Answer:
The vector equation in terms of v1 and v2 is x₁v₁ +x₂v₂ = [296 2454]
Step-by-step explanation:
Solution
The aim is to write down a vector equation in terms of v1 and v2, when solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver.
Thus,
Suppose that b = [ 296 2454] is the corresponding vector which is representing the total needed output.
Now,
If the company operates mine 1 for x1 days and mine #2 for x2 days
Then,
The total output becomes x₁v₁ +x₂v₂ which is the same output to b = [296 2454]
Hence, x₁ and x₂ should be satisfactory to the needed vector equation x₁v₁ +x₂v₂ = [296 2454]
So, the vector equation becomes x₁v₁ +x₂v₂ = [296 2454]
Consider the relation S(x, y) : x is a brother or sister of y on the set, H, of living humans. (For the purposes of this problem, a sibling of a person means another person with the same two parents, so don’t consider half siblings.) Determine which of the three properties, reflexive, symmetric, transitive, hold for the relation S (explain your three answers). Is S an equivalence relation on H?
Answer:
- Not reflexive
- Symmetric
- Transitive
Step-by-step explanation:
- A person is not a sibling of himself so the relation is NOT reflexive
- If a person is a sibling of an other person, the other person is a sibling of the person. Therefore the relation is SYMMETRIC
- If a person A is a sibling of B, and a person B is a sibling of C then, person A is a sibling of person C. Therefore the relation is TRANSITIVE.
55c + 13 < 75c + 39
Solve for c
Answer:
c>-13/10
Step-by-step explanation:
55c+13<75c+39
55c+13-75c<39
-20c+13<39
-20c<39-13
-20c<26
c>26/-20
c>-13/10
A company determines that monthly sales S(t), in thousands of dollars, after t months of marketing a product is given by S(t)equals2 t cubed minus 45 t squared plus 180 t plus 130. a) Find Upper S prime(1), Upper S prime(2), and Upper S prime(4). b) Find Upper S double prime(1), Upper S double prime(2), and Upper S double prime(4). c) Interpret the meaning of your answers to parts (a) and (b).
Answer: a) S'(1) = 136; S'(2) = 104; S'(4) = 76;
b) S''(1) = -38; S''(2) = -26; S''(4) = -2
Step-by-step explanation:
a) S' means first derivative;
[tex]\frac{d}{dt}[/tex](6t³ - 45t² +180t +130) = 6t² - 50t + 180
S'(1) = 6.1² - 50.1 + 180
S'(1) = 136
S'(2) = 6.2² - 50.2 + 180
S'(2) = 104
S'(4) = 6.4² - 50.4 + 180
S'(4) = 76
b) S'' is the second derivative of S:
[tex]\frac{d^2}{dt^2}[/tex](6t² - 50t + 180) = 12t - 50
S''(1) = 12.1 - 50
S''(1) = -38
S''(2) = 12.2 - 50
S"(2) = -26
S"(4) = 12.6 - 50
S"(4) = -2
c) Derivative is the rate of change of a function. The first derivative is the slope of the tangent line to the graph if the function in a determined point, while the second derivative measures how the rate of change is changing.
Analysing the values, we can conclude that the sales of the product after t months is decreasing at a rate of 12.
I need help please help me is it 30?
Answer:
i think is 30$
Step-by-step explanation:
Answer:
B. $15.00
Step-by-step explanation:
Think about it this way:
3 = 1.50
6 = 3.00
8 = 4.00
12 = 6.00
If you divide each of the first numbers by the second, you'll get 2.
This means that every doughnut costs $0.50.
From there you just multiply .5 by 30
30
x .5
15
30 Donuts would cost 15 dollars.
Ok so the above is a little bit more of a complicated way to do it, but it'll be more efficient for a similar, but more difficult problem. The general goal of these problems is to find out what 1 of the item would cost. In this case it's $0.50, but you need to find that out in all of these problems.
brainliest is appreciated.
A recent research show that only 40% of the customers are willing to pay more for the service. Now we have selected 10 customers randomly. What are the expected value and standard deviation
Answer:
The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they are willing to pay more for the service, or they are not. Customers are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
40% of the customers are willing to pay more for the service.
