The probability that at least 3 out of 9 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.8575.
To find the probability, we can use the binomial probability formula. Let's define a success as an adult using their smartphone in meetings or classes, with a probability of success (p) of 0.57.
We want to find the probability of getting at least 3 successes in 9 trials. This includes scenarios where we have 3, 4, 5, 6, 7, 8, or 9 successes. We can calculate the probability for each of these scenarios and sum them up.
Using the binomial probability formula:
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
where C(n, k) is the binomial coefficient, n is the number of trials, and k is the number of successes.
Calculating each term and summing them up:
P(X ≥ 3) = C(9, 3) * (0.57)^3 * (1 - 0.57)^(9 - 3) + C(9, 4) * (0.57)^4 * (1 - 0.57)^(9 - 4) + C(9, 5) * (0.57)^5 * (1 - 0.57)^(9 - 5) + C(9, 6) * (0.57)^6 * (1 - 0.57)^(9 - 6) + C(9, 7) * (0.57)^7 * (1 - 0.57)^(9 - 7) + C(9, 8) * (0.57)^8 * (1 - 0.57)^(9 - 8) + C(9, 9) * (0.57)^9 * (1 - 0.57)^(9 - 9)
Using the binomial coefficient values and simplifying:
P(X ≥ 3) ≈ 0.8575
The probability that at least 3 out of 9 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.8575. This means that in a random selection of 9 adult smartphone users, there is an 85.75% chance that at least 3 of them will use their smartphones in meetings or classes.
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[ -1 5 7] [9] [x1]
Given A = [ 0 -2 4], B = [6] and x = [x2] [0] Calculate: (a) Al (b) /A (c) 1x (d) x′1 Indicate the dimension of the identity matrix used in each case.
The exercise involves calculations with matrices A, B, and x. We need to perform various operations, including taking the inverse of matrix A, multiplying matrix A by matrix B, multiplying matrix x by the transpose of x, and calculating the dimension of the identity matrix used in each case.
Let's perform the calculations step by step:
(a) To find the inverse of matrix A, denoted as A^(-1), we need to check if matrix A is invertible. If the determinant of A is non-zero, then A^(-1) exists. If the determinant is zero, A is not invertible.
Determinant of A = |A| = 0*(-8*(-8) - 20) + 2(0*(-8) - 40) - 4(02 - (-8)(-8))
= 0 + 0 - 4*(-128)
= 512
Since the determinant is non-zero, matrix A is invertible. To find A^(-1), we can use the formula:
[tex]A^{-1} = (1/|A|) * adj(A)[/tex]
where adj(A) is the adjugate of matrix A. The adjugate can be found by taking the transpose of the cofactor matrix of A.
Calculating the adjugate of A:
Cofactor matrix of A:
C = [0 -8 16]
[0 0 0]
[4 8 0]
Transposing C:
adj(A) = [0 0 4]
[-8 0 8]
[16 0 0]
Calculating [tex]A^{-1}:[/tex]
[tex]A^{-1}= (1/512) * adj(A)[/tex]
= (1/512) * [0 0 4]
[-8 0 8]
[16 0 0]
= [0 0 1/128]
[-1/64 0 1/64]
[1/32 0 0]
(b) To calculate matrix B divided by matrix A, denoted as B/A, we need to multiply matrix B by the inverse of matrix A, which we already found in part (a).
[tex]B/A = B * A^{-1}[/tex]
= [6] * [0 0 1/128]
[-1/64 0 1/64]
[1/32 0 0]
= [60 + 0(-1/64) + 1/1280]
[60 + 00 + 1/640]
[61/32 + 00 + 1/128*0]
= [0]
[0]
[3/512]
(c) To calculate the product of matrix x and the transpose of x, denoted as xx', we simply multiply each element of x by the corresponding element in the transpose of x.
xx' = [x2x2 00]
[00 00]
= [x2^2 0]
[0 0]
(d) The dimension of the identity matrix used in each case:
For part (a), the dimension of the identity matrix used is 3x3 since the inverse of A is a 3x3 matrix.
For part (b), the dimension of the identity matrix used is 3x3 since we are multiplying a 3x1 matrix (B) by the inverse of A, which is a 3x3 matrix.
