Answer:
a) 26.79%, b) 50.42% and c) 22.79%
Step-by-step explanation:
a. What is the probability that both Dave and Mike will show up?
As decisions of showing up can be assumed to be independent, the probability will be given by
(1-0.53)(1-0.43)=(0.47)(0.57)=0.2679=26.79%
b. What is the probability that at least one of them will show up?
There are two possibilities for this to happen:
Dave shows up but Mike does not. The probability of Dave to show up is (1-0.53)=0.47 and the probability that Mike does not is 0.43. Then, as these events are independent, the probability for both of them to happen is (0.47)(0.43)=0.2021=20.21%
Mike shows up but Dave does not. The probability of Mike to show up is (1-0.43)=0.57 and the probability that Mike does not is 0.53. Then, as these events are independent, the probability for both of them to happen is (0.57)(0.53)=0.3021=30.21%
Therefore, the probability that at least one of them will show up? is 20.21%+30.21%=50.42%.
c. What is the probability that neither Dave nor Mike will show up?
As decisions of showing up can be assumed to be independent, the probability will be given by
(0.53)(0.43)=0.2279=22.79%
Find angle picture below
Answer:
72
Step-by-step explanation:
have a great day
PLEASE HELPPPPPPPPPP IM RLLY STUCK
Answer: 28.5cm squared
Answer:
4cm². Hop it helped
Step-by-step explanation:
PLS HELPLPPPPOPPPP I’ll mark brainiest
All these answers correct
Look at picture
Complementary angles
Answer: All of them are correct expect number 5
Step-by-step explanation: 43 divided by 25 is 43/25 and that’s not right so the correct answer is 1950 because if you divide 1950 by 25 you get 78 and 78 + 12 = 90
A television has a normal price of £670. In a sale the price is reduced by 30%. Work out the price of the television in the sale.
colocar verdadero (v) o falso (f) según corresponda: -3 € N..................... ( )
5 € N................ ( )
N c Z...................( )
-8 c Z............... ( )
7 € Z................ ( )
0 € Z................ ( )
Answer:
what is this............
Let X be a normal random variable with mean 3 and variance 4. (a) Find the probability P(2 < X < 6). (b) Find the value c such that P(X > c) = 0.33. (c) Find E[X2 ]. Hint: You can integrate with the density function, but it is quicker to relate E[X2 ] to the mean and variance.
Answer:
a) the probability of (2 < X < 6) is 0.6247
b) the value of c is 3.878
c) the value of E[ x² ] is 13
Step-by-step explanation:
Given that;
mean μ = 3
variance = 4
standard deviation s = √variance = √4 = 2
(a) Find the probability P(2 < X < 6)
P(2 < X < 6) = p( (x - μ / s ) < z < (x - μ / s ) )
= p( (2 - 3 / 2 ) < z < (6 - 3 / 2 ) )
= p( -0.5 < z < 1.5)
from z-score table, 1.5; z = 0.9332 and -0.5; z = 0.3085
so
P(2 < X < 6) = 0.9332 - 0.3085 = 0.6247
Therefore, the probability of (2 < X < 6) is 0.6247
b) Find the value c such that P(X > c) = 0.33
with p-value = 0.33, the corresponding z -score to the right is 0.439
we know that;
z = x - μ / s
we substitute
0.439 = x - 3 / 2
x - 3 = 2 × 0.439
x - 3 = 0.878
x = 0.878 + 3
x = 3.878
Therefore, the value of c is 3.878
c) Find E[ x² ].
Variance = E[ x² ] - [ mean ]²
E[ x² ] = Variance + [ mean ]²
we substitute
E[ x² ] = 4 + [ 3 ]²
E[ x² ] = 4 + 9
E[ x² ] = 13
Therefore, the value of E[ x² ] is 13
The distribution follows a normal distribution.