This means that [tex]p = 0.4[/tex]
Now we have selected 10 customers randomly.
This means that [tex]n = 10[/tex]
What are the expected value and standard deviation
[tex]E(X) = np = 10*0.4 = 4[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.4*0.6} = 1.55[/tex]
The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.
∠BAD is bisected by . If m∠BAC = 2x - 5 and m∠CAD = 145, the value of x is:
Answer:
x = 75
Step-by-step explanation:
Assuming the angles are equal ( bisected means divided in half)
2x-5 = 145
Add 5 to each side
2x-5+5 = 145+5
2x = 150
Divide by 2
2x/150/2
x = 75
Answer:
x=75
Step-by-step explanation:
∠BAD is bisected by AC and measurement of BAC is equal to 2x - 5 and measurement of CAD is equal to 145. Since they are bisected, they are equal and the solution is shown below:
m ∠ BAC = m ∠ CAD
2x - 5 = 145 , transpose -5 to the opposite side such as:
2x = 145 + 5 , perform addition of 145 and 5
2x = 150
2x / 2 = 150 / 2 , divide both sides by 2
x = 75
The answer is 75 for the x value.
I need help this question is kinda confusing
Answer:
Geometric Sequence.
Step-by-step explanation:
Geometric sequence. If you take a close look at the graph, it never touches the x - axis. If you use division in a geometric sequence, you will get a very small number, but you will never touch the axis.
What is an equation of the line that passes through the points (-7, -5) and
(-7, -2)?
Answer:
y=3x-1
Step-by-step explanation:
you first find the gradient
(-7,-5). (-7,-2)
x¹ y¹ x² y²
gradient=y²-y¹
x²-x¹
-2+5
-7+7
3/1=3. gradient is 3
equation formula= y=mx+c
(among the two sets of value you were given use one eg I will use -7 and -2)
y-(-7)/x-(-2)=3
y+7/x+2=3
y+7=3(x+2)
y+7=3x+6
y=3x+6-7
y=3x-1
A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 41% of the cameras sold have been of the basic model. Of those buying the basic model, 31% purchase an extended warranty, whereas 48% of all deluxe purchasers do so. If you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model
Answer:
[tex]75.6\%[/tex]
Step-by-step explanation:
Let B be the event of buying a basic model.
Given that P(B) = 41%
Let D be the event of buying a basic model.
Given that P(D) = 1 - 41% = 59%
Let E be the event of extended warranty.
Given that:
P(E [tex]\cap[/tex] B) = 31% and
P(E [tex]\cap[/tex] D) = 48%
P(E) = P(E [tex]\cap[/tex] B) [tex]\times[/tex] P(B) + P(E [tex]\cap[/tex] D) [tex]\times[/tex] P(D)
P(E) = 31% [tex]\times[/tex] 41% + 48% [tex]\times[/tex] 59% = 0.4103
To find: P(B/E)
Formula:
[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]
[tex]\Rightarrow \dfrac{0.31}{0.41}\\\Rightarrow 0.756\\\Rightarrow 75.6\%[/tex]
So, the correct answer is [tex]75.6\%[/tex].
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
HELP PLEASE
Answer:
y=2/3x+1
Step-by-step explanation:
The slope is 2/3 and the y-intercept is 1.
find the equivalent expression using the same bases. (21 x15)9
Answer:
2835
Step-by-step explanation:
(21×15)9=
(315)9=
2835
An orange is shot up into the air with a catapult. The function h given by
h(t) = 15 + 60t – 16t2 models the orange's height, in feet, 1 seconds after it was
launched.
Question 5 What is the initial speed at which the orange is shot in the air?
Answer:
Velocity = 59 feet/second
Step-by-step explanation:
h(t) = 15 + 60t – 16t2
Time t = 1 second
Let's substitute time into the equation to get the distance
h(t) = 15+60(1)-16(1)²
h(t) = 15 + 60 - 16
h(t) = 59 feet
Speed or velocity = distance/time
Distance = 59 feet
Time = 1 second
Velocity = 59/1
Velocity = 59 feet/s
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
According to theorem, congruent angles has congruent sides opposite to them so,
RS = TU
Now
12x+4 = 11x+15
12x-11x = 15-4
So
x = 11
Now
TU = 11x+15
= 11(11)+15
= 121+15
= 136 units
A battery with 20% percent of its full capacity is connected to a charger. Every minute that passes, an additional 5% percent of its capacity is charged. How do you graph this
Answer:
The relation between battery capacity and time is:
[tex]Y=0.05t+0.2[/tex]
The graph is attached.