For part (c), the dimension of the identity matrix used is 2x2 since xx' is a 2x2 matrix.
For part (d), it seems there is a typo in the question, as it asks for x'1 which suggests it should be a column vector. However, x is given as [x2 0] which suggests it is a row vector. Therefore, the dimension of the identity matrix used cannot be determined in this case.
In summary:
(a) A^(-1) = [0 0 1/128]
[-1/64 0 1/64]
[1/32 0 0]
(b) B/A = [0]
[0]
[3/512]
(c) xx' = [x2^2 0]
[0 0]
(d) The dimension of the identity matrix used cannot be determined for part (d) due to the inconsistency in the provided data.
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Please help fast!!!!
Solve the equation N/-2=-15
Answer:
30
Step-by-step explanation:
N/-2=-15
N= -15 times -2
N= 30
Answer:
N = 30
Step-by-step explanation:
Step 1: Write equation
N/-2 = -15
Step 2: Solve for N
Multiply both sides by -2: N = 30Step 3: Check
Plug in N to verify it's a solution.
30/-2 = -15
-15 = -15
The cities Youngstown, Prairieville; and Dorchester, in respective order, lie approximately in a straight line. The distance from Youngstown to Prairieville is 102 miles. The distance from Youngstown to Dorchester is 213 miles. Find the distance from Prairieville to Dorchester.
You sells It in Dest for will 9 $13000 bond $13 161 currently. mature in 6 6 years. thut Yield to maturity is Q What is the coupon rate? a) 11,987. b 16,28%. c) 18,61%. d) 14,32%
The coupon rate of the bond is 9.04% as calculated in the main answer.
Given:Selling price of bond= $13000Maturity value= $13161Time to maturity= 6 yearsThe yield to maturity of the bond is not given.Coupon rate refers to the rate of interest that is paid on the face value of the bond.
The formula to calculate the coupon rate is as follows: Coupon rate = (Annual coupon payment / Face value of the bond) x 100%The main answer to the given problem is as follows:We can find the annual coupon payment by using the formula as shown below:
Annual coupon payment = Yield to maturity x Face value of the bondSubstituting the given values, we getAnnual coupon payment = Yield to maturity x $13161Let the yield to maturity be ‘y’.Annual coupon payment = y x $13161We are given that the selling price of the bond is $13000
. Therefore, using the formula for yield to maturity, we can find the yield to maturity as shown below: 13000 = Annual coupon payment / (1+y/2)⁶ + $13161 / (1+y/2)¹²Simplifying the above expression,
we get a quadratic equation as shown below:2y² + 35y – 629 = 0On solving the above equation, we get y = 0.090398 or y = -17.540398We can ignore the negative value of ‘y’.
Therefore, the yield to maturity of the bond is 9.04%. Substituting this value in the formula for annual coupon payment,
we get Annual coupon payment = 9.04% x $13161. Annual coupon payment = $1189.72Using the formula to calculate the coupon rate, we get:
Coupon rate = (Annual coupon payment / Face value of the bond) x 100%Coupon rate = ($1189.72 / $13161) x 100%Coupon rate = 9.04%Therefore, the coupon rate of the bond is 9.04%.Option A - 11.987
The coupon rate of the bond is 9.04% as calculated in the main answer.
Therefore, the correct option among the given options is (A) 11.987. The solution to the given problem is explained in detail.
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What are the solutions to (X-7)(x+1)(x-9)=0?
Answer:
Just take the opposite of the number in the factor.
x = 7, x = -1, x = 9
Convert 87/15 to a mixed number
Answer:
5 and 4/5
Step-by-step explanation:
Answer:
5 4/5 (5 12/15 not reduced)
Step-by-step explanation:
15 will go into 87 5 times.
15x1 = 15. 15x2 = 30. 15x3 = 45. 15x4 = 60. 15x5 = 75. 15x6 = 90. 90 can not go into 87, so you have to work with 75. 87-75=12. So, now your answer is
5 12/15. You are able to divide each of those numbers by 3, so let’s reduce. 12 divided by 3 is 4, and 15 divided by 3 is 5. So your reduced answer is 5 4/5. Hope that helped.
