49)
= 7
|B| = √((4)² + (-3)² + (1)²)
= √(16 + 9 + 1)
= √(26)
Now, we can substitute these values into the formula to find the angle theta:
0 = [tex](7)(\sqrt(26)) cos(\theta)[/tex]
Since the dot product is 0, we know that the angle between A and B is either 90 degrees or 270 degrees.
To determine which one it is, we can look at the sign of the dot product. If it's positive, the angle is acute (less than 90 degrees) and if it's negative, the angle is obtuse (greater than 90 degrees).
The dot product is 0, so the angle is orthogonal (perpendicular) and is exactly 90 degrees.
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HELPPP
MA.7.DP.1.2
A group of students in the book club are debating whether high school juniors or seniors
spend more time on homework. A random sampling of juniors and seniors at the local high
school were surveyed about the average amount of time they spent per night on homework.
The results are listed in the table below.
Average Amount of Time on Homework Per Night (in minutes)
Juniors 125 90 95
80 100 100 120- 85 95 120 95 85
Seniors 135 70 65 100 35 175 80 80 90 65 120 60
Part A. Calculate and compare the measures of center for the data sets.
Part B. Calculate and compare the variability in each distribution.
Part C. Does the data support juniors or seniors spending more time on homework?
Explain your reasoning.
Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42
Median (Juniors) = (95 + 95) / 2 = 95
Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25
Median (Seniors) = (80 + 80) / 2 = 80
How to solve for the median of centerJuniors: 125, 90, 95, 80, 100, 100, 120, 85, 95, 120, 95, 85
First, sort the data: 80, 85, 85, 90, 95, 95, 95, 100, 100, 120, 120, 125
Sum = 1085
Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42
Median (Juniors) = (95 + 95) / 2 = 95
Seniors: 135, 70, 65, 100, 35, 175, 80, 80, 90, 65, 120, 60
First, sort the data: 35, 65, 65, 70, 80, 80, 90, 100, 120, 120, 135, 175
Sum = 1095
Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25
Median (Seniors) = (80 + 80) / 2 = 80
Variability
Juniors:
Range = max - min = 125 - 80 = 45
Seniors:
Range = max - min = 175 - 35 = 140
C. Based on the mean and median, it appears that seniors spend slightly more time on homework on average (mean ≈ 91.25) compared to juniors (mean ≈ 90.42).
However, the median time spent for seniors (80 minutes) is less than that of juniors (95 minutes), indicating that the data for seniors might be skewed by some outliers.
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geometery I need help please
The value of the given angle which is N and that is rounded to the nearest hundredth would be =45.58°
How to calculate the measure of the missing angle?To calculate the missing angle N, the sine formula should be used and it is given below;
= a/sin A = b/sin B
Where;
a= 7
A= 90°
b= 5
B= N
That is;
7/sin90°= 5/sinN
sinN= 5×1/7
= 5/7
= 0.714285714
N = Sin-1(0.714285714)
= 45.58°
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can some one
factor 7a10 - 112a2
The factored of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
How to find the factor 7a10 - 112a2To factor the expression [tex]7a^{10} - 112a^2[/tex] we can identify the greatest common factor (GCF) and factor it out. Let's break down the steps:
The coefficients 7 and 112 have a common factor of 7.
The lowest power of "a" in each term.
In this case, the lowest power of "a" is 2.
Factoring out [tex]7a^2[/tex] from both terms, we get:
[tex]7a^2(a^8 - 16)[/tex]
Therefore, the factored form of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
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Sarah wants to buy a new laptop. Store A is currently selling the laptop for $1,640 with an additional 20% off. Store B is selling the laptop for $1,500 with an additional 10% off. Which store offers a better deal?
Answer:
Store A
Step-by-step explanation:
If an item is 20% off, then you pay 80% of the price.
If an item is 10% off, then you pay 90% of the price.
Store A
80% of $1640 = 0.8 × $1640 = $1312
Store B
90% of $1500 = 0.9 × $1500 = $1350
Answer: Store A
Answer:
Store A
Step-by-step explanation:
Store A offers a 20% discount which is equivalent to 0.20 x $1,640 = $328.
