C. The two statements agree in point of truth or falsehood in virtue of their logical structure alone, i.e. the two statement are true or false in exactly the same conditions.
Step-by-step explanation:For two statements to be logically equivalent, their truth values (true or false) must be the same for every variation of their constituent variables. In other words, if the truth tables of both statements are the same for every possible value of their variables, then they are logically equivalent.
For example;
The two statements P ∩ (Q U R) and (P ∩ Q) ∪ (P ∩ R) are logically equivalent.
If P, Q and R are all true, then;
P ∩ (Q U R) = true
(P ∩ Q) ∪ (P ∩ R) = true
If P, Q and R are all true, then;
P ∩ (Q U R) = false
(P ∩ Q) ∪ (P ∩ R) = false
If P = false, Q = true and R = true, then;
P ∩ (Q U R) = false
(P ∩ Q) ∪ (P ∩ R) = false
Checking for all other possible combinations of truth values of P, Q and R will always give the same results for the two statements, therefore, they are logically equivalent.
7.109) The leading brand of dishwasher detergent has a 30% market share. A sample of 25 dishwasher detergent customers was taken. a. What is the probability that 10 or fewer customers choose the leading brand
Answer:
0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they choose the leading brand, or they do not. The probability of a customer choosing the leading brand is independent of any other customer, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The leading brand of dishwasher detergent has a 30% market share.
This means that [tex]p = 0.3[/tex]
A sample of 25 dishwasher detergent customers was taken.
This means that [tex]n = 25[/tex]
a. What is the probability that 10 or fewer customers choose the leading brand?
This is:
[tex]P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{25,0}.(0.3)^{0}.(0.7)^{25} = 0.0001[/tex]
[tex]P(X = 1) = C_{25,1}.(0.3)^{1}.(0.7)^{24} = 0.0014[/tex]
[tex]P(X = 2) = C_{25,2}.(0.3)^{2}.(0.7)^{23} = 0.0074[/tex]
[tex]P(X = 3) = C_{25,3}.(0.3)^{3}.(0.7)^{22} = 0.0243[/tex]
[tex]P(X = 4) = C_{25,4}.(0.3)^{4}.(0.7)^{21} = 0.0572[/tex]
[tex]P(X = 5) = C_{25,5}.(0.3)^{5}.(0.7)^{20} = 0.1030[/tex]
[tex]P(X = 6) = C_{25,6}.(0.3)^{6}.(0.7)^{19} = 0.1472[/tex]
[tex]P(X = 7) = C_{25,7}.(0.3)^{7}.(0.7)^{18} = 0.1712[/tex]
[tex]P(X = 8) = C_{25,8}.(0.3)^{8}.(0.7)^{17} = 0.1651[/tex]
[tex]P(X = 9) = C_{25,9}.(0.3)^{9}.(0.7)^{16} = 0.1336[/tex]
[tex]P(X = 10) = C_{25,10}.(0.3)^{10}.(0.7)^{15} = 0.0916[/tex]
Then
[tex]P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0001 + 0.0014 + 0.0074 + 0.0243 + 0.0572 + 0.1030 + 0.1472 + 0.1712 + 0.1651 + 0.1336 + 0.0916 = 0.9021[/tex]
0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand
Use Lagrange multipliers to solve the following exercise. A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume of the room is 18042.75 cubic ft. The cost of wall paint is $0.06 per square foot and the cost of ceiling paint is $0.11 per square foot. Find the room dimensions that result in a minimum cost for the paint.
Answer:
Let the width of the garden =x meter
Then length=(x+4) meter
Half perimeter =36 m
So perimeter of garden =(2×36)=72 meters
According to the question
⇒2(l+b)=72
⇒2(x+x+4)=72
⇒2x+2x+4=74⇒4x=64⇒x=16 meters
Hence,the width of the garden =16 meters
The length of the garden =(16+4)=20 meters
2 starting terms of a diginacci sequence when the 2021st term is 11
Hello,
In a diginacci sequence, all term is the sum off digits of the 2 terms before.