Solve for x: -243 = -9(10 + x)
Answer:
x=17
Step-by-step explanation:
−243=−9(10+x)
Step 1: Simplify both sides of the equation.
−243=−9(10+x)
−243=(−9)(10)+(−9)(x)(Distribute)
−243=−90+−9x
−243=−9x−90
Step 2: Flip the equation.
−9x−90=−243
Step 3: Add 90 to both sides.
−9x−90+90=−243+90
−9x=−153
Step 4: Divide both sides by -9.
−9x/−9
= −153/−9
x=17
Answer:
x=17
Step-by-step explanation:
I took the test!
Find the midpoint M of the line segment joining the points A = (-7, -6) and B = (3, 4).
B
M=
COD
Answer:
The midpoint is (-2,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
( -7+3)/2 = -4/2 =-2
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
(-6+4)/2 = -2/2 =-1
The midpoint is (-2,-1)
Find the values of x and y in the following parallelogram
D
C
17
+ 13/ 5y + 4
16- X
A
B
Answer:
A b
Step-by-step explanation:
i m very frendly ask me anyrhing
∠A and ∠B are complementary angles. If m∠A=(6x+1) ∘ and m∠B=(8x-23) ∘, then find the measure of∠B.
Given that <A and <B are complementary angles, the measure of angle B is: [tex]41^{\circ}[/tex]
Apply the knowledge of what complimentary angles are to solve for x then find the measure of <B.
Since <A and <B are both complimentary angles, therefore:
<A + <B = 90 degrees.Given:m<A = (6x+1)
m<B = (8x-23)
Substitute[tex](6x+1) + (8x-23) = 90[/tex]
Open the bracket[tex]6x+1 + 8x-23 = 90[/tex]
Add like terms[tex]6x+1 + 8x-23 = 90\\\\14x - 22 = 90[/tex]
Add 22 to both sides[tex]14x = 90 + 22\\\\14x = 112[/tex]
Divide both sides by 14[tex]x = 8[/tex]
Find m<B by plugging in the value of x[tex]m \angle B = 8x-23\\\\m \angle B = 8(8) - 23\\\\m \angle B = 41^{\circ}[/tex]
Therefore, given that <A and <B are complementary angles, the measure of angle B is: [tex]41^{\circ}[/tex]
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Which expression is equivalent
Two dice are cast. What is the probability that the sum of the two numbers does not exceed 10 (i.e. is less than or equal to 10)?
The probability is approximately 0.9167 or 91.67%.
To find the probability that the sum of two dice numbers does not exceed 10, we need to determine the favorable outcomes (sums less than or equal to 10) and the total possible outcomes when rolling two dice.
There are 36 possible outcomes when rolling two dice because each die has six faces (1, 2, 3, 4, 5, and 6), and the total number of outcomes is obtained by multiplying the number of outcomes for each die (6 * 6 = 36).
Now let's determine the favorable outcomes (sums less than or equal to 10):
When the sum is 2: There is only one combination (1 + 1).
When the sum is 3: There are two combinations (1 + 2 and 2 + 1).
When the sum is 4: There are three combinations (1 + 3, 2 + 2, and 3 + 1).
When the sum is 5: There are four combinations (1 + 4, 2 + 3, 3 + 2, and 4 + 1).
When the sum is 6: There are five combinations (1 + 5, 2 + 4, 3 + 3, 4 + 2, and 5 + 1).
When the sum is 7: There are six combinations (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1).
When the sum is 8: There are five combinations (2 + 6, 3 + 5, 4 + 4, 5 + 3, and 6 + 2).
When the sum is 9: There are four combinations (3 + 6, 4 + 5, 5 + 4, and 6 + 3).
When the sum is 10: There are three combinations (4 + 6, 5 + 5, and 6 + 4).
Adding up the favorable outcomes, we get: 1 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 = 33.
Therefore, the probability that the sum of the two dice numbers does not exceed 10 is given by:
Probability = Favorable outcomes / Total outcomes = 33 / 36 = 11/12 ≈ 0.9167.
So, the probability is approximately 0.9167 or 91.67%.