The laptop is therefore sold for $1,640 - $328 = $1,312 at Store A.
Store B offers a 10% discount which is equivalent to 0.10 x $1,500 = $150.
The laptop is therefore sold for $1,500 - $150 = $1,350 at Store B.
Therefore, Store A offers a better deal at $1,312 compared to Store B at $1,350.
t is 40% of u
y is half of t
Write the ratio t : u : v in its simplest form.
Answer will mark as brainiest
The ratio t : u : v in its simplest form is 0.4 : 1 : v/0.4.
To find the ratio t : u : v, we'll need to express each variable in terms of one another. Given the information provided, we know that:
T = 0.4u (T is 40% of u)
Y = 0.5t (Y is half of t)
We can substitute the value of t from the second equation into the first equation:
T = 0.4u
Y = 0.5(0.4u) = 0.2u
Now, we have the values of T and Y in terms of u. To find v, we need additional information since it is not provided.
Without that information, we cannot determine the specific value of v or its relationship to the other variables. Therefore, we cannot simplify the ratio t : u : v any further.
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Given the supply curve below, how many AirPods would Apple produce at a price of $185?
Supply Curve for Airpods- Qs = 6700 + 75P
O 25600
6775
O20575
6960
The given supply curve is: Qs = 6700 + 75P
To find how many AirPods Apple would produce at a price of $185, we can substitute P = $185 in the equation and find the corresponding quantity (Qs).
Qs = 6700 + 75P Qs = 6700 + 75($185) Qs = 6700 + 13875 Qs = 20575
Therefore, at a price of $185, Apple would produce 20,575 AirPods according to the given supply curve.
evaluate 3y(9-x) when y=3 and w=7
The numeric value of the expression 3y(9 - x) when y = 3 and x = 7 is given as follows:
18.
How to find the numeric value of a function at a point?To obtain the numeric value of a function or even of an expression, we must substitute each instance of the variable of interest on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The expression in the context of this problem is given as follows:
3y(9 - x).
Hence the numeric value when x = 7 and y = 3 is given as follows:
3 x 3 x (9 - 7) = 3 x 3 x 2 = 18.
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Fatoumata has a bag that contains orange chews, apple chews, and watermelon chews. She performs an experiment. Fatoumata randomly removes a chew from the bag, records the result, and returns the chew to the bag. Fatoumata performs the experiment 29 times. The results are shown below: A orange chew was selected 6 times. A apple chew was selected 10 times. A watermelon chew was selected 13 times. Based on these results, express the probability that the next chew Fatoumata removes from the bag will be orange or apple as a percent to the nearest whole number
The probability that the next chew Fatoumata removes from the bag will be orange or apple, rounded to the nearest whole number, is approximately 55%.
To calculate the probability that the next chew Fatoumata removes from the bag will be either orange or apple, we need to determine the total number of times an orange or apple chew was selected.
From the given results, Fatoumata selected an orange chew 6 times and an apple chew 10 times. To find the probability, we add the number of occurrences for each chew:
Orange chews: 6 times
Apple chews: 10 times
Total occurrences of orange or apple chews: 6 + 10 = 16
Fatoumata performed the experiment a total of 29 times. So, the probability of selecting an orange or apple chew can be calculated as:
Probability = (Total occurrences of orange or apple chews) / (Total number of experiments) = 16 / 29
To express this probability as a percentage, we multiply the probability by 100:
Probability (as a decimal) = 16 / 29 ≈ 0.5517
Probability (as a percentage) = 0.5517 × 100 ≈ 55.17%
Therefore, the probability that the next chew Fatoumata removes from the bag will be orange or apple, rounded to the nearest whole number, is approximately 55%.
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Which sample uses the substance(s) that Jacob and Natalie
should use to make a cold pack that will do the BEST job of
keeping food cool?
Note that the substance(s) that Jacob and Natalie should use to make a cold pack that will do the BEST job of keeping food cool is " Sample 1, because it absorbs the most energy" (option A)
What is energy?In physics, energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.
Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed
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Full Question:
Although part of your question is missing, you might be referring to this full question:
People use self-warming and self-cooling devices for many purposes such as keeping drinks cold or food warm. Medical professionals also use these types of devices to store medicines and other substances that need to stay colder than room temperature. These cooling and warming devices use a chemical reaction to produce their chilling and warming effects. Compounds combine in endothermic (heat absorbing) or exothermic (heat releasing) reactions within these devices to help them keep items cool or warm.
Jacob and Natalie are asked by their science teacher to design a warming or cooling device. They decide to design a cold pack that can be used to help keep food cool. Jacob
and Natalie read about different substances that can be used inside cold packs and learn that most cold packs use endothermic reactions to cool objects. They find the table below while researching.
Which sample uses the substance(s) that Jacob and Natalie should use to make a cold pack that will do the BEST job of keeping food cool?
answer choices
Sample 1, because it absorbs the most energy
Sample 2, because it absorbs the most energy
Sample 3, because it absorbs the least energy
Sample 4, because it absorbs the least energy
Find g(x), where g(x) is the translation 2 units left and 4 units down of f(x)=x^2.
Write your answer in the form a(x–h)^2+k, where a, h, and k are integers.
g(x) =
The function g(x) in the form a(x-h)^2 + k is: [tex]g(x) = (x + 2)^2 - 4[/tex]
Starting with[tex]f(x) = x^2[/tex], the translation 2 units left and 4 units down would result in the following transformation:
g(x) = f(x + 2) - 4
Substituting[tex]f(x) = x^2:[/tex]
[tex]g(x) = (x + 2)^2 - 4[/tex]
Expanding the square:
[tex]g(x) = x^2 + 4x + 4 - 4[/tex]
Simplifying:
[tex]g(x) = x^2 + 4x[/tex]
Now we need to rewrite this expression in the form [tex]a(x-h)^2 + k.[/tex] To do this, we will complete the square:
[tex]g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4[/tex]
Therefore, the function g(x) in the form a(x-h)^2 + k is:
[tex]g(x) = (x + 2)^2 - 4[/tex]
Where a = 1, h = -2, and k = -4.
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Which graph has the same end behavior as f(x)=(10x^(3)+x^(2)+3)/(2x^(2)+1)?
The graph that has the same end behavior as f(x)= (10x³+x²+3)/(2x²+1) is Option A. See the attached.
What is the end behavior of the above graph?the end behavior of the graph of f(x) is:
As x → +∞ , f(x) → +∞ (approaches positive infinity).
As x → -∞, f(x) → -∞ (approaches negative infinity).
End behavior of a function f defines the behavior of the function's graph at the "ends" of the x- axis.
In other words, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +∞) and the left end of the x -axis (as x approaches - ∞ ).
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please help me solve for x image is attached ive been stuck on it for a few days now
The value of x will be 10.
Given a triangle we need to set a proportion to solve for the value of x,
Therefore, according to the definition of the similar triangles,
x / 5 = 15+5 / x
x² = 5 × 20
x² = 100
x = 10
Hence the value of x will be 10.
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A person buy a lot of tickets for Rs.136 each execution class ticket cost rupees12 and each local class ticket cost for Rs 4 each make an equation and fine explain possible solutions
Answer:
3.98
Step-by-step explanation:
Answer:
the second method may be through graph
La siguiente gráfica muestra las calificaciones de un grupo de 40 alumnos que van desde el mínimo 7 hasta el máximo 10 de calificación. ¿Cuántos alumnos sacaron 9?
The specific data points or the Frequency distribution of grades for the 40 students.
The specific information from the graph , the exact number of students who received a grade of 9.
