Answer:
Use induction for the prove
Step-by-step explanation:
Mathemathical induction is an useful method to prove things over natural numbers, you check for the first case, supose for the n and prove using your hypothesis for n+1
there says any integer bigger than 12 can be written as 4r+5s
so first number n can be is 13.
we can check n=13 = 4*2+5*1 r=2 and s=1 give 13.
Now we suppose n can be written as 4r+5s
and we can check if n+1=4r'+5s' with r' and s' integers.
we replace n as 4r+5s because that is our hypotesis
n+1=4r+5s+1
if we write that 1 as 5-4
4r+5s+1
4r+5s+5-4
then we can write
4(r-1)+5(s+1) , we got n+1= 4 (r-1) +5(s+1) where r-1 and s+1 are non negative integers. because r and s were no negative integers ( if r is not 0)
what if r=0?
if r is 0 , n is a multiple of 5 and n+1 can be written as 5s+1
first multiple of 5 we can write is 15 since n is bigger than 12 , then smaller s is 3.
for any n+1 we can write
n+1=5s+1=5 (s-3) +3*5+1=5(s-3)+4*4, s-3 is 0 or bigger.
(check 3*5+1 is 16, the same as 4*4)
Final answer:
Any integer greater than 12 can be expressed as the sum 4r + 5s with nonnegative integers r and s by providing concrete examples for n values from 13 to 17 and then proving for any n > 17 using number theory.
Explanation:
To show that any integer n greater than 12 can be written as the sum 4r + 5s for some nonnegative integers r and s, we can provide examples and create a general proof. We know that for n = 13 through n = 17, specific values of r and s can be found that satisfy the equation:
n = 13 = 4(1) + 5(1)
n = 14 = 4(3) + 5(0)
n = 15 = 4(0) + 5(3)
n = 16 = 4(4) + 5(0)
n = 17 = 4(1) + 5(3)
For n > 17, we can write n = 17 + k, where k is a nonnegative integer. Since every nonnegative integer can be expressed as a multiple of 4 plus an additional 0, 1, 2, or 3 (as k = 4q + r, with 0 ≤ r < 4), we can substitute into our equation for n to n = 17 + 4q + r. The key is to notice that for any additional 4 we add to the sum, we can simply increase r (our existing count of 4-cent stamps), ensuring that the equation 4r + 5s will always hold.
This proof shows that we can always add enough 4-cent stamps (or subtract them and add a 5-cent stamp) to reach any postage amount above 12 cents. This is a classic example of a problem that uses the concept of number theory and diophantine equations.
What is the rate of heat transfer required to melt 1-ton of ice at 32 F in 24 hours?
Answer:
3865.74 J/s
Step-by-step explanation:
mass of ice, m = 1 ton = 1000 kg
time , t = 24 hours
latent heat of fusion of ice, L = 334000 J/kg
Heat required to melt, H = m x L
where, m is the mass of ice and L be the latent heat of fusion
So, H = 1000 x 334000 = 334 xx 10^6 J
Rate of heat transfer = heat / time = [tex]\frac{334\times 10^{6}}{86400}[/tex]
Rate of heat transfer = 3865.74 J/s
thus, the rate of heat transfer is 3865.74 J/s.
Fill in the blank The retail cost of a TV is 40% more than its wholesale cost. Therefore, the retail cost is _times the wholesale cost The retail cost is 1.4 times the wholesale cost. (Type an integer or a decimal
Answer:
Step-by-step explanation:
let whole sale cost=100
retail cost=100+40% of 100=100+40=140
to find the ratio
(retail cost)/(whole cost)=140/100=14/10=1.4
so retail cost=1.4*whole cost
or retail cost is 1.4 times the whole cost.
The retail cost of a TV, which is 40% more than its wholesale cost, is 1.4 times the wholesale cost. For instance, if the wholesale cost is $500, the retail cost would be $700.
The retail cost of a TV is 40% more than its wholesale cost. To find out how many times more the retail cost is compared to the wholesale cost, we need to understand percentage increase calculations.
Let the wholesale cost of the TV be represented by 1 (or 100%). An increase of 40% on this cost means the TV now costs:
1 + 0.40 = 1.40.
Therefore, the retail cost of the TV is 1.4 times the wholesale cost.
For example, if the wholesale cost of a TV is $500, then the retail cost would be:
$500 × 1.4 = $700.
