Answer:
FV= $3,716.32
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $3,500
Interest rate (i)= 1.2% compounded monthly
First, we need to determine the monthly nominal interest rate:
Monthly interest rate= 0.012/12= 0.001
Now, to calculate the future value after 't' months, we need to use the following formula:
FV= PV*(1 + i)^t
For example, for 60 months:
FV= 3,500*(1.001^60)
FV= $3,716.32
The first digits of data entries in most real-world data sets are not uniformly distributed. The most common first digit is 1, followed by 2, and so on, with 9 being the least common first digit. This phenomenon is known as Benford's Law.
The table below is the probability distribution for Benford's Law where the random variable D represents the first digit in a data entry.
What is the probability that a randomly selected data entry has a first digit greater than 7?
According to the given data,
Probability of D1 = 0.301Probability of D2 = 0.176By adding the probabilities, we get
→ [tex]P (D \leq = 2) = 0.301+0.176[/tex]
[tex]= 0.477[/tex]
Thus the response above is appropriate.
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Answer:
0.097
Step-by-step explanation:
1) "First digit greater than 7" means that the first digit is 8 or 9.
2) P(first digit greater than 7)=0.051+0.046=0.097
3) 0.097
someone help pls and thanks
The standard gasoline engine for the 2017 Toyota Corolla includes the following data: Configuration: In-line four-stroke, four-cylinder engine Bore: 3.17 in Stroke: 3.48 in Compression ratio: 10.6:1 Assuming an ideal Otto cycle to describe this engine. Consider the working fluid to be air, modeled as an ideal gas with variable specific heat. Determine: (a) The total engine volume VBDC for all cylinders (cu.in). (b) The mass of air (lbm) contained in the engine assuming ambient conditions of 540 R and 14.7 psia. (c) The efficiency of the engine (%). The maximum temperature that occurs during the cycle is 3600 R.
Answer:
a) The total engine volume is 30.3265 in³
b) the mass of air contained in the engine is 0.00129 lbm
c) The efficiency of the engine is 55.6%
Step-by-step explanation:
Given the data in the question;
The configuration is in line with four-stroke, four-cylinder engine.
Bore ( d ) = 3.17 in
Stroke ( L ) = 3.48 in
compression ratio ( r ) = 10.6 : 1
First, we calculate the swept Volume V₁ = π/4 × d²L
we substitute
V₁ = π/4 × (3.17 )² × (3.48) = 27.4655 in³
Now, Compression Ration; r = Vs + Vc / Vc
r = (V₁ + V₂) / V₂
we substitute
10.6 = (27.4655 + V₂) / V₂
10.6V₂ = 27.4655 + V₂
10.6V₂ - V₂ = 27.4655
9.6V₂ = 27.4655
V₂ = 2.861 in³
So
a) total engine volume
[tex]V_{BDC[/tex] = V₁ + V₂
we substitute
[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³
[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³
[tex]V_{BDC[/tex] = 30.3265 in³
Therefore, The total engine volume is 30.3265 in³
b) The mass of air
given that; T = 540°R, P = 14.7 psia
we know that; PV = mRT { R is constant }
we solve for m
m = PV / RT
we substitute
m = (14.7 × 30.3265) / ( 0.3704 × 1728 )540
m = 445.79955 / 345627.648
m = 0.00129 lbm
Therefore, the mass of air contained in the engine is 0.00129 lbm
c) The efficiency
from table { properties of air}
At 540°R; u₁ = 92.04 BTu/lbm, u[tex]_r[/tex]₁ = 144.32
Now process 1 - 2 ( Isentropic ) u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂ = V₁/V₁ = r
so, u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂ = r
144.32 / u[tex]_r[/tex]₂ = 10.6
u[tex]_r[/tex]₂ = 144.32/10.6
u[tex]_r[/tex]₂ = 13.61