If the graph represents the distribution of grades of 40 students on a scale from 7 to 10, we can estimate the number of students who received a grade of 9 by considering the shape of the graph.
the graph is a normal distribution or bell curve, with the majority of students clustered around the mean (which is likely to be around 8.5 or 9), we can expect a significant number of students to have received a grade of 9. In a typical bell curve distribution, the highest density of scores is around the mean.
without additional information about the shape of the graph or the specific values represented on the x-axis, it is difficult to provide an accurate estimation of the number of students who received a grade of 9. The graph may represent a variety of distributions, such as skewed, bimodal, or uniform.
the exact number of students who received a grade of 9, the specific data points or the frequency distribution of grades for the 40 students.
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Based on the information given regard to the graph, there are 6 students who got 9.
How to explain the valueA graph is a diagram such as a series of one or more points, lines, line segments, curves, or areas which represents the variation of a variable in comparison with that of one or more other variables.
The collection of all points whose coordinates satisfy a given relation such as a function.
The graph shows that there are 4 students who got 7, 8 students who got 8, and 12 students who got 10. This leaves:
40 - 4 - 8 - 12
= 6 students who got 9.
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Find the gradient of the line segment between the points (-2,3) and (0,2).
Give your answer in its simplest form.
Answer:
[tex]\dfrac{-1}{2}[/tex]
Step-by-step explanation:
Slope or gradient:(-2 , 3) ⇒ x₁ = -2 & y₁ = 3
(0 , 2) ⇒ x₂ = 0 & y₂ = 2
[tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{2-3}{0-[-2]}\\\\\\=\dfrac{-1}{0+2}\\\\=\dfrac{-1}{2}[/tex]
1 secX + 3 = cosX + tanX (2+ sinX)
The solution for X is X ≈ [tex]tan^{(-1)(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.
Given: 1 secX + 3 = cosX + tanX (2 + sinX)
To simplify the equation, let's express secX and tanX in terms of sinX and cosX:
1/cosX + 3 = cosX + sinX/cosX (2 + sinX)
Now, multiply both sides by cosX to eliminate the denominators:
[tex]1 + 3cosX = cos^2X + sinX(2 + sinX)[/tex]
Expanding the equation:
[tex]1 + 3cosX = cos^2X + 2sinX + sin^2X[/tex]
Since [tex]sin^2X + cos^2X[/tex] equals 1 (based on the Pythagorean identity), we can substitute it into the equation:
[tex]1 + 3cosX = 1 + 2sinX + sin^2X[/tex]
Rearranging the terms:
[tex]3cosX = 2sinX + sin^2X[/tex]
Now, let's express cosX in terms of sinX using the Pythagorean identity:
cosX = √(1 - [tex]sin^2X[/tex])
Substituting this into the equation:
3√(1 - [tex]sin^2X) = 2sinX + sin^2X[/tex]
Squaring both sides to eliminate the square root:
[tex]9(1 - sin^2X) = (2sinX + sin^2X)^2[/tex]
Expanding the right side:
[tex]9(1 - sin^2X) = (2sinX)^2 + 2(2sinX)(sin^2X) + (sin^2X)^2\\9 - 9sin^2X = 4sin^2X + 4sin^3X + sin^4X[/tex]
Rearranging the terms:
[tex]sin^4X + 4sin^3X + 4sin^2X + 9sin^2X - 9 = 0[/tex]
Combining like terms:
[tex]sin^4X + 4sin^3X + 13sin^2X - 9 = 0[/tex]
Unfortunately, this equation does not have a simple algebraic solution. It needs to be solved numerically or graphically. Using numerical methods or a graphing calculator, we can find that one solution to this equation is sinX ≈ 0.7429.
Taking the inverse tangent (arctan) of both sides, we have:
X = arctan(0.7429)
Therefore, the solution for X is X ≈ t[tex]an^{(-1)}(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.
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Last week, Jorge Sanchez assembled 317 game boards. Find Jorge’s gross earnings for the week if the manufacturer pays at the following differential piece rates:
Boards assembled per week
Pay per board
First 100
$1.82
Next 200
$1.92
Over 300
$2.08
Find his gross pay for the week.
Jorge's gross earnings for the week assembling 317 game boards would be $633.