[tex]\mathbf{P(2 < x < 6) =0.6247}[/tex]The value of c is 3.878The value of [tex]\mathbf{E(x^2) }[/tex] is 13The given parameters are:
[tex]\mathbf{\mu = 3}[/tex] --- mean
[tex]\mathbf{\sigma^2= 4}[/tex] --- variance
(a) P(2 < x < 6)
Start by calculating the standard deviation
[tex]\mathbf{\sigma = \sqrt{\sigma^2}}[/tex]
This gives
[tex]\mathbf{\sigma = \sqrt{4}}[/tex]
[tex]\mathbf{\sigma =2}[/tex]
Calculate the z-scores for x = 2 and 6
[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]
So, we have:
[tex]\mathbf{z = \frac{2 - 3}{2} = -0.5}[/tex]
[tex]\mathbf{z = \frac{6 - 3}{2} = 1.5}[/tex]
So, the probability becomes
[tex]\mathbf{P(2 < x < 6) = P(-0.5 < z < 1.5)}[/tex]
Using z table of probabilities, we have:
[tex]\mathbf{P(2 < x < 6) =0.9332 - 0.3085}[/tex]
[tex]\mathbf{P(2 < x < 6) =0.6247}[/tex]
(b) Calculate c if P(X > c) = 0.33
Start by calculating the z-score for p-value = 0.33
From the z table, z = 0.439 when p-value = 0.33
Recall that:
[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]
So, we have:
[tex]\mathbf{0.439 = \frac{x - 3}{2}}[/tex]
Multiply both sides by 2
[tex]\mathbf{0.878= x - 3}[/tex]
Add 3 to both sides
[tex]\mathbf{3.878= x}[/tex]
Rewrite as:
[tex]\mathbf{x = 3.878}[/tex]
Replace x with c
[tex]\mathbf{c = 3.878}[/tex]
The value of c is 3.878
(c) Calculate E[x²]
The variance of a dataset is:
[tex]\mathbf{\sigma^2 =E(x^2) - \mu^2}[/tex]
Substitute known values
[tex]\mathbf{4 =E(x^2) - 3^2}[/tex]
[tex]\mathbf{4 =E(x^2) - 9}[/tex]
Add 9 to both sides
[tex]\mathbf{13 =E(x^2) }[/tex]
Rewrite as:
[tex]\mathbf{E(x^2) = 13 }[/tex]
Hence, the value of [tex]\mathbf{E(x^2) }[/tex] is 13
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Store A sells 12 juice bottles for $4 and store B sells 18 juice bottles for $6. Are these rates equivalent? Explain your reasoning.
Answer:
these rates are equivalent.
12bottles/$4= 18bottles/$6= 3bottles/$1
Step-by-step explanation:
a) Find all the square numbers that are greater than 10 but less than 40.
Answer:
16, 25, 36
Step-by-step explanation:
The square numbers that are greater than 10 but less than 40 are 16, 25 and 36
What is Square numbers?A square number is a number multiplied by itself. This can also be called a number squared.
Given,
Square numbers that are greater than 10 and less than 40
[tex]4^{2}=16\\ 5^{2}=25\\ 6^{2}=36[/tex]
Hence, the square numbers that are greater than 10 but less than 40 are 16, 25 and 36
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Please help ASAP if you know how. Thanks so much
Answer:
The answer is C.
Step-by-step explanation:
You should plug the numbers into the quadratic formula to get the answer.
Answer:
A: -5 ± √ 17 / 2
Step-by-step explanation:
Consider the following equations:
ax^2 + bx + c - This is an equation you use in understanding quadratic functions.
x= (−b± √b^2−4ac) / 2a - This is the quadratic formula used to solve quadratic functions
So: ax^2 + bx + c = x^2 + 5x + 2
SOLVE:
-(5) ± √ 5^2−4(1)(2)) / 2(1)
= -5 ± √ 25− 8 / 2
= -5 ± √ 25− 8 / 2
= -5 ± √ 17 / 2
List the elements of the set of all letters in the word 'true'
Answer:
t r u e
Step-by-step explanation:
The scale of a map is 1 inch : 250 miles. City A is 750 miles from City B. How far is its distance on the map?
Measure of Pairs of Angles: Calculate the measure for
160 degrees
or
20 degrees
or
180 degrees
or
90 degrees
The angle vertical to 160 is also 160.
So you have 320
You have 320 out of a full circle, 360.