What is buffer and what is dissolve? (4 pts)
Answer:
The buffer is the solution which basically oppose pH change upon the expansion of an acidic or fundamental parts. It can kill limited quantities of included corrosive or base, in this way keeping up the pH of the arrangement generally stable and steady.
Acidic buffer is the arrangements are usually produced using weak acidic nature and also by the sodium salt.
Dissolve is the process of break down is to make a solute go into an solution. Dissolving is likewise called disintegration. Regularly, this includes a strong going into a fluid stage, however disintegration can include different changes too.
For instance, when compounds structure, one strong breaks down into another to frame a strong arrangement.
Food mix A contains 2% fat, and food mix B contains 7% fat. A 20-kilogram diet mix of foods A and B is formed. If x kilograms of food A are used, write an algebraic expression that represents the total number of kilograms of fat in the final food mix. Simplify the expression.
Answer:
The required expression is y = 1.4 - 0.05x
Step-by-step explanation:
Consider the provided information.
Food mix A contains 2% fat and food mix B contains 7% fat.
Let x kilograms of food A are used, in a 20-kilogram mixture.
Thus, 20 - x kilograms of food B are used, in a 20-kilogram mixture.
Now It is given that A contains 2% fat and food mix B contains 7% fat.
2% and 7% can be written as 0.02 and 0.07 respectively. Let represent the total fat with y.
Thus, the required expression is:
y = 2% (x) + 7% (20 - x)
y = 0.02 (x) + 0.07 (20 - x)
y = 0.02x + 1.4 - 0.07x
y = 1.4 - 0.05x
Hence, the required expression is y = 1.4 - 0.05x
The tensile strength of silicone rubber is thought to be a function of curing temperature. A study was carried out in which samples of 12 specimens of the rubber were prepared using curing temperatures of 20◦C and 45◦C. The data below show the tensile strength values in megapascals.(20 C) 2.07 2.14 2.22 2.03 2.21 2.03 2.05 2.18 2.09 2.14 2.11 2.05(45 C) 2.52 2.15 2.49 2.03 2.37 2.05 1.99 2.42 2.08 2.42 2.29 2.01(a) Show the dot plot of the data with both low and high temperature tensile strength value(b) Compute sample mean tensile strength for both samples
Answer:
Sample mean tensile strength for 20°C [tex]\bar X_{20} =2.11[/tex]Mp
Sample mean tensile strength for 45°C [tex]\bar X_{45} =2.235[/tex]Mp
Step-by-step explanation:
A dot plot for combined data allows comparison between the responses of an experiment to two or more independent factors. In this case there are 12 experimental observations of tensile strength on silicone rubber for two levels of the curing temperature factor (30°C and 45°C)
The sample mean can be calculated by:
[tex]\bar X_{20} = \frac{1}{n}\sum{x_i}=2.11[/tex]Mp
[tex]\bar X_{45} = \frac{1}{n}\sum{x_i}=2.235[/tex]Mp
The dot plot can be observed in the attached file.
Solve the following logarithmic equation: In(x +31)-In(4-3x)-5In2 0 x = 2 1 points x= 0 x-0.5 ○ x=0.25 None of the above to save all
Answer:
The solution is [tex]x = 1[/tex]
Step-by-step explanation:
We have the following logarithmic properties:
[tex]ln a + ln b = ln ab[/tex]
[tex]ln a - ln b = ln \frac{a}{b}[/tex]
[tex]n ln a = ln a^{n}[/tex]
We have the following logarithmic equation:
[tex]ln(x + 31) - ln (4-3x) - 5 ln 2 = 0[/tex]
Lets simplify, and try to find properties.
[tex]ln(x + 31) - (ln (4-3x) + 5 ln 2) = 0[/tex]
[tex]ln(x + 31) - (ln (4-3x) + ln 2^{5}) = 0[/tex]
[tex]ln(x + 31) - (ln (4-3x) + ln 32) = 0[/tex]
[tex]ln(x + 31) - ln 32*(4-3x) = 0[/tex]
[tex]ln(x+31) - ln (128 - 96x) = 0[/tex]
[tex]ln \frac{x + 31}{128 - 96x} = 0[/tex]
To eliminate the ln, we apply the exponential to both sides, since e and ln are inverse operations.