Thus, at u[tex]_r[/tex]₂ = 13.61, u₂ = 235 BTU/lbm, T₂ = 1340°R
Now, we know that;
P₁V₁/T₁ = P₂V₂/T₂ ⇒ (P₁/V₁)r = P₂/T₂
⇒ ( 14.7 / 540 )10.6 = P₂/1340
P₂ = 386.664 psia
process 2 - 3; constant volume heat addition;
Now, At T₃ = 3600°R, u₃ = 721.44 BTU/lbm, u[tex]_r[/tex]₃ = 0.6449
so, [tex]q_{in[/tex] = u₃ - u₂
we substitute
so, [tex]q_{in[/tex] = 721.44 - 235 = 486.44 BTU/lbm
Next, process 3 - 4; Isentropic
u[tex]_r[/tex]₄/u[tex]_r[/tex]₃ = V₄/V₃ = r
u[tex]_r[/tex]₄ / 0.6449 = 10.6
u[tex]_r[/tex]₄ = 6.8359
At u[tex]_r[/tex]₄ = 6.8359; u₄ = 308 BTU/lbm
∴
Heat Rejection [tex]q_{out[/tex] = u₄ - u₁ = 308 - 92.04 = 215.96 BTU/lbm
so, [tex]W_{net[/tex] = [tex]q_{in[/tex] - [tex]q_{out[/tex]
[tex]W_{net[/tex] = 486.44 - 215.96
[tex]W_{net[/tex] = 270.48 BTU/lbm
so the efficiency; η[tex]_{thermal[/tex] = ([tex]W_{net[/tex] / [tex]q_{in[/tex] ) × 100%
η[tex]_{thermal[/tex] = ( 270.48 / 486.44 ) × 100%
η[tex]_{thermal[/tex] = ( 0.55604 ) × 100%
η[tex]_{thermal[/tex] = 55.6%
Therefore, The efficiency of the engine is 55.6%
What is the answer to this problem?
Answer:
[tex]r=\dfrac{2}{3}\ yards[/tex]
Step-by-step explanation:
Given that,
The volume of a sphere is, [tex]V=\dfrac{32}{81}\pi[/tex] cubic yards
We need to find the radius of the sphere. The formula for the volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^2[/tex]
Put all the values,
[tex]\dfrac{32}{81}\pi=\dfrac{4}{3}\pi r^3\\\\r^3=\dfrac{8}{27}\\\\r=\dfrac{2}{3}\ yards[/tex]
So, the radius of the sphere is equal to [tex]\dfrac{2}{3}\ yards[/tex].
Entras a una tienda ropa y hay un pantalón que valia 150 y ahora vale 90 y una camiseta que valia 40 ahora vale 24 ¿ tienen el mismo porcentaje de rebaja ? Justifica tu respuesta
Answer:
Entras a una tienda ropa y hay un pantalón que valia 150 y ahora vale 90 y una camiseta que valia 40 ahora vale 24 ¿ tienen el mismo porcentaje de rebaja ? Justifica tu respuesta
Question 3 of 10
When the input is x = 0 for the parent function f(x) = 2*, what is the output?
A. f(x) = 2
B. f(x) = 1
C. f(x) = 0
D. f(x) = 3
The figures in the picture are similar to each other. Find the value of x, rounded to the nearest whole number.
Answer:
x=5
Step-by-step explanation:
2(x-1)=x+3
x=5
(5-1)=4
4*2=8
5+3=8
ANSWER 5
Have a great day!
Quadrilateral CDEF is dilated by a scale factor of į to form quadrilateral C'D'E'F'.
What is the measure of side EF?
Given:
CDEF is dilated by a scale factor of [tex]\dfrac{3}{4}[/tex] to form the quadrilateral C'D'E'F'.
To find:
The measure of side E'F'.
Solution:
If a figure is dilated by a scale factor of k, then the side of dilated figure is k times of corresponding side of original figure.
CDEF is dilated by a scale factor of [tex]\dfrac{3}{4}[/tex] to form the quadrilateral C'D'E'F'. So,
[tex]E'F'=\dfrac{3}{4}\times EF[/tex]
From the given figure it is clear that [tex]EF=12[/tex]. So,
[tex]E'F'=\dfrac{3}{4}\times 12[/tex]
[tex]E'F'=9[/tex]
Therefore, the measure of side E'F' is 9 units.
What is the area of this polygon? Im really bad a geometry so can I have help please.
brendan has $200 in a saving account with a 1% interest rate. using the formula for simple interest, how much will he earn in interest after 7 years?
answer:
$14
step-by-step explanation:
the formula for simple interest is-
i=prt
meaning interest=principal (the starting amount of money) * rate * time
=200*0.01*7
(we have to turn 1% into a decimal so 1/100=0.01)
=14
i=14
good luck :)
i hope this helps
brainliest would be highly appreciated
have a nice day!