If there's two angles left, equal to each other
Then they each would be 20 degrees.
I'm not sure what you tried to solve for but I guess this is a simple rundown of the image.
Answer:
The remaining angles are 20°, 160° and 20°
Step-by-step explanation:
Since a circle has 360° and one angle is know, the remaining angles can be found.
Angle U = 160° and the angle in the opposite side must be equal to Angle U so the angle opposite to U is 160° as well.
The remaining two angles are equal to each other and since the total degrees must be 360° and 2 angles are known, we can solve for the remaining angles.
Let's say the remaining angles are values "x".
360° must equals 160° + 160° + x + x
360 = 160 + 160 + x + x
360 = 320 + 2x
40 = 2x
x = 20
The remaining two angles are 20°
list the multiple of 4 and 5 up to 50
Really? Here we go...
0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
and
0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
or if you wanted conjuction
0, 20, 40
Answer:
Step-by-step explanation:
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
The same factors are bolded
Aaron borrowed money to start a new
business. The simple interest rate on the
loan is 2.5%. He will pay back the loan by
making a total of 12 payments of $266.50
each. How much did he borrow?
Answer:
$6.69448
Step-by-step explanation:
I=?
P=$266.50
R=2.5*1/100=2.5/100
T=12
P*R*T
$266.50*2.5/100*12=$6.69448
A snail desperately needs to make it to the center garden to avoid being squashed by students once
school starts. If the garden is 6 meters away, and the snail's top speed is 0.8 meters per hour, how long
will it take the snail to make it to safety? Give the answer in hours, minutes, and seconds.
Answer:
12hr, 66mins, 1.23245 sedconda
Step-by-step explanation:
fvavdfbgthujiugfd
THERE ARE 3 STUDENTS IN ART AND 2 SHEETS OF CONSTURCTION PAPER FOR THEM TO SHARE EQUALLY. WHAT PART OF CONSTRUCTIONS PAPER WILL EACH STUDENT GET
Answer: 2/3 of paper
Step-by-step explanation: 2 papers divided by 3 students would be 2/3 of paper for each
Please help with this question and give an explanation if possible
Answer:
B. -15
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Swapping Limits]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = -\int\limits^a_b {f(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int\limits^3_{-1} {[2g(x) + 4]} \, dx = 22[/tex]
[tex]\displaystyle \int\limits^{-1}_{10} {g(x)} \, dx = 12[/tex]
[tex]\displaystyle \int\limits^{10}_{3} {g(x)} \, dx = z[/tex]
Step 2: Redefine
Manipulate the given integrals.
[Integrals] Combine [Integration Property - Splitting Integral]: [tex]\displaystyle \int\limits^{-1}_{10} {g(x)} \, dx + \int\limits^{10}_3 {g(x)} \, dx = \int\limits^3_{10} {g(x)} \, dx[/tex][Integrals] Rewrite: [tex]\displaystyle \int\limits^3_{10} {g(x)} \, dx = \int\limits^{-1}_{10} {g(x)} \, dx + \int\limits^{10}_3 {g(x)} \, dx[/tex][Integrals] Substitute in variables: [tex]\displaystyle \int\limits^{-1}_3 {g(x)} \, dx = 12 + z[/tex][Integrals] Rewrite [Integration Property - Swapping Limits]: [tex]\displaystyle -\int\limits^3_{-1} {g(x)} \, dx = 12 + z[/tex][Integrals] [Division Property of equality] Isolate integral: [tex]\displaystyle \int\limits^3_{-1} {g(x)} \, dx = -(12 + z)[/tex][Integrals] [Distributive Property] Distribute negative: [tex]\displaystyle \int\limits^3_{-1} {g(x)} \, dx = -12 - z[/tex]Step 3: Solve