Step-by-step explanation:
We will graph the charged capacity of the battery in function of time.
The rate of charge is constant, so we can conclude the relation is linear.
At time t=0, the battery capacity is at 0.2 (or 20%).
Every minute that passes, an additional 5% percent of its capacity is charged. So we can say that at t=1, the battery capacity is 0.2+0.05=0.25 (or 25%).
We can calculate the slope of the linear function as:
[tex]m=\dfrac{\Delta Y}{\Delta t}=\dfrac{0.05}{1}=0.05[/tex]
Then, the relation between battery capacity and time is:
[tex]Y=0.05t+0.2[/tex]
Find the volume of the prism.
The volume is cubic meters.
For a particular diamond mine, 78% of the diamonds fail to qualify as "gemstone grade". A random sample of 106 diamonds is analyzed. Find the mean μ.
Answer:
Mean of the binomial distribution μ = 82.68
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 106 diamonds
The probability that the diamonds fail to qualify as "gemstone grade
p = 78% =0.78
We will use binomial distribution
Mean of the binomial distribution
μ = n p
μ = 106 × 0.78
μ = 82.68
conclusion:-
Mean of the binomial distribution μ = 82.68
A 40-foot ladder leans against a building. If
the base of the ladder is 6 feet from the
base of the building, what is the angle
formed by the ladder and the building?
Answer:
Step-by-step explanation:
draw it out and use trig function to solve for the angle. Keep in mind, after getting trig, need to do inverse
A group of neighbors are constructing a community garden that is 80 m wide and 40 m long the top to vertex are plotted below at 10, 70 and 90, 70 what are the coordinates from the bottom to vertex of the garden
Question Correction
A group of neighbors are constructing a community garden that is 80 meters wide and 40 meters long. The top two vertices are plotted below at (10, 70) and (90, 70). What are the coordinates for the bottom two vertices of the garden?
Answer:
(10,30) and (90,30)
Step-by-step explanation:
The community garden is 80 m wide and 40 m long.
The top two vertex are plotted at: (10, 70) and (90, 70).
Horizontal Distance =90-10=80
This serves as the Width of the garden.
Since the length is 40m, the bottom two vertex can be derived by the transformation: (x,y-40).
(x,y-40)-->(10, 70)=(10,30); and
(x,y-40)-->(90, 70)=(90,30)
The coordinates for the two bottom vertices are (10,30) and (90,30).
Write an integral for the area of the surface generated by revolving the curve y equals cosine (2 x )about the x-axis on negative StartFraction pi Over 5 EndFraction less than or equals x less than or equals StartFraction pi Over 5 EndFraction .