[tex]e^{ln \frac{x + 31}{128 - 96x}} = e^{0}[/tex]
[tex]\frac{x + 31}{128 - 96x} = 1[/tex]
[tex]x + 31 = 128 - 96x[/tex]
[tex]97x = 97[/tex]
[tex]x = \frac{97}{97}[/tex]
[tex]x = 1[/tex]
The solution is [tex]x = 1[/tex]
How many possible ways are there to fill in answers to a
quizwith five multiple choice questions when the choices are a, b,
andc?
Answer: There are 15 possible ways to fill in answers .
Step-by-step explanation:
Given : The number of multiple choice questions = 5
The total number of choices for each question {a, b,
and c} = 3
Now by using the fundamental principle of counting , the number of possible ways to fill in answer is given by :-
[tex]5\times3=15[/tex]
Therefore, there are 15 possible ways to fill in answers .
Show in fact that 1=9m + 20n for some integers m and n
Answer:
[tex]1=9\cdot 9+20\cdpt (-4)=81-80[/tex]
Step-by-step explanation:
The greatest common divisor between 9 and 20 is 1, so we know the equation [tex] 1=9m+20n[/tex] has a solution. A solution can be found either by inspection, or by applying Euclidean algorithm.
By inspection we just list some multiples of 9:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
and also list some mutiples of 20:
20, 40, 60, 80, 100, 120
And so we see that we can find a multiple of 9 (81) which is 1 away from a multiple of 20 (80). Which is the solution given at the start.
For the Euclidean algorithm, we should divide the greatest of the two numbers, by the smallest one, and keep track of the remainder:
20 = 9 * 2 + 2
Then we divide 9 by the remainder we got, which is 2:
9 = 2 * 4 + 1
we would continue doing this until getting a remainder of 1 (which we just did). Finally we "solve" for 1, from the last equation:
9 - 2*4 = 1
And then we solve for 2 from the first equation, and plug that in into the previous equation:
20 - 9*2 =2
9 - ( 20 - 9*2)*4 = 1
which does give us the same solution: [tex] 9\cdot 9 +20\cdot (-4)=1[/tex]
A tank has the shape of an inverted circular cone (point at the bottom) with height 10 feet and radius 4 feet. The tank is full of water. We pump out water (to a pipe at the top of the tank) until the water level is 5 feet from the bottom. The work W required to do this is given by W= ? foot-pounds
The tank as a cone.
As per the question, the tank is given a shape of an inverted circular cone has a point to the bottom with an height of radius of 4 feet. The tank is full of water the pipe can be cued to pump out the water from the top and until which the tank ill have a level of 5 feet from the bottom.
Thus the answer is W equals to 468832 foot-pound
As per the given information the tank consists of the inverted circular cone the Height of cone is equal to 10 feet and radius = 4 feet After water pumped out height = 5 ft. Thus the volume of water pumped out Here we have r/h is constant alwaysHence the Substitute to get volume of water pumped out equals to the Mass of water = density x volume = Work done = force x displacement = mass x accents x displacement. Here acceleration = gravity = 32.2 ft/sec^2. Displacement = height reduced = 5 ft.Hence the W equals to 2912(32.2) that is 468832\pi foot-pound.Learn more about the shape of an inverted.
https://brainly.com/question/23758952.
To calculate the work required to pump water from an inverted circular cone tank, we use a formula that accounts for the weight density of water, volume of water, and height the water is lifted. We integrate from the middle of the tank, where the water level is 5 feet high, up to the top. The work is expressed in foot-pounds and involves an integral that can be solved using calculus.
Explanation:To calculate the work W required to pump water out of an inverted circular cone tank, we must use the concept of work done against gravity. The formula for work is W = γ x V x h, where γ (gamma) represents the weight density of water, V is the volume of water being lifted, and h is the distance the water is lifted.
Since the tank is a cone and water is being lifted from the current water height to the top of the tank, we have to integrate the work done for each infinitesimally small volume δV of water from the water level at 5 feet to the top at 10 feet. The water has a circular cross-section at any height y, with a radius that can be determined by similar triangles.
As the radius of the tank at the top is 4 feet and the height is 10 feet, the radius r at height y is (4/10)*y. The cross-sectional area A at height y is πr^2, which is (π * (4/10)^2 * y^2). The volume element δV is then A δy, and the work element δW is γ * A * (10 - y) δy. The total work is found by integrating δW from 5 to 10 feet.
The weight density of water γ is typically 62.4 lb/ft^3, so the integral becomes: W = ∫ γ * π * (16/100) * y^2 * (10 - y) dy from 5 to 10. This integral can then be evaluated to find the total work W in foot-pounds.