[Integral] Rewrite [Integration Property - Addition]: [tex]\displaystyle \int\limits^3_{-1} {2g(x)} \, dx + \int\limits^3_{-1} {4} \, dx = 22[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle 2\int\limits^3_{-1} {g(x)} \, dx + 4\int\limits^3_{-1} \, dx = 22[/tex][Integral] Substitute in integral: [tex]\displaystyle 2(-12 - z) + 4\int\limits^3_{-1} \, dx = 22[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle 2(-12 - z) + 4(x) \bigg| \limits^3_{-1} = 22[/tex][Integral] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle 2(-12 - z) + 4(3 - -1) = 22[/tex][Integral] (Parenthesis) Simplify: [tex]\displaystyle 2(-12 - z) + 4(3 + 1) = 22[/tex][Integral] (Parenthesis) Add: [tex]\displaystyle 2(-12 - z) + 4(4) = 22[/tex][Integral] Multiply: [tex]\displaystyle 2(-12 - z) + 16 = 22[/tex][Integral] [Subtraction Property of Equality] Subtract 16 on both sides: [tex]\displaystyle 2(-12 - z) = 6[/tex][Integral] [Division Property of Equality] Divide 2 on both sides: [tex]\displaystyle -12 - z = 3[/tex][Integral] [Addition Property of Equality] Isolate z term: [tex]\displaystyle -z = 15[/tex][Integral] [Division Property of Equality] Isolate z: [tex]\displaystyle z = -15[/tex][Integral] Back-Substitute: [tex]\displaystyle \int\limits^{10}_{3} {g(x)} \, dx = -15[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
Solve the simultaneous equations
2x+3y=20
X+5y=31
Answer: wwoww you don't know math
way
Step-by-step explanation:
Time Remaining
This Question: 1 pt
9 of 9
T
The perimeter of a rectangular garden is 68 yards. The width of the garden is five yards less than twice the length.
(a) Find the length and width of the garden.
(b) What is the area of the garden?
The length of the garden is
(Type an integer or a decimal.)
The width of the garden is
V (Type an integer or a decimal.)
The area of the garden is
(Type an integer or a decimal.)
Answer:
a. Length = 13 yards and Width = 21 yards.
b. Area of rectangle = 273 square yards.
Step-by-step explanation:
Let the length of the rectangular garden be L
Let the width of the rectangular garden be W
Given the following data;
Perimeter of garden = 68 yards
Translating the word problem into an algebraic equation, we have;
W = 2L - 5 ......equation 1
Note: The formula for calculating the perimeter of a rectangle is;
[tex]P = 2L + 2W[/tex]
68 = 2L + 2W ........equation 2
Substituting eqn 1 into eqn 2;
68 = 2L + 2(2L - 5)
68 = 2L + 4L - 10
68 = 6L - 10
6L = 68 + 10
6L = 78
L = 78/6
L = 13 yards
To find the width;
W = 2L - 5
W = 2(13) - 5
W = 26 - 5
W = 21 yards.
b. To find the area of the garden;
Area of rectangle = length * width
Area of rectangle = 13 * 21
Area of rectangle = 273 square yards.
A figure skater begins spinning counterclockwise at an angular speed of 4.5 π rad/s. During a 4.8 s interval, she slowly pulls her arms
inward and finally spins at 7.2 π rad/s.
What is her average angular acceleration
during this time interval?
Answer in units of rad/s
2
.
Answer:
[tex]\alpha =1.76\ rad/s^2[/tex]
Step-by-step explanation:
Given that,
Initial angular speed of the skater, [tex]\omega_i=4.5\pi\ rad/s[/tex]
Final angular speed of the skater, [tex]\omega_f=7.2\pi\ rad/s[/tex]
Time interval, t = 4.8 s
We need to find her average angular acceleration during this time interval. Let [tex]\alpha[/tex] be the average acceleration of the skater. So,
[tex]\alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{7.2\pi -4.5\pi}{4.8}\\\\\alpha =1.76\ rad/s^2[/tex]
So, her angular acceleration is [tex]1.76\ rad/s^2[/tex].
Marking brainliest
Please help
Answer:
D
Step-by-step explanation:
That's the answer.......
Answer:
D
Step-by-step explanation:
if the maker of the promissory note fails to pay the note on the due date,the note is said to be
Answer:
When the maker of a promissory note fails to pay, the note is said to be dishonored.
Step-by-step explanation:
Write and equation in slope intercept form to model the situation.