After 7 years and a 1% interest rate, Brendan will have a total of 214$.
What is simple interest?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
Given, Brendan has $200 in a saving account with a 1% interest rate.
The simple interest is given as
Interest = (PRT/100)
where
P = Amount deposited = 2,00
R = Rate = 1%
T= Time = 7 years
Interest = (PRT/100)
Interest = (200 × 7 × 1/100)
Interest = 14
Total amount = SI + principal amount
Total amount = 14 + 200 = 214
Therefore, Brendan will have 214 $ after 7 years and a 1% interest rate.
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Find XS, VY, and YZ. I am very confused on what to do.
Answer:
Do you see the lines and how they are named? I am going to try and explain this in less words than I can. Where it says XS you have to match it up with the lines. But if it says that you have to find XSU (which it does not) you would have to go up all the way but you stop where it says the S so you wont go all the way up to the U. I hope this helps!
What is the probability of choosing a clubs or a numbered card from a deck of cards? Type your answer as a fraction.
Answer:
13/52
Step-by-step explanation:
if jose says that 75% of his class of 28 students rides the bus every day, how many students rides the bus?
Answer:
21 students ride the bus
Tom has finished 75% of a 12 mile run. How many miles has he run so far?
Answer: Tom has run 9 miles so far
Step-by-step explanation:
3/4 of 12 if equal to 9
Answer:
9 miles
Step-by-step explanation:
3 is 25 percent of 12.
to figure out how much he runs in 755 of two miles you multiply 3x3=9.
Let corn denote per capita consumption of corn in bushels at the county level, let price be the price per bushel of corn, let income denote per capita county income, and let rainf all be inches of rainfall during the last corn-growing season. The following simultaneous equations model imposes the equilibrium condition that supply equals demand:
corn = alpha1 price + beta1 income + mu1
corn = alpha2 price + beta2 rainfall + gamma rainfall2 + mu2
Which is the supply equation, and which is the demand equation? Explain.
Answer:
[tex]Corn = \alpha_1 *price + \beta_1 * income + \mu_1[/tex] --- Demand
[tex]Corn = \alpha_2 *price + \beta_2 * rainfall + \gamma * rainfall_2 + \mu_2[/tex] --- Supply
Step-by-step explanation:
Given
[tex]Corn = \alpha_1 *price + \beta_1 * income + \mu_1[/tex]
[tex]Corn = \alpha_2 *price + \beta_2 * rainfall + \gamma * rainfall_2 + \mu_2[/tex]
Required
Identify the demand and the supply equation.
To identify which is the demand equation and which is the supply equation, we simply look through the constraints of the equation.
For (1):
[tex]Corn = \alpha_1 *price + \beta_1 * income + \mu_1[/tex]
We have: Price and Income
For (2):
[tex]Corn = \alpha_2 *price + \beta_2 * rainfall + \gamma * rainfall_2 + \mu_2[/tex]
We have: Price and Rainfall
In (1), price and income determines the demand of a product.
Hence, (1) represents the demand equation
In (2), price and weather condition (rainfall) determines the supply of a product.
Hence, (2) represents the supply equation.
In which quadrant does the point (-1, 24) lie?
OA.
Quadrant 1
OB. Quadrant II
OC. Quadrant IV
D. Quadrant III
Which expression is equivalent to 10x2 - (2 – 3x) + (5x - 3x2)?
Answer:
H) 7x² + 8x - 2
Step-by-step explanation:
You saved $180 on your new laptop because you bought it online. If this was a 20% savings from the original price, find the original cost of the laptop.
Answer:
$900
Step-by-step explanation:
$180 divided by 0.20 is $900
A percentage is a way to describe a part of a whole. The original cost of the laptop is $900.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let the original cost of the laptop be represented by x.
Given that you saved $180 on your new laptop, which is a 20% saving from the original price. Therefore, the percentage can be written as,
20% of original price = $180
(20/100) × x = $180
x = ($180×100)/20
x = $900
Hence, the original cost of the laptop is $900.