To calculate Jorge's gross earnings for the week, we need to determine how many game boards fall into each pay rate category and then multiply the quantity by the corresponding pay rate. Let's break down the calculation step by step:
Determine the number of game boards that fall into each pay rate category:
First 100 boards: 100 boards (as the rate applies to the first 100 boards).
Next 200 boards: Since Jorge assembled 317 boards in total and the first 100 boards are already accounted for, we subtract 100 from 317 to get 217 boards that fall into this category.
Over 300 boards: We check if the total number of boards exceeds 300. In this case, since Jorge assembled 317 boards, we have
317 - 300 = 17
boards that fall into this category.
Calculate the earnings for each category by multiplying the number of boards by the corresponding pay rate:
Earnings for the first 100 boards:
100 boards * $1.82 per board = $182.
Earnings for the next 200 boards:
217 boards * $1.92 per board = $416.64.
Earnings for the over 300 boards:
17 boards * $2.08 per board = $35.36.
Sum up the earnings from each category to find the gross pay for the week:
Gross pay = Earnings for the first 100 boards + Earnings for the next 200 boards + Earnings for the over 300 boards
Gross pay = $182 + $416.64 + $35.36
Gross pay = $633.
Therefore, Jorge's gross earnings for the week assembling 317 game boards would be $633.
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use the linear combination method to solve the system of equations. Explain each step of your solution. 2x-3y=13 x+2y=-4
Answer:
Solution: x = 2, y = -3.
Step-by-step explanation:
Given system of equations:
Equation 1: 2x - 3y = 13
Equation 2: x + 2y = -4
Multiply Equation 2 by 2:
2(x + 2y) = 2(-4)
Simplified: 2x + 4y = -8
Add Equation 1 and Equation 3:
4x + y = 5
Solve Equation 4 for y:
y = 5 - 4x
Substitute y into Equation 2:
x + 2(5 - 4x) = -4
Simplify:
-7x + 10 = -4
Solve for x:
x = 2
Substitute x into Equation 5:
y = 5 - 4(2)
y = -3
Solution: x = 2, y = -3.
What’s the lateral area of this
Answer:
240 in²
Step-by-step explanation:
You want the lateral area of a triangular prism with triangular base having sides 6 in, 8 in, and 10 in, and a distance between them of 10 in.
Lateral areaThe lateral area of a triangular prism is the area of the three rectangular faces. The width of those faces is the "height" of the prism, given as 10 in. The total length of those faces is the perimeter of the base:
6 in + 8 in + 10 in = 24 in
The lateral area is ...
A = LW = (24 in)(10 in) = 240 in²
<95141404393>
How many centimeters equal 128.9 meters?
Answer:12,890 centimeters
Step-by-step explanation: 1 meter equals 100 centimeters.
The required, 128.9 meters is equal to 12,890 centimeters, as following the unit system.
To convert meters to centimeters, we can use the conversion factor that states there are 100 centimeters in one meter.
Therefore, to find out how many centimeters are equal to 128.9 meters, we multiply the number of meters by 100:
128.9 meters * 100 centimeters/meter = 12,890 centimeters
In summary, when converting meters to centimeters, we multiply the number of meters by 100 to obtain the equivalent length in centimeters. In this case, 128.9 meters is equal to 12,890 centimeters.
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The cost of packing a box of chocolates is given by 1/4 x^2, where x is the number of chocolates (a box can never have fewer than 3 chocolates). If the weight of a box of
chocolates is given by x + 2, what is the cost of packaging per weight unit
The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.
We have,
To find the cost of packaging per weight unit, we need to calculate the cost of packaging (C) and divide it by the weight of the chocolates (W).
Given:
Cost of packaging (C) = 1/4 x²
Weight of chocolates (W) = x + 2
To find the cost of packaging per weight unit, we can express it as C/W.
Substituting the given expressions:
C/W = (1/4 x²) / (x + 2)
To simplify the expression, we can first simplify the numerator:
C/W = (1/4 x²) / (x + 2)
= (1/4) x (x² / (x + 2))
= (1/4) x (x(x) / (x + 2))
= (1/4) x (x / (x + 2)) * x
Now, we can rewrite the expression as:
C/W = (1/4) x (x / (x + 2)) x
Therefore,
The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.