When an object falls through air, there is a drag force that depends on the product of the cross sectional area of the object and the square of its velocity, that is, Fair = CAv2, where C is a constant. Determine the dimensions of C. (Use the following as necessary: M for mass, T for time, and L for length.)
Answer:
[tex]\textrm{Dimension of C }=\ [ML^{-3}T^{0}][/tex]
Step-by-step explanation:
As given in question drag force depends upon the product of the cross sectional area of the object and the square of its velocity
and drag force can be given by
[tex]F=CAv^2[/tex] (1)
It is given that
Dimension of mass = [M]
Dimension of length = [L]
Dimension of time = [T]
So, by using above dimension we can write
the dimension of force,
[tex]F=[MLT^{-2}][/tex]
dimension of cross-section area,
[tex]A=[L^2][/tex]
and dimension of velocity
[tex]v=[LT^{-1}][/tex]
now, by putting these values in equation (1), we will get
[tex]F=CAv^2[/tex]
[tex]=>[MLT^{-2}]=C[L^2][LT^{-1}]^2[/tex]
[tex]=>C=[ML^{-3}T^0][/tex]
Hence, the dimension of constant C will be,
[tex]C=[ML^{-3}T^0][/tex]
The dimensions of C from the expression above is ML^-3
Units and DimensionGiven the function that relates drag force with the cross-sectional area of the object and the square of its velocity expressed as:
[tex]F_{air} = CAv^2[/tex]
Make C the subject of the formula to have:
[tex]C =\frac{F}{Av^2}[/tex]
Given the following dimensions
[tex]M =MLT^{-2}[/tex]
A = L²
v = [tex]LT^{-1}[/tex]
Substitute into the formula. the dimension of C will be given as:
[tex]C=\frac{MLT^{-2}}{L^2L^2T^{ -2}}\\C= ML^{-3}[/tex]
Henc the dimensions of C from the expression above is ML^-3
Learn more on Units and Dimension here: https://brainly.com/question/28464
How to do exponents a quicker way!! Please help my brother!
Determine if each statement would relate to a lean manufacturing system or a traditional manufacturing system.
a. Employees are cross-trained for several machines in one division.
b. Management emphasizes that defects should not occur.
c. Products are manufactured based upon estimated sales.
Answer:
answered
Step-by-step explanation:
A)lean
B)lean
C)traditional
In Lean manufacturing system works are done reduce inventory levels below what would be found in a traditional manufacturing system. The company does so by reducing batches into smaller batch sizes rather than large batch sizes. Goods are produced through product cells rather than departments.
Within-batch wait time is time that product waits in a product cell for the other products in a batch, it is calculated by multiplying the value-added time per unit by number of other products ,one less the total batch size
One-half liter of solution for intravenous infusion contains 2 g of drug. How many milliliters of the solution would contain 0.5 mg of drug?
Final answer:
To find out how many milliliters of the solution would contain 0.5 mg of the drug, we can set up a proportion using the given information. The solution would contain 0.125 mL of the drug.
Explanation:
To find out how many milliliters of the solution would contain 0.5 mg of the drug, we need to set up a proportion using the given information. We have 2 g of the drug in one-half liter of solution, so the concentration is 4 g/L. We can convert milligrams to grams by dividing by 1000. By setting up the proportion, we have:
4 g/L = 0.5 mg/x mL
Cross-multiplying, we get:
4 g * x mL = 0.5 mg * 1 L
Converting mg to g and mL to L:
4 * x = 0.5 / 1000
x = (0.5 / 1000) / 4
x = 0.000125 L
Since there are 1000 mL in 1 L, we can convert the answer:
x = 0.000125 L * 1000 mL/L
x = 0.125 mL
one interior angle of a polygon is equal to 800 and each of the other interior angles are 128 degrees. Find the number of sides of the polygon.
Answer:
6
Step-by-step explanation:
Given information:
Interior angle of a polygon cannot be more that 180°.
One interior angle = [tex]80^{\circ}[/tex]
Other interior angles are = [tex]128^{\circ}[/tex]
Let n be the number of sides of the polygon.
Sum of interior angles is
[tex]Sum=80+128(n-1)[/tex]
[tex]Sum=80+128n-128[/tex]
Combine like terms.
[tex]Sum=128n-48[/tex] .... (1)
If a polygon have n sides then the sum of interior angles is
[tex]Sum=(n-2)180[/tex]
[tex]Sum=180n-360[/tex] .... (2)
Equating (1) and (2) we get
[tex]180n-360=128n-48[/tex]
Isolate variable terms.