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4.75x=+54+2.50x
Can you help me with the above equation?
x/5 - 3 = 9/1
x=
PLEASE HELP I WILL MARK BRAINLIEST
15. Increase 600 by 8/3%. (a) 50 (b) 450 (c) 550 (d) 605 (e) 650
To increase 600 by 8/3%, we can use the formula: New value = Old value + (Percent increase/100) x Old value. So, Rounding off to the nearest whole number, we get: New value ≈ 616
Using this formula, we can calculate the new value of 600 as follows:
New value = 600 + (8/3)% x 600
First, we need to convert the percent to a decimal by dividing it by 100:8/3% = 8/3 ÷ 100 = 0.0266
Substitute this value into the formula:
New value = 600 + 0.0266 x 600
Simplify by multiplying: New value = 600 + 15.96
New value = 615.96
Rounding off to the nearest whole number, we get: New value ≈ 616
Therefore, the correct answer should be approximately 616
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the quotient of 10 and 2
Answer:
5
Step-by-step explanation:
10 divided by 2 is 5
Answer:
5
Step-by-step explanation:
you divided 10 by 2
While playing volleyball, Ralph drank 3/4 of a jug of water. If the jug held 64 fluid ounces of water, how much water did Ralph drink?
Answer:
48
Step-by-step explanation:
no explanation im just big brain
PLEASE HELP ME WITH THIS 20 points!!!!!
Answer:
4x+10=28
We simplify the equation to the form, which is simple to understand
4x+10=28
We move all terms containing x to the left and all other terms to the right.
+4x=+28-10
We simplify left and right side of the equation.
+4x=+18
We divide both sides of the equation by 4 to get x.
x=4.5
Step-by-step explanation:
12r2s + 21rs2 – 3rs=
What is6.24 divided by 10
Answer:
.624
Step-by-step explanation:
Hope this helps.
Answer: 0.624
Step-by-step explanation:
tres pintores van a pinatr tres bardas y entres los tres lo pagaran cuanto pagara cada uno?
The amount paid by person is given as follows:
400.
How to obtain the amount paid by person?The amount paid by person is obtained applying the proportions in the context of the problem.
The total cost is given as follows:
1200.
The number of people is given as follows:
3.
Hence the amount paid by person is given as follows:
400.
Missing InformationThe total cost is of 1200.
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HELP HELP WILL GIVE BRAINLEST
Answer:
y = 3/2x + 2
Step-by-step explanation:
first things first write the equation is y = mb+b form which would be 2y = 3x + 14 then divide everything by 2 to get y by itsself --> 3/2x + 7 for an equation to be paralle the equation needs the same slope which is -6 so 3/2(-6) = -9 so the next equation would also start with 3/2x, so you would then do this:
-11 = -9 + b (y = mx+b)
b = -9 + 11 --> b = 2
so the equation is
y = 3/2x + 2
If two triangles have equal perimeters, then they could also have which of the following? Select all that apply.
equal heights
equal bases
equal volumes
equal areas
Answer:
Equal heights, equal bases, and equal areas.
Step-by-step explanation:
What's the present value of $13,000 discounted back 5 years if the appropriate interest rate is 9%, compounded semiannually? Select the correct answer.
The present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% can be calculated by the formula:PV = FV / (1 + r/m)^(m*t)Here, PV stands for Present Value FV stands for Future Valuer stands for the interest rate (9%)m is the number of times the interest is compounded (semi-annually, so m = 2)t is the number of years (5)
After substituting the values in the formula, we get:PV = 13,000 / (1 + 0.045)^10PV = 13,000 / 1.55709768854PV = $8,349.58. We can use the concept of present value (PV) and future value (FV) to solve this question. When the cash flow is considered at different points of time, the money's value changes with the time value of money. The time value of money takes into consideration the amount of interest that could be earned on the sum of money if invested. Present value (PV) is a mathematical concept that represents the current worth of a future sum of money, taking into account the time value of money and the given interest rate. PV is calculated by using a discount rate that is determined by the interest rate and the length of time between the present and future payment dates. Future value (FV) is a mathematical concept that represents the future worth of a present sum of money, taking into account the time value of money and the given interest rate. FV is calculated by using a compound interest rate that is determined by the interest rate and the length of time between the present and future payment dates. To calculate the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9%, we can use the formula PV = FV / (1 + r/m)^(m*t), where PV is the present value, FV is the future value, r is the interest rate, m is the number of times the interest is compounded per year, and t is the number of years. In this case, we know that FV is $13,000, r is 9%, m is 2 (since it is compounded semi-annually), and t is 5. After substituting these values into the formula, we get PV = $8,349.58. Therefore, the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% is $8,349.58.
