Answer:
Total cost= $5,425
Step-by-step explanation:
Giving the following information:
Month Machine _Hours Amount
January 200 $2,800
February 350 3,000
March 450 4,000
April 500 5,000
May 600 5,200
June 580 5,800
First, we need to calculate the fixed and variable costs. To do it, we will use the high-low method:
Variable cost per unit= (Highest activity cost - Lowest activity cost)/ (Highest activity units - Lowest activity units)
Variable cost per unit= (5,800 - 2,800) / (600 - 200)
Variable cost per unit= $7.5 per hour
Fixed costs= Highest activity cost - (Variable cost per unit * HAU)
Fixed costs= 5,800 - (7.5*600)
Fixed costs= $1,300
Fixed costs= LAC - (Variable cost per unit* LAU)
Fixed costs= 2,800 - (7.5*200)
Fixed costs= $1,300
Now, we can determine the total cost for 550 hours:
Total cost= 1,300 + 7.5*550
Total cost= $5,425
Predict whether the product is greater than, less than, or equal to 2/3
Answer:
Greater than.
1 1/27 or 28/27.
Step-by-step explanation:
You're multiplying more than 2/3, so it is greater than.
2/3 x 1 5/9 is the same as 2/3 x 14/9. The answer to this is 28/27. Simplify to a mixed number which is 1 1/27.
Hope it helps!
Answer:
2/3 is less than and the answer is 28/27 = 1 1/27 = 2/3 x 1 5/9
Step-by-step explanation:
2/3 x 1 5/9 = 28/27 = 2/3 x 14/9 = 1 1/27
2/3 ≤ 28/27 = 1 5/9
Consider a square-based straight pyramid. Suppose that the base is a square with sides 10 km long, and all other edges are 17 km long. Find an approximate value of the angle formed between the base and a triangular face. Present your answer in degrees, accurate up to four or more decimal places.
Answer:
72.06
Step-by-step explanation:
Given that :
Side Lenght, a = 10
Edge length, b = 17
Using Pythagoras :
h = height of pyramid
h = sqrt (b² - 1/2a²)
h = sqrt(17^2 - 10^2/2)
h = sqrt(289 - 50)
h = 15.46
Slant height :
L = sqrt(h² + a²/4)
L = sqrt(15.46² + 25)
L = sqrt(239 + 25)
L = sqrt(264)
L = 16.25
Sinα = h/L
α = sin^-1 (15.46/16.25)
α = 72.060933
= 72.06
The approximate value of the angle formed between the base and a triangular face is 72.0775°.
Let [tex]h[/tex] be the distance between the center of the square base and the midpoint of the side of the square and let [tex]H[/tex] the height of the triangular face of the pyramid. By properties of the square and the Pythagorean theorem we derive expressions for [tex]h[/tex] and [tex]H[/tex], respectively:
Square base
[tex]h = 0.5\cdot L[/tex] (1)
Triangular face
[tex]H = \sqrt{l^{2}-0.25\cdot L^{2}}[/tex] (2)
Where:
[tex]L[/tex] - Side length of the square base, in kilometers.[tex]l[/tex] - Remaining side length of the triangular face, in kilometers.Finally, by trigonometry we can derive an expression for the angle between the base and a triangular face ([tex]\theta[/tex]), in sexagesimal degrees:
[tex]\theta = \cos^{-1} \frac{h}{H}[/tex] (3)
If we know that [tex]L = 10\,km[/tex] and [tex]l = 17\,km[/tex], then the angle between the base and a triangular face is:
[tex]h = 5\,km[/tex]
[tex]H = \sqrt{17^{2}-5^{2}}[/tex]
[tex]H \approx 16.248\,km[/tex]
[tex]\theta = \cos^{-1} \frac{5\,km}{16.248\,km}[/tex]
[tex]\theta \approx 72.0775^{\circ}[/tex]
The approximate value of the angle formed between the base and a triangular face is 72.0775°.
We kindly invite to check this question on pyramids: https://brainly.com/question/16303112
while shopping for clothes Jaclyn spent 38 less than 2 times what Daniel spent. Jaclyn spent $10. Writes and solve an equation to find how much Daniel spent. Let x represent how much Daniel spent.
How much did Daniel spend?
Cuáles son los divisores de 7 y 2 a la vez
Answer:
72 o de 7 y 2
Step-by-step explanation:
7: 7 y 1
2:2y1
72:1 2 3 4 5 6 8 9 12 24 36 y 72
science 8th grade 10 pts
What best explains the relationship between photosynthesis and cellular respiration?
The higher the rate of formation of products in respiration, the lower the rate of photosynthesis.
Photosynthesis depends on the carbon dioxide released during cellular respiration.
Cellular respiration depends on the water released during photosynthesis.
They have the same set of product molecules.
Answer:
Photosynthesis depends on the carbon dioxide released during cellular respiration.
Step-by-step explanation:
i can’t figure out how to do this
Answer:
i need to know the answer choices
Step-by-step explanation:
Answer:
-25 is correct I think
Step-by-step explanation:
pls help me pls help me pls help me
Step-by-step explanation:
area of triangle = 1/2 × base × height
= 1/2 × 6×4
= 12 cm²
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you.
thankyou.