[tex]180n-128n=360-48[/tex]
[tex]52n=312[/tex]
Divide both sides by 52.
[tex]n=\frac{312}{52}[/tex]
[tex]n=6[/tex]
Therefore the number of sides of the polygon is 6.
Describe how an unbounded solution occurs
Answer and explanation :
Unbounded solutions :
Unbounded solution is the case where we can't find the exact solution. In this case there are infinite number of solutions and it is not possible to find exact solution in which these situations occurs.
When we use graphical method to solve the problem then in unbounded solution there is no boundary so that we can determine the maximum possible region in which solution occurs.
The United States has 435 members of the House of Representatives in Congress. If there are 325.7 million people in the country, what the ratio of members to the people? (Write your answer in scientific notation with 2 digits after the decimal.) рrt sex V8
Answer:
[tex]1.36\times 10^{-6}:1[/tex]
Step-by-step explanation:
We have been given that the United States has 435 members of the House of Representatives in Congress. There are 325.7 million people in the country.
To find the ratio of members to the people, we will find compare both numbers.
1 million equals 1,000,000.
[tex]\text{325.7 million}=325.7\times 1,000,000[/tex]
[tex]\text{325.7 million}=3257,000,000[/tex]
Ratio of members to the people:
435: 3257,000,000
[tex]0.0000013355848941:1[/tex]
[tex]1.3355848941\times 10^{-6}:1[/tex]
[tex]1.36\times 10^{-6}:1[/tex]
Therefore, our required ratio would be [tex]1.36\times 10^{-6}[/tex] members per person.
What is the total resistance of a parallel circuit that has two loads? Load one has a resistance of 10 ohms. Load two has a resistance of 24 ohms. (YOU MUST SHOW YOUR WORK)!!
Answer:
The total resistance is [tex]7.0588\Omega[/tex]
Step-by-step explanation:
Attached please find the circuit diagram. The circuit is composed by a voltage source and two resistors connected in parallel: [tex]R_1=10\Omega [/tex] and [tex]R_2=24\Omega [/tex].
First step: find the total current
For finding the current that the voltage source can provide, you must find the current consumed by each load and then add both. To do that, take first into account that the voltage is the same for both resistors ([tex]R_1[/tex] and [tex]R_2[/tex]).
[tex]I_{R_1}=\frac{V_S}{R_1}[/tex][tex]I_{R_2}=\frac{V_S}{R_2}[/tex]The total current is:
[tex]I_{TOTAL}=I_{R_1}+I_{R_2}=\frac{V_S}{R_1}+\frac{V_S}{R_2}=\frac{R_2\cdot V_S+R_1\cdot V_S}{R_1\cdot R_2}[/tex]
[tex]I_{TOTAL}=V_S\cdot \frac{R_1+R_2}{R_1\cdot R_2}[/tex]
Now, the total resistance ([tex]R_{TOTAL}[/tex]) would be the voltage divided by the total current:
[tex]R_{TOTAL}=\frac{V_S}{I_{TOTAL}}[/tex]
If you replace [tex]I_{TOTAL}[/tex] by the expression obtained previously, the total resistance would be:
[tex]R_{TOTAL}=\frac{V_S}{V_S\cdot \frac{R_1+R_2}{R_1\cdot R_2}}[/tex]
After simplifying the terms you should get:
[tex]R_{TOTAL}=\frac{R_1\cdot R_2}{R_1 + R_2}}[/tex]
Now, you must replace the values of the resistors:
[tex]R_{TOTAL}=\frac{(10\Omega )\cdot (24\Omega)}{10\Omega + 24\Omega}}=\frac{120}{17}\Omega=7.0588\Omega [/tex]
Thus, the total resistance is [tex]7.0588\Omega[/tex]
A TV costs $125.67 with a discount of 15% and 8.5% tax. What is the total that you will have to pay?
Answer:
The total you have to pay for the TV is $115.9
Step-by-step explanation:
When we have a discount we have to make a substraction, when we have tax we have to sum so:
$125.67 * 15 % = 18.85
125.67 - 18.85 = 106.82
Now we have to add the tax
106.82 * 8.5% = 9.08
106.82 + 9.08 = 115.9
An infusion pump is infsing heparin at a rate of 11.3 mL/hr. The infusion bag hanging has 25,000 units of heparin in 500 mL solution. Calculate the flow rate (units/hr) for these heparin infusions. Round the answer to the nearest whole number.