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Table 13-15
Labor Output Marginal
Product Variable
Cost Fixed
Cost
0 0 -- $0 $5
1 100 100 $5 $5
2 250 $10 $5
3 350 $15 $5
4 50 $20 $5
5 25 $25 $5
6 430 $30 $5
5. Refer to Table 13-15. What is the marginal product of the second worker?
150
6. Refer to Table 13-15. What is the total output of five workers?
7. Refer to Table 13-15. What is the marginal product of the sixth worker?
8. Refer to Table 13-15. What is the average total cost of producing 425 units of output?
9. Refer to Table 13-15. What is the average variable cost of producing 400 units of output?
10. Refer to Table 13-15. What is the average fixed cost of producing 430 units of output?
1. The marginal product of the second worker is 150 units.
2. The total output of five workers is 75 units.
3. The marginal product of the sixth worker is 405 units.
4. The average total cost of producing 425 units of output is $30.
5. The average variable cost of producing 400 units of output is $20.
6. The average fixed cost of producing 430 units of output is $0.07.
What is the answers to the question?The marginal product of the second worker:
= (Output of 2 workers - Output of 1 worker)
= (250 - 100)
= 150 units
The total output of five workers is:
= Output of 4 workers + Marginal product of the fifth worker
= 50 + 25
= 75 units
The marginal product of the sixth worker is:
= (Output of 6 workers - Output of 5 workers)
= (430 - 25)
= 405 units.
The average total cost to produce 425 units is:
= (Total variable cost + Total fixed cost) / Total output
The total variable cost is $30 * 425 = $12,750
The total fixed cost is $5 * 6 = $30
Total cost = $12,750 + $30 = $12,780
The Average total cost is:
$12,780 / 425
= $30
The average variable cost to produce 400 units is:
= Total variable cost / total output
Total variable cost is $20 * 400 = $8,000
Average variable cost = $8,000 / 400 = $20
The average fixed cost to produce 430 units is:
= Total fixed cost / Total output
Total fixed cost is $5 * 6 = $30
The average fixed cost is:
= $30 / 430
= $0.07.
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The following table represents the highest educational attainment of all adult residents in a certain town. If an adult is chosen randomly from the town, what is the probability that they have a high school degree or some college, but have no college degree? Round your answer to the nearest thousandth.
The probability that a random adult has a high school degree or some college, but has no college degree is 53. 50 % .
How to find the probability ?The number of adults with some high school degree or some college would be :
= 3, 561 + 6, 058
= 9, 619 people
The probability that a random adult would have high school degree or some college is therefore :
= Adults with high school degree or some college / Total adults in the town
= 9, 619 / 17, 981
= 53. 50 %
In conclusion, the probability is 53. 50%.
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NO LINKS!! URGENT HELP PLEASE!!!
Find the area of ΔABC
5. c = 17, b = 13, a = 15
6. a = 23, b = 25, c = 14
Answer:
5. 94 square units.
6. 159 square units.
Step-by-step explanation:
By using Heron's Formula: [tex]\bold{\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
5.
Using the values c = 17, b = 13, and a = 15,
Calculate the semi-perimeter of the triangle as:
s =[tex]\frac{a+b+c}{2}[/tex]
s =[tex]\frac{15 + 13 + 17}{2}=22.5[/tex]
Using Heron's formula, the area of the triangle is:
A = [tex]\bold{\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
A = [tex]\sqrt{22.5(22.5-15)(22.5-13)(22.5-17)}=93.90[/tex] ≈94 approximately
Therefore, the area of triangle ABC is approximately 94 square units.
6.
Using the values, a = 23, b = 25, and c = 14,
we can calculate the semi-perimeter of the triangle as:
s =[tex]\frac{a+b+c}{2}[/tex]
s =[tex]\frac{ 23 + 25 + 14}{2}[/tex]
s = 31
Using Heron's formula, the area of the triangle is:
A = [tex]\bold{\sqrt{s(s-a)(s-b)(s-c)}}[/tex]
A = [tex]\sqrt{31(31-23)(31-25)(31-14)}=159.05[/tex]≈159 approximately
Therefore, the area of triangle ABC is approximately 159 square units.