I think it’s 12cm but I am not sure sorry dude
Riley got 6 out of 10 problems correct on her practice
test. If there are 150 problems on the actual test,
predict how many problems Riley will get correct.
Assume this relationship is proportional.
Answer:
90
Step-by-step explanation:
6/10 of 100 is 60, now add half of that, 30, add those together 60+30=90.
Answer:
my answer is 90
Step-by-step explanation:
i gogt 90 and i solve it too
Can you help me do this or you can write it on a piece of paper to help as well!
0.4y − 0.2y + 10 = 11.8
Answer:
0.2y+10
Step-by-step explanation:
Answer:
We have this equation:
0.4y - 0.2y + 10 = 11.8
You can simplify
0.2y + 10 = 11.8
Then, you can substract 10 in both sides:
0.2y = 11.8 - 10
0.2y = 1.8
You can now divide right and left side by 0.2 and get y:
0.2y/0.2 = 1.8/0.2
y = 14
You hike 165 meters up a hill that has a 17 degree angle of elevation as shown in the diagram.
Give each side and angle measure rounded to the nearest whole number.
a=
b=
m∠B=
Answer:
a.) 48m
b.) 158m
m<B.) 73 degrees
Step-by-step explanation:
Which statements are true about the graph shown below. There are more than one answer.
Answer:
cant see the choices what the graph is a function
Step-by-step explanation:
HELP ASAP!! What is angle 1 called??
A ladder is leaned against a wall with its base 6m from the wall. The ladder makes a 50 degree angle with the ground. How long is the ladder?
Answer:
b
Step-by-step explanation:
What is 10 to the power of 18
Answer:
1e+18
Step-by-step explanation:
A sample of assistant professors on the business faculty at state supported institutions in Ohio revealed the mean income to be $32,000 for 9 months with a standard deviation of $3,000. Using Chebyshev's Theorem, what is the proportion of faculty that earns more than $25,250 but less than $38,750
Answer:
The proportion of faculty that earns more than $25,250 but less than $38,750 is 0.8025.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question, we have that:
Mean of 32000, Standard deviation of 3000.
Using Chebyshev's Theorem, what is the proportion of faculty that earns more than $25,250 but less than $38,750
This is within 38,750 - 32,000 = 32,000 - 25,250 = $6,750 of the mean.
Value of k:
This is k standard deviations from the mean. k is given by:
[tex]k = \frac{6750}{3000} = 2.25[/tex]
Proportion:
The percentage is:
[tex]p = 100(1 - \frac{1}{(2.25)^{2}}) = 80.25[/tex].
So the proportion is 0.8025
Multiply Binomials
(x + 3)(2x + 1)
Answer: 2x^2 + 7x + 3
Step-by-step explanation:
(x+3)(2x+1)
(2x^2+1x+6x+3)
2x^2 + 7x + 3
Please help will mark brainlist .
It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance. Athletes are tested to see if they are using illegal drugs or not using illegal drugs and the test can come back positive or negative. The test for this drug is 90% accurate for non-drug users (this means there is a 90% chance the test comes back negative if the person is a non-user). What is the probability that an athlete tests negative and is not a user of an illegal drug
Answer:
0.873 = 87.3% probability that an athlete tests negative and is not a user of an illegal drug
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Not a user of an illegal drug.
Event B: Tests negative.
The test for this drug is 90% accurate for non-drug users (this means there is a 90% chance the test comes back negative if the person is a non-user)
This means that [tex]P(B|A) = 0.9[/tex]
It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance.
So 100 - 3 = 97% probability that the athlete does not use the drug, so [tex]P(A) = 0.97[/tex]
What is the probability that an athlete tests negative and is not a user of an illegal drug
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = 0.9*0.97 = 0.873[/tex]
0.873 = 87.3% probability that an athlete tests negative and is not a user of an illegal drug
The segments shown below could form a triangle.
Answer:
False
Step-by-step explanation:
It's been a while since I did this but here we go:
So to find if the triangle lengths are possible, we take the shorter two lengths and we add them.
Those shorter two lengths sum have to be greater than the longest length.
I hope this helps.
Find the 4th term in the sequence
with the following definition:
a1 = 2
an = (an-1)2
The sum of the first four terms of the given sequence which is aₙ = (aₙ ₋ ₁)² is gotten as; 278
How to solve arithmetic sequence?We are given the arithmetic sequence as;
a₁ = 2
aₙ = (aₙ ₋ ₁)²
We already have the first term. Thus;
Second Term;
a₂ = (a₂ ₋ ₁)²
a₂ = 2² = 4
Third Term;
a₃ = 4²
a₃ = 16
Fourth Term;
a₄ = 16²
a₄ = 256
Thus;
Sum of first four terms is;
S₄ = 2 + 4 + 16 + 256
S₄ = 278
Read more about Arithmetic Sequence at; https://brainly.com/question/6561461
#SPJ2
Answer:
a1=2 an-(an-1)2 = 256
Step-by-step explanation:
please help me find slope
Answer:
the slope is 3 because y2-y1/x2-x1 is equal to your slope.