Answer: 2,3
[tex]u_{-2}=1\\u_{-1}=1\\u_0=digit(u_{-2})+digit(u_{-1})=1+1=2\\u_1=1+2=3\\u_2=2+3=5\\u_3=3+5=8\\u_4=5+8=13\\u_5=8+1+3=12\\...\\u_{18}=11\\u_{19}=8\\u_{20}=10\\u_{21}=9\\u_{22}=10\\u_{23}=10\\u_{24}=2**********\\u_{25}=3**********\\2020=24*84+4\\u_{2020}=u_{4}=13\\[/tex]
We must begin with 13 , 10
Proof:
Dim a As Long, b As Long, c As Long, nb As Integer
a = 13
b = 10
nb = 1
Print nb, a
While nb < 2021
nb = nb + 1
c = somme&(a, b)
a = b
b = c
' Print nb, a
Wend
Print nb, a
End
Function somme& (a1 As Long, b1 As Long)
Dim strA As String, strB As String, n As Long
strA = LTrim$(Str$(a1))
strB = LTrim$(Str$(b1))
n = 0
For i = 1 To Len(strA)
n = n + Val(Mid$(strA, i, 1))
Next i
For i = 1 To Len(strB)
n = n + Val(Mid$(strB, i, 1))
Next i
somme& = n
End Function
I need to find a but I don’t know how to, could you please explain
Answer:
87
Step-by-step explanation:
Given is a figure of cyclic quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
Therefore,
z° + 93° = 180°
z° = 180° - 93°
z° = 87°
z = 87
Un automóvil consume 4 galones de gasolina al recorrer 180 kilómetros y para recorrer 900 kilómetros necesita 20 galones ¿cuántos kilómetros recorre por galón? ¿Cuantos galones consumirá en 2700 kilómetros?
Answer:
45 km por galón
60 galones en 2700 Km
Step-by-step explanation:
180 / 4
45 km por galón
900 / 45
20 galones
2700 / 45
60 galones en 2700 Km
NEED ANSWER QUICK WITH STEP BY STEP!!!
Check out this app! It's millions of students helping each other get through their schoolwork. https://brainly.app.link/qpzV02MawO
Answer: this app help me
Step-by-step explanation: it is so fun the answers is it is so good
In the figure below. JLM is similar to JKN if JM=14 inches what is the length of JN
Answer:
Hello good evening friend
Suppose that a survey was taken and it showed that 18% of online shoppers in the United States would prefer to do business only with large well-known retailers. If 2700 online shoppers were surveyed, how many are willing to do business with any size retailers?
Step-by-step explanation:
You can conclude that 82% of all shoppers will do business with any retailer of any size aslong as they are on the internet.
82% of 2700 = 0.82 * 2700 =2214
which makes the other responder correct.
Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find the value.
f(x)=6x^2+12x
Answer:
(-1, -6)
Step-by-step explanation:
This a term in this function is not negative, which would make it be flipped over the x-axis. Therefore this function takes the typical parabola shape, and it will have a minimum point.
To find the x-value of the minimum use the formula -b / 2a.
-12 / 2(6) = -1
Then plug in the x-value and find the y-value for this function
f(-1) = 6(-1)^2 + 12(-1) = -6
Which statement is true about quadrilateral ABCD with vertices A(2, 8), B(3, 11), C(4, 8), and D(3, 5)?