Answer:
565 units/hour
Step-by-step explanation:
As given in question,
rate of infusion of pump = 11.3 mL/hr
amount of heparin infusion bag contains = 25,000 units
amount of solution in infusion bag = 500 mL
Since, 500 mL of solution contains 25000 units of heparin
[tex]\textrm{So, 1 mL of solution will contain heparin of amount}=\dfrac{25000}{500}units[/tex]
= 50 units
Since, 11.3 mL of solution can flow in 1 hour
So, the heparin contains in 11.3 mL of solution = 11.3 x 50
= 565 units
As, 565 units of heparin can flow in 1 hour so the rate of flow of heparin will be 565 units/hour.
If A, B, and C are mutually exclusive events with P(A) = 0.21, P(B) = 0.32, and P(C) = 0.43, determine the following probabilities. Round your answers to two decimal places.
(a) P(A U B U C)
(b) P(A n B n C)
(c) P(A n B)
(d) P[(A U B) n C]
By their mutual exclusivity,
[tex]P(A\cup B\cup C)=P(A)+P(B)+P(C)=0.96[/tex]
[tex]P(A\cap B\cap C)=0[/tex]
[tex]P(A\cap B)=0[/tex]
For the last probability, first distribute the intersection:
[tex](A\cup B)\cap C=(A\cap C)\cup(B\cap C)[/tex]
Recall that for two event [tex]X,Y[/tex],
[tex]P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)[/tex]
so that
[tex]P((A\cap C)\cup(B\cap C))=P(A\cap C)+P(B\cap C)-P((A\cap C)\cap(B\cap C))[/tex]
[tex]P((A\cap C)\cup(B\cap C))=P(A\cap C)+P(B\cap C)-P(A\cap B\cap C)=0[/tex]
(a) How many prime numbers are (b) How many prime numbers are also abundant numbers?
Answer:
a) There are infinite prime numbers, b) All prime numbers are also abundant numbers
Step-by-step explanation:
To prove a) let's first prove that if n divides both integers A and B then also divides the difference A-B
If n divides A and B, there are integers j, k such that
A = nj and B= nk,
So
A-B= nj - nk = n(j-k)
But j-k is also an integer, which means that n divides also A-B
Now, to prove that there are infinite prime numbers , we will proceed with Reductio ad absurdum.
We will suppose that there are only a finite number of primes and then arrive to a contradiction.
Suppose there are only n prime numbers,
{p1,p2,... pn}
then take P=p1.p2...pn the product of all of them
and consider P+1
If P+1 is prime the proof is complete for P+1 is not in the list.
if P+1 is not prime then by the Fundamental Theorem of Arithmetic there is a prime in the list that must divide P+1, let's say pk
Then pk also divides P+1-P=1 which is a contradiction because no prime divides 1.
b) To prove this, recall that an abundant number is a number for which the sum of its proper divisors is greater than the number itself.
Given that a prime number P is only divided by P and 1, the sum of its divisors is P+1 which is greater than P. So P is abundant
Convert 500 cubic feet to liters
Answer:
500 cubic feet is equal to 14158.4 liters.
Step-by-step explanation:
Since, we know that,
1 square feet = 28.3168 liters,
Thus, the number of liters in 500 cubic feet = 500 × number of liters in 1 square feet
[tex]=500\times 28.3168[/tex]
[tex]=14158.4[/tex]
Therefore, 500 cubic feet is equal to 14158.4 liters.
500 cubic feet is 14158.4 liters.
To convert 500 cubic feet to liters, follow these steps:
Using the conversion factor:
1 ft³ = 28.3168 L
So, to convert 500 cubic feet to liters:
500 ft³ × 28.3168 L/ft³ = 14158.4 L
The following data describes the magnitude measurements randomly selected from 6 earthquakes recorded in one year from a location in southern Califormia: 6.6 2.2 18.5 7.0 13.7 5.9 The magnitude is measured by MAG on the Richter scale. What type of the data is the magnitude? a) Continuous numeric b) Discrete numeric c) Continuous categorical d) Nominal categorical
Answer: The magnitude is: a) continuous numeric.
Step-by-step explanation:
The magnitude is a numeric variable because it represents quantities. These are variables that you can measure or count. A numeric variable can be classified into discrete or continuous. In the present problem, the magnitude is a continuous variable. It can take any number within a scale, and you can find infinite values between two values on the scale. For example, you could measure earthquakes of magnitude 2.3, 2.4, 2.5, 2.6… and so on, following a continuous scale.