5-2 is 3 and 2-1 is 1, 3/1 is equal to 3.
Step-by-step explanation:
Answer:
The answer is 3
Step-by-step explanation:
Have a great Thursday!
:)
Based on what you've read, answer the following
1. What's the temperature change?
a. 35° F to 72° F
b. 40° F to 21° F
c. 120° F to 250° F
d. 15° F to 68° F
Answer:
a.+37 b.-19 c.+130 d.+43
Step-by-step explanation:
a.72-35 b.21-40 c.250-120 d,68-15
find the volume of a cylinder with radius 3cm and height 7cm
Answer:
Step-by-step explanation:
[tex]V=h\pi r^2\\ \\ h=7\ and\ r=3\\ \\ V=8(3^2)\pi\\ \\ V=72\pi cm^3\\ \\ V\approx 226.2cm^3[/tex]
Bowler world charges $5.00 to rent shoes and $1.10 per game. Lucky Spares charges $3.00 dollars for shoes and $1.50 per game
Answer:
6.10 for 1 and 4.50 . for 2
Step-by-step explanation:
What's the radius of a circle with area 9π units2?
Question options:
A)
81 units
B)
18 units
C) CORRECT ANSWER
3 units
D)
9 units
Answer:
option C : 3 units
Step-by-step explanation:
radius of circle is 3 units
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you .
I dont understand can someone help me ill mark brainliest
4 A numerical expression is shown below. Evaluate the expression.
help please explain too
Answer:
H
Step-by-step explanation:
What is the correct answer?
A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the concentration of salt in the brine entering the tank is 0.2 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.1 kg/L?
Answer:
a. [tex]m(t) = 26.67 - 26.67e^{-0.03t}[/tex] b. 7.44 s
Step-by-step explanation:
a. If the concentration of salt in the brine entering the tank is 0.2 kg/L, determine the mass of salt in the tank after t min.
Let m(t) be the mass of salt in the tank at any time, t.
Now, since a brine solution flows in at a rate of 4 L/min and has a concentration of 0.2 kg/L, the mass flowing in per minute is m' = 4 L/min × 0.2 kg/L = 0.8 kg/min
Now, the concentration in the tank of volume 100 L at any time, t is m(t)/100 L. Since water flows out at a rate of 3 L/min, the mass flowing out per minute is
m(t)/100 × 3 L/min = 3m(t)/100 kg/min
Now the net rate of change of mass of salt in the tank per minute dm/dt = mass flowing in -mass flowing out
dm/dt = 0.8 kg/min - 3m(t)/100 kg/min
So, dm/dt = 0.8 - 0.03m(t)
The initial mass of salt entering m(0) = 0 kg
dm/dt = 0.8 - 0.03m(t)
separating the variables, we have
dm/[0.8 - 0.03m(t)] = dt
Integrating, we have
∫dm/[0.8 - 0.03m(t)] = ∫dt
-0.03/-0.03 × ∫dm/[0.8 - 0.03m(t)] = ∫dt
1/(-0.03)∫-0.03dm/[0.8 - 0.03m(t)] = ∫dt
-1/0.03㏑[0.8 - 0.03m(t)] = t + C
㏑[0.8 - 0.03m(t)] = -0.03t - 0.03C
㏑[0.8 - 0.03m(t)] = -0.03t + C' (C'= -0.03C)
taking exponents of both sides, we have
[tex]0.8 - 0.03m(t) = e^{-0.03t + C'} \\0.8 - 0.03m(t) = e^{-0.03t}e^{C'}\\0.8 - 0.03m(t) = Ae^{-0.03t} A = e^{C'}\\0.03m(t) = 0.8 - Ae^{-0.03t}\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\when t = 0 \\m(0) = 0\\m(0) = 26.67 - \frac{A}{0.03} e^{-0.03(0)}\\\\0 = 26.67 - \frac{A}{0.03} e^{0}\\26.67 = \frac{A}{0.03} \\\frac{A}{0.03} = 26.67\\\frac{A}{0.03} = 6.67\\A = 26.67 X 0.03\\A = 0.8\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\\\m(t) = 26.67 - \frac{0.8}{0.03} e^{-0.03t}\\[/tex]
So, the mass of the salt after t min is
[tex]m(t) = 26.67 - 26.67e^{-0.03t}[/tex]
b. When will the concentration of salt in the tank reach 0.1 kg/L?
When the concentration of the salt reaches 0.1 kg/L, m(t) = 0.1 kg/L
Solving the equation for t,
[tex]m(t) = 26.67 - 6.67e^{-0.03t}\\0.1 = 26.67 - 26.67e^{-0.03t}\\26.67e^{-0.03t} = 26.67 - 0.1\\26.67e^{-0.03t} = 26.57\\e^{-0.03t} = 26.56/26.67\\e^{-0.03t} = 0.9963\\[/tex]
taking natural logarithm of both sides, we have
-0.03t = ㏑0.9963
-0.03t = -0.0038
t = -0.0038/-0.03
t = 0.124 min
t = 0.124 × 60 s
t = 7.44 s