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A pair of shoes has been marked up by 65%. If the original price was $40.00, what is the new price?
Answer:
First we need to see how many times 65% will make the price go up by 100%. We can see this by dividing 100 by 65. 100 divided by 65 is 1.53846153846. Now we can multiply 40 by 1.53846153846 and see what we get. 40x1.53846153846=$61.5384615384.
This is a lot of decibal numbers so if you seek more help then contact me on discord at Mousycritter#2842 for free advice!
Step-by-step explanation:
Rectangle VWXY is dilated by a scale factor of 2 to form rectangle V'W'X'Y'. Side X'Y'
measures 22. What is the measure of side XY?
9514 1404 393
Answer:
11
Step-by-step explanation:
X'Y' = 2XY . . . . lengths are related by the dilation factor
22 = 2XY . . . substitute the given value
11 = XY . . . . . divide by 2
The measure of side XY is 11.
what would this be??
Answer:
The area would be 15.75 feet squared!
(4+5/2)(3.5) = 15.75
A movie complex is showing the same movie in three theaters. In theater A, 56 of the 80 seats are taken. In theater B, seats are taken and seats are empty. In theater C, of the seats are empty. Which theater has the greatest percent of its seats taken?
Also, I need this ASAP.
Answer:
Theatre A has the greatest percent
Expand the following expression
(x + 2)(x² – 3x - 1)
Answer:
[tex]x^{3} - x^{2} - 7x -2[/tex]
Step-by-step explanation:
Give me brainllest
Answer:
[tex] {x}^{3} - {x}^{2} - 7x - 2[/tex]
Step-by-step explanation:
[tex](x + 2)( {x}^{2} - 3x - 1)[/tex]
Multiply the first term.
[tex]x \times {x}^{2} = {x}^{3} [/tex]
Multiply x by everything on the right, dont do x squared we already done that.
[tex]x \times - 3x = - 3 {x}^{2} [/tex]
[tex]x \times - 1 = - x[/tex]
Multiply 2 by everything on the left expect -1. ( that our next step).
[tex]2 \times {x}^{2} = 2 {x}^{2} [/tex]
[tex]2 \times - 3x = - 6x[/tex]
Multiply the last term, 2 and -1.
[tex]2 \times - 1 = - 2[/tex]
Add like with like.
[tex] {x}^{3} - {x}^{2} - 7x - 2[/tex]
Sort these fractions in ascending order.
4/5
3/7
1/6
2/3
Answer:
1/6, 3/7, 2/3, 4/5
Step-by-step explanation:
Write 44 as a product of primes. Use index notation
Answer:
2 x 2 x 11 or 2^2 x 11
Prime factorization: 44 = 2 x 2 x 11, which can also be written 2² x 11.26
What is the area of the kite 10 12 12 18
QUICK ITS TIMED WILL GIVE BRAINLYIST
Which measurements are in the correct order from largest to smallest?
A. quart, pint, cup, fluid ounce
B. gallon, quart, cup, pint
C. gallon, pint, quart, cup
D. gallon, cup, fluid ounce, quart
solve the system of inequalities:
3x-10<0
2x>0
HELPPP WILL MARK BRAINLIEST
Answer:
Solve each inequality and combine solutions:
3x - 10 < 0 ⇒ 3x < 10 ⇒ x < 10/3 2x > 0 ⇒ x > 0Combination of the two is:
0 < x < 10/3or
x ∈ (0, 10/3)Answer: <0<x<10/3
Step-by-step explanation:
Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y produced after t hours of production is y = 102t +
1
2
t2 − t3, 0 ≤ t ≤ 8.
in which is the vaule of the 6 ten times the vaule of the 6 in the number 6000
Answer:
Consider matrix A.
What is the inverse of A? Fill in the missing elements in the matrixs.
Step-by-step explanation:
Consider matrix A.
What is the inverse of A? Fill in the missing elements in the matrixs.
Answer:
Hello! Your answer would be, 600
Step-by-step explanation:
if we start backwards, the value of 6 in 6000 is equal to 1/1000. If you want to find what is 10 times that, multiply 1/1000 with ten and you get 1/100. That is equal to 6/600. The value of 6 is 600.
Hope I helped! Brainiest plz!♥ Have a nice morning! Hope you make a 100%! -Abby