Answer:
The quadrilateral is a rhombus
Step-by-step explanation:
Given
[tex]A = (2, 8)[/tex]
[tex]B = (3, 11)[/tex]
[tex]C = (4, 8)[/tex]
[tex]D=(3, 5)[/tex]
Required
The true statement
Calculate slope (m) using
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Calculate distance using:
[tex]d= \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]
Calculate slope and distance AB
[tex]m_{AB} = \frac{11 - 8}{3 - 2}[/tex]
[tex]m_{AB} = \frac{3}{1}[/tex]
[tex]m_{AB} = 3[/tex] -- slope
[tex]d_{AB}= \sqrt{(3 - 2)^2 + (11 -8)^2}[/tex]
[tex]d_{AB}= \sqrt{10}[/tex] -- distance
Calculate slope and distance BC
[tex]m_{BC} = \frac{8 - 11}{4 - 3}[/tex]
[tex]m_{BC} = \frac{- 3}{1}[/tex]
[tex]m_{BC} = -3[/tex] -- slope
[tex]d_{BC} = \sqrt{(4-3)^2+(8-11)^2[/tex]
[tex]d_{BC} = \sqrt{10}[/tex] --- distance
Calculate slope CD
[tex]m_{CD} = \frac{5 - 8}{3 - 4}[/tex]
[tex]m_{CD} = \frac{- 3}{- 1}[/tex]
[tex]m_{CD} = 3[/tex] -- slope
[tex]d_{CD} = \sqrt{(3-4)^2+(5-8)^2}[/tex]
[tex]d_{CD} = \sqrt{10}[/tex] -- distance
Calculate slope DA
[tex]m_{DA} = \frac{8 - 5}{2 - 3}[/tex]
[tex]m_{DA} = \frac{3}{- 1}[/tex]
[tex]m_{DA} = -3[/tex] -- slope
[tex]d_{DA} = \sqrt{(2-3)^2 + (8-5)^2}[/tex]
[tex]d_{DA} = \sqrt{10}[/tex]
From the computations above, we can see that all 4 sides are equal, i.e. [tex]\sqrt{10}[/tex]
And the slope of adjacent sides are negative reciprocal, i.e.
[tex]m_{AB} = 3[/tex] and [tex]m_{CD} = -3[/tex]
[tex]m_{CD} = 3[/tex] and [tex]m_{DA} = -3[/tex]
The quadrilateral is a rhombus
which is the correct answer ?
Answer:
11/12 cups
Step-by-step explanation:
2/3+1/4 = ( 2x4 + 3x1 )/( 3x4 ) = ( 8+3 )/12 = 11/12
Unit sales for new product ABC have varied in the first seven months of this year as follows:
Month Jan Feb Mar Apr May Jun Jul
Unit Sales 314 285 158 482 284 310 281
What is the (population) Pearson's coefficient of skewness of the data?
Unit sales for new product ABC have varied in the first seven months of this year as follows:
Month Jan Feb Mar Apr May Jun Jul
Unit Sales 314 285 158 482 284 310 281
What is the (population) standard deviation of the data?
Answer:
Coefficient of skewness = 0.5785
Population standard deviation = 88.154
Step-by-step explanation:
Given the data:
Month Jan Feb Mar Apr May Jun Jul
Unit Sales 314 285 158 482 284 310 281
Reordered data : 158, 281, 284, 285, 310, 314, 482
The population mean of the data :
Mean, μ = Σx / n = 2114 / 7 = 302
The median :
1/2(n+1)th term
n = 7
1/2(8)th term
Median = 4th term = 285
The population standard deviation, s :
s = √(Σ(x - μ)²/n)
s = √[(158-302)^2 + (281-302)^2 + (284-302)^2 + (285-302)^2 + (310-302)^2 + (314-302)^2 + (482-302)^2] / 7
s= √(54398 / 7)
s = √7771.1428
s = 88.154
The Pearson Coefficient of skewness :
[3(μ - median)] / s
3(302 - 285) / 88.154
3(17) / 88.154
51 / 88.154
= 0.5785
Help plz I just need the awnser to this question
Answer:
A seems to be correct
Step-by-step explanation:
Parallel Lines never intersect because...
Answer:
Parallel lines are lines that never intersect because they have the same slope (m). So, this means that they only possible difference in there equations is the y-intercept (b). ... The slope in each equation is one-half, but each equation has a different y-intercept.
X is less than or equal to 2 Write in interval notation.
If 3x^2+2x-8=(3x-4)(x+2), which equations should be solved to find the roots of 3x^2+2x-8=0
9514 1404 393
Answer:
C, E
Step-by-step explanation:
The solutions are found by setting each of the factors to zero:
3x -4 = 0 . . . . . matches C
x +2 = 0 . . . . . matches E
E. Engagement Time Frame: Dox2) Leaming Task 2: Mate lists of possible combinations of snacks in your notebook. Use O for Orange Juice, M for Mango Juice, B for Blue Lemonade, O for Oreo, s for Skyflakes and R for Rebisco. Juices Biscuit Orange Juice Oreo Mango Juice Skyflakes Blue Leronode Rebisco
Answer:
The maximum number of possible combinations are 9.