A candle is 8 inches tall and burns at 3/4 inch each hour.
Answer:
The equation that models the situation is [tex]y = 8 - 0.75t[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line, in slope-intercept formula, has the following format:
[tex]y = mx + b[/tex]
In which m is the slope(how much y changes when x changes by 1 unit) and b is the intercept, which is the value of t when x = 0.
A candle is 8 inches tall and burns at 3/4 inch each hour.
Using t as number of hours and y as the height.
Initial height of 8 inches, that is, when [tex]t = 0, y = 8[/tex], so [tex]b = 8[/tex]
Burns at 3/4 inch each hour.
That is, the height decreases by a rate of 3/4 inch each hour, so [tex]m = -\frac{3}{4} = -0.75[/tex]
So
[tex]y = 8 - 0.75t[/tex]
For the following integral, give a power or simple exponential function that if integrated on a similar infinite domain will have the same convergence or divergence behavior as the given integral, and use that to predict whether the integral converges or diverges. Note that for this problem we are not formally applying the comparison test; we are simply looking at the behavior of the integrals to build intuition.
∫(x+5)/x^3+7x+5 dx
Answer:
hello your question is incomplete attached below is the complete question
answer :
for I1 = [tex]\frac{1}{x^2} + \frac{4}{x^3}[/tex] The integral converges
for I2 = [tex]\frac{2x + 6}{2(x^2 + 6x + 4 )}[/tex] The integral diverges
for I3 = [tex]\frac{1}{x^2}[/tex] The integral converges
for I4 = 1 The integral diverges
Step-by-step explanation:
The similar integrands and the prediction ( conclusion )
for I1 = [tex]\frac{1}{x^2} + \frac{4}{x^3}[/tex] The integral converges
for I2 = [tex]\frac{2x + 6}{2(x^2 + 6x + 4 )}[/tex] The integral diverges
for I3 = [tex]\frac{1}{x^2}[/tex] The integral converges
for I4 = 1 The integral diverges
attached below is a detailed solution
an 1-pod shuffle cost R820.99 calculate how much VAT are paying on this item
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]Price = R820.99[/tex]
Required
Calculate the VAT
To solve this question, we need the percentage VAT. Assume that the % VAT is 2%, the amount to pay is:
[tex]Amount = 2\% * R820.99[/tex]
[tex]Amount = 0.02 * R820.99[/tex]
[tex]Amount = R16.4198[/tex]
If you multiply two integers together and then add 4, the result is 40. Which of the following could NOT be the sum of the two numbers?
- 12
- 13
- 15
- 18
- 20
Answer:
18
Step-by-step explanation:
xy + 4 = 40
xy = 40 - 4
xy = 36
What two numbers can b multiplied to give 36? Then add them.
9 + 4 = 13
18 + 2 = 20
6 + 6 = 12
12 + 3 = 15
The odd option is 18
The 18 will not be the sum of the two numbers for the given option so option (D) will be correct.
How to form an equation?
Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say that two numbers are x and y
Given,
Multiply two integers together and then add 4, the result is 40.
So,
xy + 4 = 40
xy = 36
The possible two numbers whose multiplication gives 36 are
(6 ,6) , (9,4),(12,3) and (18,2)
So the sum would be 12, 13, 15 and 20
The Remaining is 18.
Hence "The 18 will not be the sum of the two numbers".
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The function d =
45t gives the distance d Juan traveled in miles after t hours.
is this discrete or continuous data?
Answer:
Continuous data
Step-by-step explanation:
Given
[tex]d = 45t[/tex]
Required
Discrete or Continuous?
From the question, we understand that t represents time in hours. This is a continuous data.
When multiplied by 45 to give distance, the resulting data is also continuous.
Hence, [tex]d = 45t[/tex] is continuous
Answer:
d = 2.5t, continuous
Step-by-step explanation:
Just did it on Edge and got it right
I NEED HELP THIS IS GEOMETRY
Answer:
x=14 ; y= √153.
Step-by-step explanation:
1) x=7 / sin30°=14.
2) y=√(x²-7²)=√153.
what is the diameter of a pizza that has a radius of 9