On the other hand, if the variable is numeric and discrete, it can only take certain finite values. For example, when you count the number of trees per acre. The number of trees will be always an integer. You can find 1, 2, or 3 trees, but you’ll never count 2.5 trees.
Categorical variables don’t represent quantities. They represent attributes. For example, apple colors: green and red.
An die (six faces) has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face. Assume that each face is equally likely to come up. Find a sample space for this experimen
Answer: {1 ,2 ,3 }
Step-by-step explanation:
We know that a sample space is a set of possible occurring oin an experiment.
Given : An die (six faces) has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face.
We assume that each face is equally likely to come up.
When we toss a dice , then the possible occurring = 1 , 2, 3
Then, the sample space for this experiment will be {1 ,2 ,3 }
Final answer:
Explaining the sample space for an experiment with a die displaying numbers in different frequencies.
Explanation:
An die (six faces) has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face. The sample space for this experiment would be: {1, 1, 1, 2, 2, 3}.
This means that when you roll the die, the possible outcomes are: 1, 1, 1, 2, 2, 3.
What percent of 1600 is 2?
Answer: 0.125%
Step-by-step explanation:
Let 1600 corresponds to the 100% value and 2 is a part of the total 100% value 1600.
The formula to find the percent of a part :_
[tex]\%=\dfrac{\text{Part}}{\text{Total}}\times100[/tex]
Substitute Part= 2 and Total = 1600 in the formula, we get :-
[tex]\%=\dfrac{2}{1600}\times100\\\\\Rightarrow\ \%=\dfrac{1}{8}\%=0.125\%[/tex]
Therefore, 2 is 0.125% of 1600.
Hence, the percent of 1600 is 2 = 0.125%
To find what percent of 1600 is 2, divide 2 by 1600 and multiply by 100, resulting in 0.125%. Thus, 2 is 0.125% of 1600.
To determine what percent of 1600 is 2, you can use the formula for percentage:
Percentage = (Part / Whole) × 100
Here, the part is 2 and the whole is 1600. Plug these values into the formula:
Percentage = (2 / 1600) × 100
First, perform the division:
2 / 1600 = 0.00125
Next, multiply by 100 to convert to a percentage:
0.00125 × 100 = 0.125%
Therefore, 2 is 0.125% of 1600.
Show that if A CB, then A = B ( B A ). Show that if A C B, then A U (B \ A) = B. Show, by example, that for sets A, B, and C, AN B = An C does not imply B = C.
Answer: If A ⊂ B, then A = B \ ( B \ A)
ok, when you do B \ A, you are subtracting all the elements in A∩B from B. So the only elements remaining are those who aren't in A.
If we subtract this of B again, we are subtracting of B all the elements that aren't in A, so the only elements remaining are those who belongs in A.
If A ⊂ B then A U (B \ A) = B.
Again, when you do B \ A you are extracting all the elements that belongs to the A∩B from B. So you are extracting al the elements from A. and when you add all the elements of A again, then you recuperate B.
if AnC = AnC does not imply that B = C.
if A = {1,2}, B = {1,2,3,4,5} and C = {1,2,3}
then AnC = {1,2} and AnB = {1,2} but B and C are different.
Ellen said she spent half her money for lunch and half of what was left for a movie. She now has $1.20. How much did she spend for lunch?
Devise a plan
Carry out the plan
Look back (is it reasonable? Did we answer the question?)
Answer: She spend $1.20 for lunch.
Step-by-step explanation:
Let the total amount be 'x'.
Half of her money spend for lunch be [tex]\dfrac{x}{2}[/tex]
Half of her money left for a movie be [tex]\dfrac{x}{2}[/tex]
Amount she has now = $1.20
So, According to question, it becomes ,
[tex]\dfrac{x}{2}=1.20\\\\x=1.20\times 2\\\\x=\$2.40[/tex]
Hence, Amount she spend for lunch is [tex]\dfrac{x}{2}=\dfrac{2.40}{2}=\$1.20[/tex]
Therefore, she spend $1.20 for lunch.
Northwest Molded molds plastic handles with a variable cost of $1.00 per handle. The fixed cost to run the molding machine is $2560 per week. If the company sells the handles for $3.00 each, how many handles must be molded weekly to break even? What is the profit if 1500 handles are produced and sold?