Step-by-step explanation:
There are three types of juices :
Orange, Mango and Blue lemonade
There are three types of biscuits:
Oreo, Skyflakes and Rebisco
So, the number of possible combinations are
= (3 C 1) x (3 C 1)
= 3 x 3 = 9
The maximum number of possible combinations are 9.
Suppose we increase the overall number of doctors in the U.S. in all fields and specialties of medical practice by equal percentages, which would shif
Answer: hi your question is incomplete below is the complete question
Suppose we increase the overall number of doctors in the U.S. in all fields and specialties of medical practice by equal percentages, which would shift the supply curves in all the respective medical practice markets. Suppose we were to analyze two separate medical practice markets: Plastic Surgery Cardiology Which markets' price would be most impacted by this increase in the supply of doctors? Which markets' quantity would be most impacted by this increase in the supply of doctors?
answer :
Change in Market price = Cardiology
Change in Quantity = Plastic surgery
Step-by-step explanation:
Given that we are analyzing two separate markets with different levels of importance .
The demand for plastic surgery is more elastic when compared with Cardiology and this is due to the importance of Cardiology over plastic surgery.
The market price that will be affected by the increase in doctors supply is Cardiology market price while the Market quantity that would be affected by the increase is quantity of Plastic surgery
A radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now. What will be the amount of the material right after 20 years
Answer:
x = 960.4
Step-by-step explanation:
980 = 1000[tex]e^{kt}[/tex]
.98 = [tex]e^{10 k}[/tex]
ln(.98) = 10k ln(e)
k = ln(.98)/10
k=-0.00202
~~~~~~~~~~~~~~
x = 1000[tex]e^{20 *-.00202}[/tex]
x = 960.4
The amount of the material right after 20 years will be x = 960.4.
What is an exponential expression?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."
Given that radioactive material is known to decay at a yearly rate proportional to the amount at each moment. There were 1000 grams of the material 10 years ago. There are 980 grams right now.
The amount of the material will be calculated as,
980 = 1000
[tex]0.98 = e^{10k}[/tex]
ln(.98) = 10k ln(e)
k = ln(.98)/10
k=-0.00202
The value after 20 years will be,
[tex]x = 1000e^{20\times 0.00202}[/tex]
x = 960.4
Therefore, the amount of the material right after 20 years will be x = 960.4.
To know more about an exponential expression follow
https://brainly.com/question/2456547
#SPJ5
30 students in grade 8 finished their summer packet before August 15.
This was 12% of all the students. How many students are in grade 8?
Step-by-step explanation:
12/100=30/x
12x=3000
x=250
hiii! !!
Solve the following differential equations using classical methods. Assume zero initial conditions.
a. dx/dy +7x = 5cos2t
b. d^2x/dt^2 + 6 dx/dt + 8x = 5sin3t
I'll use the integrating factor method for the first DE, and undetermined coefficients for the second one.
(a) Multiply both sides by exp(7t ):
exp(7t ) dx/dt + 7 exp(7t ) x = 5 exp(7t ) cos(2t )
The left side is now the derivative of a product:
d/dt [exp(7t ) x] = 5 exp(7t ) cos(2t )
Integrate both sides:
exp(7t ) x = 10/53 exp(7t ) sin(2t ) + 35/53 exp(7t ) cos(2t ) + C
Solve for x :
x = 10/53 sin(2t ) + 35/53 cos(2t ) + C exp(-7t )
(b) Solve the corresonding homogeneous DE:
d²x/dt ² + 6 dx/dt + 8x = 0
has characteristic equation
r ² + 6r + 8 = (r + 4) (r + 2) = 0
with roots at r = -4 and r = -2. So the characteristic solution is
x (char.) = C₁ exp(-4t ) + C₂ exp(-2t )
For the particular solution, assume an ansatz of the form
x (part.) = a cos(3t ) + b sin(3t )
with derivatives
dx/dt = -3a sin(3t ) + 3b cos(3t )
d²x/dt ² = -9a cos(3t ) - 9b sin(3t )
Substitute these into the non-homogeneous DE and solve for the coefficients:
(-9a cos(3t ) - 9b sin(3t ))
… + 6 (-3a sin(3t ) + 3b cos(3t ))
… + 8 (a cos(3t ) + b sin(3t ))
= (-a + 18b) cos(3t ) + (-18a - b) sin(3t ) = 5 sin(3t )
So we have
-a + 18b = 0
-18a - b = 5
==> a = -18/65 and b = -1/65
so that the particular solution is
x (part.) = -18/65 cos(3t ) - 1/65 sin(3t )
and thus the general solution is
x (gen.) = x (char.) + x (part.)