Answer:
The integral is
∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx
x₁ = (-π/5)
x₂ = (π/5)
And the area of the surface generated by revolving = 9.71 square units
Step-by-step explanation:
When a function y = f(x) is revolved about the x-axis, the formula for the area of the surface generated is given by
A = 2π ∫ˣ²ₓ₁ f(x) √[1 + (f'(x))²] dx
A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx
For this question,
y = cos 2x
x₁ = (-π/5)
x₂ = (π/5)
y' = -2 sin 2x
1 + y'² = 1 + (-2 sin 2x)² = (1 + 4 sin² 2x)
So, the Area of the surface of revolution is
A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx
= ∫ˣ²ₓ₁ 2πy √[1 + y'²] dx
Substituting these variables
A = ∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx
Let 2 sin 2x = t
4 cos 2x dx = dt
2 Cos 2x dx = (dt/2)
dx = (1/2cos 2x)(dt/2)
Since t = 2 sin 2x
when x = (-π/5), t = 2 sin (-2π/5) = -1.90
when x = (π/5), t = 2 sin (2π/5) = 1.90
A
= ∫¹•⁹⁰₋₁.₉₀ π (2 Cos 2x) √(1 + t²) (1/2cos 2x)(dt/2)
= ∫¹•⁹⁰₋₁.₉₀ (π/2) √(1 + t²) (dt)
= (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
But note that
∫ √(a² + x²) dx
= (x/2) √(a² + x²) + (a²/2) In |x + √(a² + x²)| + c
where c is the constant of integration
So,
∫ √(1 + t²) dt
= (t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)| + c
∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
= [(t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)|]¹•⁹⁰₋₁.₉₀
= [(1.90/2) √(1 + 1.90²)+ 0.5In |1.90+√(1 + 1.90²)|] - [(-1.9/2) √(1 + -1.9²) + (1/2) In |-1.9 + √(1 + -1.9²)|]
= [(0.95×2.147) + 0.5 In |1.90 + 2.147|] - [(-0.95×2.147) + 0.5 In |-1.90 + 2.147|]
= [2.04 + 0.5 In 4.047] - [-2.04 + 0.5 In 0.247]
= [2.04 + 0.70] - [-2.04 - 1.4]
= 2.74 - [-3.44]
= 2.74 + 3.44
= 6.18
Area = (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)
= (π/2) × 6.18
= 9.71 square units.
Hope this Helps!!!
Answer 5x + 8 − 3x = −10
Answer:
-9
Step-by-step explanation:
5x+8-3x = -10
Combine like terms
2x+8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
Answer:
-9
Step-by-step explanation:
5x + 8 - 3x = -10
Combine like terms
2x + 8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
A hotel with 95 room has 65 for doubles and 25 for singles. Singles can be booked in any room, but reservations for two or more people must be booked in double rooms. Let x be the number for single reservations and y the reservations for two or more. Which system of inequality represents this situation? Click the correct answer y is greater than or equal to 65 x+y less than or equal to 95 y is less than or equal to 65 x+y less than or equal to 95 x is greater than or equal to 25 x+y less than or equal to 95 x is less than or equal to 25 x+y less than or equal to 95
Answer: Y is less than or equal to 65 and X + y= less than or equal to 95
Five people have just won a $100 prize, and are deciding how to divide the $100 up between them. Assume that whole dollars are used, not cents. Also, for example, giving $50 to first person and $10 to the second is different from vice versa. (a) How many ways are there to divide up the $100, such that each gets at least $10?
Answer:
give $20 to each person
Step-by-step explanation:
At a football game, a vender sold a combined total of 152 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answer:
38 hot dogs114 sodasStep-by-step explanation:
Sometimes problems of this nature are easily worked by considering groups of items. Here, it is convenient to consider a group as 1 hot dog and 3 sodas, so the number of sodas in the group is 3 times the number of hotdogs in the group.
Each group is 4 items, so 152/4 = 38 groups were sold.
In the 38 groups, there were 38 hot dogs and 3×38 = 114 sodas.
114 sodas and 38 hot dogs were sold.
The perimeter of an equivalent triangle is 15 inches. A side of the triangle is x-2. What is the length of each side of the triangle
Answer:
5
Step-by-step explanation:
We have x-2 = 5
x-2 = 5 we separate parenthesis.
x(-2) = 5(+2)
x = 7
We can check this as what the x-2 is saying is 7-2 = 5
Answer:
Since it is an equilateral triangle,
Perimeter = 3s = 3 x side
=> 15 = 3 X (x - 2)
=> 15 = 3(x - 2)
=> 15 = 3x - 6
=> 3x = 15 + 6
=> 3x = 21
=> x = 21/3
=> x = 7
When x = 7,
=> Side = 7 - 2 = 5 inches
Since, it is an equilateral triangle all sides are of 5 inches each.
Suppose a simple random sample of size 50 is selected from a population with σ=10σ=10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).
a. The population size is infinite.
b. The population size is N=50,000.N=50,000.
c. The population size is N=5000.N=5000.
d. The population size is N=500.N=500.