Therefore, the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% is $8,349.58.
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Find the y-intercept of the line on the graph.
Answer:
(0, 4)
Step-by-step explanation:
The y-intercept is the y-value when x = 0.
From the graph, we see that when x = 0, y = 4.
Find all complex numbers z satisfying the equation cos z = 4. Find all complex numbers z satisfying the equation cos z = i sin z.
To find all complex numbers z satisfying the equation cos z = 4, we need to use the identity:
cos z = cos(x + iy) = cos(x)
cosh(y) - i sin(x)sinh(y)
Given cos(z) = 4, we have
cos(x)cosh(y) = 4 and sin(x)sinh(y) = 0
Since sin(x) and cosh(y) are non-zero, we have tan(x) = sinh(y)/cos(x)
Also, using the identity: cosh²(y) - sinh²(y) = 1, we get
cos²(x)cosh²(y) - sin²(x)sinh²(y) = 16 - 1 = 15
Dividing both sides by cos²(x), we get:
cosh²(y) - tan²(x)sinh²(y) = 15/cos²(x)
Therefore, substituting the value of tan(x) in the above expression, we get:
cosh²(y) - sinh²(y)/cos²(x) = 15/cos²(x)
Rearranging, we get:
cosh²(y) - 17/16 = 0
Therefore, cosh(y) = ±sqrt(17)/4
Taking the positive square root, we get
y = arccosh(sqrt(17)/4)
Taking the negative square root, we get
y = -arccosh(sqrt(17)/4
)Therefore, the solutions for cos(z) = 4 are
:z = nπ - arctan(tanh(y)) ± i arccosh(sqrt(17)/4)z = nπ - arctan(tanh(y)) ± i arccosh(-sqrt(17)/4)
where y = arccosh(sqrt(17)/4) or y = -arccosh(sqrt(17)/4) and n is an integer.
To find all complex numbers z satisfying the equation cos z = i sin z, we can use the identity:
cos z = i sin z, i.e., cos(x) + i sin(x) = i sin(x)cos(x) - sin(x) = 0sin(x)(cos(x) - 1) = 0
Therefore, either sin(x) = 0 or cos(x) = 1When sin(x) = 0, we have x = nπ where n is an integer When cos(x) = 1, we have x = 2nπ where n is an integer
Therefore, the solutions for cos(z) = i sin(z) are:z = nπ + i(nπ + π/2)z = 2nπ + i(2nπ) where n is an integer
The complex numbers z satisfying the equation cos z = 4 are:z = nπ - arctan(tanh(y)) ± i arccosh(sqrt(17)/4)z = nπ - arctan(tanh(y)) ± i arccosh(-sqrt(17)/4)where y = arccosh(sqrt(17)/4) or y = -arccosh(sqrt(17)/4)and n is an integer.The complex numbers z satisfying the equation cos z = i sin z are:z = nπ + i(nπ + π/2)z = 2nπ + i(2nπ)where n is an integer.
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a) 8 + (5 + 3) =16
b) (12 + 15) + (3 + 2 + 1) + 4 (5 + 3 + 2 + 8) =
c) 150 – [18 + (5 – 3) + (6 – 2)] =
d) (15 + 2) – (6 + 2) =
e) (17 – 3) – (11 – 3) =
f) [(6 – 4) – (3 – 2)] – [(9 – 7) – (6 – 5)] =
g (14 + 6 – 4) – (9 – 7 – 2) =
Write in a standard notation
3.6 x 104
Help me and explain please
Answer:
36000
Step-by-step explanation:
Move the decimal to the right four times because of 10^4
On a recent glider flight, Lucy took a tow to 3000 feet above ground level. She found a good thermal and climbed 1800 feet. Then she hit big sink and lost 2200 feet. What was her altitude at that point?
peacekeeper yesyklll