x = C₁ exp(-4t ) + C₂ exp(-2t ) - 18/65 cos(3t ) - 1/65 sin(3t )
What is the ratio of 6 inches to 2 feet?
Answer:
3
Step-by-step explanation:
Answer:
1 : 4
Step-by-step explanation:
2 feet is 24 inches so we are finding the ratio between
6 and 24
Simplify
1 : 4
Solve the portion
6/x = 18/27
Answer:
x=9 answer...Step-by-step explanation:
6/x=18/27162=18xx=162/18x=9hope it helps.stay safe healthy and happy..Answer:9
Step-by-step explanation: 18/6=3 so 27/3 should equal the answer. If u know ur multiplication, the answer would be 9
Answer correctly and 40 points. Thx. Will report if wrong. ASAP plz! Thx!
Answer:
-7
Step-by-step explanation:
if you multiply by 7 positive it wont work because u cant cancel 7x out and a fraction wont work because theres no fraction involved in this so ur answer is A
At the Fidelity Credit Union, a mean of 5.8 customers arrive hourly at the drive-through window. What is the probability that, in any hour, more than 5 customers will arrive
Answer:
0.5217
Step-by-step explanation:
P(more than 5 customer arrive):
P(X>=6)=1-P(X<=5)= 1-∑x=0x e-λ*λx/x!= 0.5217
Roger has found a home to be purchase for $120,372 and has agreed to pay 28% down. Find the amount of Roger's down payment. Find the amount of money that Roger would need to borrow through a mortgage in order to purchase the home.
If Roger found a 30 year mortgage with a 5.9% APR. Find Roger's monthly payment. Using the monthly payment how much did Roger pay over the life of the mortgage?
Round your answer to the nearest cent.
Answer:
He needs to borrow: 86667.84
His monthly payment would be: 514.06
He would pay a total of: 185061.6 over the life of the loan
Step-by-step explanation:
roger would need to borrow .72*120372= 86667.84
2.)
calculate the effective rate .059/12= .004916667
[tex]86667.84=x\frac{1-(1+.004916667)^{-30*12}}{.004916667}\\x=514.0585984[/tex]
which we round to 514.06
3.) he is going to pay a total of 514.06*30*12= 185061.6 over the life of the loan
which of these statements is true for f(x) =3x2x
Step-by-step explanation:
which of these statements is true for f(x) =3x2xsorry i think u got yr question incomplete ...stay safe healthy and happy........If f(x) = 10 + 2x and g(x) = 6x + 5, then (f+ g)(x) =
Answer:
8x +15
Step-by-step explanation:
f(x) = 10 + 2x and g(x) = 6x + 5
(f+ g)(x) = 10 + 2x + 6x + 5
Combine like terms
= 8x +15
Answer:
8x+15
Step-by-step explanation:
(f+g)(x) = f(x)+g(x)
= (10+2x) + (6x+5)
= 8x+15
hope it helped, please mark me brainliest.
Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score of a man 71.2 inches tall. (to 2 decimal places)
Answer:
0.7857
Step-by-step explanation:
Given :
Mean = 69 inches
Standard deviation, = 2.8 inches
The Zscore of a man who is 71.2 inches
The ZSCORE is obtained using the relation :
Zscore = (Score, x - mean) / standard deviation
Zscore = (71.2 - 69) / 2.8
Zscore = 2.2 / 2.8
Zscore = 0.7857