Answer:
5) 93.90 square units (2 d.p.)
6) 159.05 square units (2 d.p.)
Step-by-step explanation:
To find the area of a triangle given its side lengths, use Heron's formula.
[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]
[tex]\hrulefill[/tex]
Question 5Given side lengths of triangle ABC:
a = 15b = 13c = 17To find the half perimeter, s, half the sum of the 3 side lengths:
[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{15+13+17}{2}=22.5[/tex]
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{22.5(22.5-15)(22.5-13)(22.5-17)}\\&=\sqrt{22.5(7.5)(9.5)(5.5)}\\&=\sqrt{8817.1875}\\&=93.89988019...\\&=93.90\; \sf units^2\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the area of triangle ABC is 93.90 square units, to two decimal places.
[tex]\hrulefill[/tex]
Question 6Given side lengths of triangle ABC:
a = 23b = 25c = 14To find the half perimeter, s, half the sum of the 3 side lengths:
[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{23+25+14}{2}=31[/tex]
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{31(31-23)(31-25)(31-14)}\\&=\sqrt{31(8)(6)(17)}\\&=\sqrt{25296}\\&=159.0471628...\\&=159.05\; \sf units^2\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the area of triangle ABC is 159.05 square units, to two decimal places.
Find the slope of the line.
A. 3/2
B. -2/3
C. 4/3
D. -3/4
Answer:
-3/4, answer D
Step-by-step explanation:
Slope = rise/run. The equation is (y2-y1)/(x2-x1).
So let's pick 2 points. There are pink dots on (-2,2) and (6,-4), so we'll use those points.
slope = (2-(-4))/(-2-6)
slope = (2+4)/(-2-6)
slope = (6)/-8, which we can simplify by dividing the numerator and denominator each by 2.
slope = -3/4
Just as a quick check, this makes sense because as x increases, y decreases so we should expect the slope to be negative.
Answer:
Step-by-step explanation:
Use 2 points from the line: (-2, 2) and (6, -4)
slope = y2 -y1 = -4 - 2 = -6 = - 3
x2 - x1 6 - -2 8 4
The slope is choice D -3/4
If $850 is invested in an account that earns 2.6% yearly interested compounded quarterly, then which of the
following is the worth of this investment after 5 years?
(3) $967.60
(4) $968.25
(1) $960.50
(2) $966.40
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$850\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 850\left(1+\frac{0.026}{4}\right)^{4\cdot 5}\implies A=850(1.0065)^{20} \implies A \approx 967.60[/tex]
Can someone answer this question
The function is a quadratic function, and none of the given options is a factor of the graph of the function.
Here,, we have,
to determine the factor:
The zeros of the function are given as:
-3 and 5
This means that:
x = -3 and x = 5
Rewrite as:
x + 3 = 0 and x - 5 = 0
Multiply both equations
(x + 3)(x -5) = 0 * 0
This gives
(x + 3)(x -5) = 0
Express as a function
f(x) = (x + 3)(x -5)
The above means that the factors of the function are (x + 3) and (x -5)
Hence, none of the given options is a factor of the graph of the function
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complete question:
Graph of a function, f(x), has zeros at - 3, and 5. Which of
following is a factor of f(x)?
(2x - 3)
(2x + 3)
(3x + 2)
(x + 5)
ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
A car's speedometer has a percent error of 5%. The actual speed of the car is 60 mph.
Which statement describes what speed the speedometer could show?
A: The speedometer shows either 57 mph or 63 mph.
B: The speedometer shows either 58 mph or 62 mph.
C: The speedometer shows either 55 mph or 65 mph.
D: The speedometer shows either 30 mph or 90 mph.
Answer:
maybe a
Step-by-step explanation:
as t percent of 60 is 3
so it will show 57 or 63