Answer:
a) [tex]\sigma_{\bar x} = 1.414[/tex]
b) [tex]\sigma_{\bar x} = 1.414[/tex]
c) [tex]\sigma_{\bar x} = 1.414[/tex]
d) [tex]\sigma _{\bar x} = 1.343[/tex]
Step-by-step explanation:
Given that:
The random sample is of size 50 i.e the population standard deviation =10
Size of the sample n = 50
a) The population size is infinite;
The standard error is determined as:
[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]
[tex]\sigma_{\bar x} = 1.414[/tex]
b) When the population size N= 50000
n/N = 50/50000 = 0.001 < 0.05
Thus ; the finite population of the standard error is not applicable in this scenario;
Therefore;
The standard error is determined as:
[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]
[tex]\sigma_{\bar x} = 1.414[/tex]
c) When the population size N= 5000
n/N = 50/5000 = 0.01 < 0.05
Thus ; the finite population of the standard error is not applicable in this scenario;
Therefore;
The standard error is determined as:
[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]
[tex]\sigma_{\bar x} = 1.414[/tex]
d) When the population size N= 500
n/N = 50/500 = 0.1 > 0.05
So; the finite population of the standard error is applicable in this scenario;
Therefore;
The standard error is determined as:
[tex]\sigma _{\bar x} = \sqrt{\dfrac{N-n}{N-1} }\dfrac{\sigma}{\sqrt{n} } }[/tex]
[tex]\sigma _{\bar x} = \sqrt{\dfrac{500-50}{500-1} }\dfrac{10}{\sqrt{50} } }[/tex]
[tex]\sigma _{\bar x} = 1.343[/tex]
What measures of the cylinder do 12 and 42 describe?
A cylinder with height of 42 millimeters and radius of 12 millimeters.
radius and diameter
radius and height
diameter and height
diameter and area of base
Answer: radius and height
Step-by-step explanation:
Radius is the distance between the center of the circle to its boundary.
Height is the length of the figure from top to bottom.
Given statement : A cylinder with height of 42 millimeters and radius of 12 millimeters.
That clearly means that the cylinder is having radius of 12 millimeters i.e. 12 is representing the measure of the radius of the cylinder.
And Similarly, 42 is representing the measure of the height of the cylinder.
Hence, the 2 and 42 describe the radius and height respectively of the cylinder.
Answer:
radius and height
Step-by-step explanation:
i just took the test edge 2020. rate me 5 stars!
What is the surface area of a hemisphere with a radius 10
Answer:
Maths keeps one mentally active. The total surface of a hemisphere = 3(pi)r^2. So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.
Step-by-step explanation:
hope this helps you :)
Answer:
The total surface of a hemisphere = 3(pi)r^2.
So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.
(6x2 + 4x2 - 6x - 4) = (2x - 2)
Answer:
x = -1/5, x = 1
Step-by-step explanation:
Maybe you want to find x.
Subtract the right side and collect terms.
6x^2 +4x^2 -6x -4 -(2x -2) = 0
10x^2 -8x -2 = 0
5x^2 -4x -1 = 0 . . . . . . divide by 2
(5x +1)(x -1) = 0 . . . . . . factor
Solutions are the values of x that make these factors zero:
5x +1 = 0 ⇒ x = -1/5
x -1 = 0 ⇒ x = 1
Solutions are x = -1/5, x = 1.
A firm produces a commodity and receives $100 for each unit sold. The cost of producing and selling x units is 20x 0.25x 2 dollars. Find the number of units the company should produce in order to maximize profit, and find the maximum profit.
Answer:
160 units and $6400
Step-by-step explanation:
We have that the cost per x unit is: 20 * x + 0.25 * x ^ 2
the price per unit is 100, therefore revenue for each unit would be 100 * x
However:
profit = revenue - cost
p (x) = 100 * x - 20 * x - 0.25 * x ^ 2
for the maximum value profit we must derive and equal 0:
p '(x) = 100 - 20 - 0.5 * x
0 = 80 - 0.5 * x
0.5 * x = 80
x = 80 / 0.5
x = 160
Therefore, the maximum profit occurs when there are 160 units, replacing we have:
p (x) = 100 * 160 - 20 * 160 - 0.25 * 160 ^ 2
p (x) = 6400
that is to say that the $ 6400 is the maximum profit.
Anyone know how to solve this
Answer:
Y=1800+150x
Step-by-step explanation:
Answer:
4. Y = 150x + 1800