Answer:
To break even it must be molded 1280 handles weekly.
The profit if 1500 handles are produced and sold is $440
Step-by-step explanation:
To break even, the amount of total cost must be the same as the amount of revenues.
Total Cost is Fixed cost plus unitary variable cost multiplied by the produce quantity.
Total cost= FC + vc*Q
Where
FC=Fixed cost
vc=unitary variable cos
Q=produce quantity
Revenue= Price * Q
Break even FC + vc*Q=Price * Q
Isolating Q
FC=(Price * Q)-(vc*Q)
FC=(Price-vc) * Q
Q= FC/(Price-vc)
Q= $2560/($3.00-$1.00)=1280
If we sold 1500 handles
Profit = Revenue- Total cost =(Price * Q)-(FC + vc*Q)
P=$3.00 *1500-$2560 - $1.00*1500=
P=$4500-$2560-$1500=440
Final answer:
Northwest Molded must sell 1,280 handles to break even, based on their fixed weekly costs of $2,560 and a variable cost of $1.00 per handle with a selling price of $3.00 each. If they produce and sell 1,500 handles, they will make a profit of $440.
Explanation:
To calculate the break-even point for Northwest Molded, we need to determine the number of handles that must be sold to cover the total costs, which include both fixed and variable costs.
The fixed cost to operate the molding machine is $2,560 per week, and the variable cost per handle is $1.00.
Each handle is sold for $3.00. The break-even point is reached when total cost equals total revenue, which can be found using the break-even formula:
Break-even point in units = Fixed costs / (Selling price per unit - Variable cost per unit)
Thus, for Northwest Molded:
Break-even point in units = $2,560 / ($3.00 - $1.00) = $2,560 / $2.00 = 1,280 handles
To calculate the profit for producing and selling 1,500 handles, we need to compute the total revenue and subtract the total costs:
Total Revenue = Selling price per unit × Number of units sold = $3.00 × 1,500 = $4,500
Total Costs = Fixed costs + (Variable cost per unit × Number of units sold) = $2,560 + ($1.00 × 1,500) = $4,060
Profit = Total Revenue - Total Costs = $4,500 - $4,060 = $440
Therefore, in order to break even, Northwest Molded must mold and sell 1,280 handles weekly, and the company would make a profit of $440 if they produced and sold 1,500 handles.
Solve each of the following equations for x. (a) 5x-7=28 (b) 12-5x= x+30 (c) 5(x+2)= 1-3x
Зx-y=-5 X+2y=3
Answer:
(a) 7
(b) -3
(c) [tex]-\frac{9}{8}[/tex]
(d) -1
Step-by-step explanation:
(a) 5x - 7 = 28
5x = 28 + 7
5x = 35
⇒ x = 7
(b) 12 - 5x = x + 30
-5x = x + 30 - 12
-5x = x + 18
-5x - x = 18
-6x = 18
⇒ x = -3
(c) 5(x+2) = 1 - 3x
5x + 10 = 1 - 3x
5x = 1 - 3x - 10
5x + 3x = -9
8x = -9
⇒ x = [tex]-\frac{9}{8}[/tex],
(d) Given system of equations,
Зx-y = -5 ------(1),
x + 2y = 3 ----(2),
Equation (2) + 2 equation (1),
x + 6x = 3 - 10⇒ 7x = -7 ⇒ x = -1
Karen Price has determined that her net worth is $58,000. She has also determined that the face value of her mortgage is $89,000. She has determined that the face value of the rest of her debt is $18,000. What is Karen's debt-to-equity ratio? Multiple Cholce 184 153 3.22 4.94 0.31
Answer:
A. 1.84
Step-by-step explanation:
We have been given that Karen Price's net worth is $58,000. The face value of her mortgage is $89,000. The face value of the rest of her debt is $18,000.
[tex]\text{Debt to equity ratio}=\frac{\text{Total liabilities}}{\text{Total shareholder's equity}}[/tex]
We know that total liabilities include short term debt and long-term debt.
[tex]\text{Debt to equity ratio}=\frac{\$89,000+\$18,000}{\$58,000}[/tex]
[tex]\text{Debt to equity ratio}=\frac{\$107,000}{\$58,000}[/tex]
[tex]\text{Debt to equity ratio}=1.8448[/tex]
[tex]\text{Debt to equity ratio}\approx 1.84[/tex]
Therefore, Karen's debt-to-equity ratio 1.84 and option A is the correct choice.